Merge bitcoin/bitcoin#32545: Replace cluster linearization algorithm with SFL

75bdb925f4 clusterlin: drop support for improvable chunking (simplification) (Pieter Wuille)
91399a7912 clusterlin: remove unused MergeLinearizations (cleanup) (Pieter Wuille)
5ce2800745 clusterlin: randomize equal-feerate parts of linearization (privacy) (Pieter Wuille)
13aad26b78 clusterlin: randomize various decisions in SFL (feature) (Pieter Wuille)
ddbfa4dfac clusterlin: keep FIFO queue of improvable chunks (preparation) (Pieter Wuille)
3efc94d656 clusterlin: replace cluster linearization with SFL (feature) (Pieter Wuille)
6a8fa821b8 clusterlin: add support for loading existing linearization (feature) (Pieter Wuille)
da48ed9f34 clusterlin: ReadLinearization for non-topological (tests) (Pieter Wuille)
c461259fb6 clusterlin: add class implementing SFL state (preparation) (Pieter Wuille)
95bfe7d574 clusterlin: replace benchmarks with SFL-hard ones (bench) (Pieter Wuille)
86dd550a9b clusterlin: add known-correct optimal linearization tests (tests) (Pieter Wuille)

Pull request description:

  Part of cluster mempool: #30289.

  This replaces the cluster linearization algorithm introduced in #30126 and #30286 (a combination of LIMO with candidate-set search), with a completely different algorithm: [spanning-forest linearization](https://delvingbitcoin.org/t/spanning-forest-cluster-linearization/1419/1), which appears to have much better performance for hard clusters. See [this post](https://delvingbitcoin.org/t/how-to-linearize-your-cluster/303/68) for a comparison between various linearization algorithms, and [this post](https://delvingbitcoin.org/t/how-to-linearize-your-cluster/303/73) for benchmarks comparing them. Replaying historical mempool data on it shows that it can effectively linearize every observed cluster up to 64 transactions optimally within tens of microseconds, though pathological examples can be created which take longer.

  The algorithm is effectively a very specialized version of the [simplex algorithm](https://en.wikipedia.org/wiki/Simplex_algorithm) to the problem of finding high-feerate topological subsets of clusters, but modified to find all consecutive such subsets concurrently rather than just the first one. See the post above for how it is related.

  It represents the cluster as partitioned into a set of chunks, each with a spanning tree of its internal dependencies connecting the transactions. Randomized improvements are made by selecting dependencies to add and remove to these spanning trees, merging and splitting chunks, until no more improvements are possible, or a computation budget is reached. Like simplex, it does not necessarily make progress in every step, and thus has no upper bound on its runtime to find optimal, but randomization makes long runtimes very unlikely, and additionally makes it hard to adversarially construct clusters in which the algorithm reliably makes bad choices.

ACKs for top commit:
  instagibbs:
    reACK 75bdb925f4
  marcofleon:
    reACK 75bdb925f4

Tree-SHA512: 189d85b34f0eb847562af7da724c61e39f0a785e24ebe2d4c8ee44698d02bd17842d699987d282a79bd1de30f50de28ec0f11d594ebbfa499f6a9b9ce35aecd8

src/bench/cluster_linearize.cpp

@@ -18,21 +18,6 @@ using namespace util::hex_literals;
 
 namespace {
 
-/** Construct a linear graph. These are pessimal for AncestorCandidateFinder, as they maximize
- *  the number of ancestor set feerate updates. The best ancestor set is always the topmost
- *  remaining transaction, whose removal requires updating all remaining transactions' ancestor
- *  set feerates. */
-template<typename SetType>
-DepGraph<SetType> MakeLinearGraph(DepGraphIndex ntx)
-{
-    DepGraph<SetType> depgraph;
-    for (DepGraphIndex i = 0; i < ntx; ++i) {
-        depgraph.AddTransaction({-int32_t(i), 1});
-        if (i > 0) depgraph.AddDependencies(SetType::Singleton(i - 1), i);
-    }
-    return depgraph;
-}
-
 /** Construct a wide graph (one root, with N-1 children that are otherwise unrelated, with
  *  increasing feerates). These graphs are pessimal for the LIMO step in Linearize, because
  *  rechunking is needed after every candidate (the last transaction gets picked every time).
@@ -48,136 +33,6 @@ DepGraph<SetType> MakeWideGraph(DepGraphIndex ntx)
     return depgraph;
 }
 
-// Construct a difficult graph. These need at least sqrt(2^(n-1)) iterations in the implemented
-// algorithm (purely empirically determined).
-template<typename SetType>
-DepGraph<SetType> MakeHardGraph(DepGraphIndex ntx)
-{
-    DepGraph<SetType> depgraph;
-    for (DepGraphIndex i = 0; i < ntx; ++i) {
-        if (ntx & 1) {
-            // Odd cluster size.
-            //
-            // Mermaid diagram code for the resulting cluster for 11 transactions:
-            // ```mermaid
-            // graph BT
-            // T0["T0: 1/2"];T1["T1: 14/2"];T2["T2: 6/1"];T3["T3: 5/1"];T4["T4: 7/1"];
-            // T5["T5: 5/1"];T6["T6: 7/1"];T7["T7: 5/1"];T8["T8: 7/1"];T9["T9: 5/1"];
-            // T10["T10: 7/1"];
-            // T1-->T0;T1-->T2;T3-->T2;T4-->T3;T4-->T5;T6-->T5;T4-->T7;T8-->T7;T4-->T9;T10-->T9;
-            // ```
-            if (i == 0) {
-                depgraph.AddTransaction({1, 2});
-            } else if (i == 1) {
-                depgraph.AddTransaction({14, 2});
-                depgraph.AddDependencies(SetType::Singleton(0), 1);
-            } else if (i == 2) {
-                depgraph.AddTransaction({6, 1});
-                depgraph.AddDependencies(SetType::Singleton(2), 1);
-            } else if (i == 3) {
-                depgraph.AddTransaction({5, 1});
-                depgraph.AddDependencies(SetType::Singleton(2), 3);
-            } else if ((i & 1) == 0) {
-                depgraph.AddTransaction({7, 1});
-                depgraph.AddDependencies(SetType::Singleton(i - 1), i);
-            } else {
-                depgraph.AddTransaction({5, 1});
-                depgraph.AddDependencies(SetType::Singleton(i), 4);
-            }
-        } else {
-            // Even cluster size.
-            //
-            // Mermaid diagram code for the resulting cluster for 10 transactions:
-            // ```mermaid
-            // graph BT
-            // T0["T0: 1"];T1["T1: 3"];T2["T2: 1"];T3["T3: 4"];T4["T4: 0"];T5["T5: 4"];T6["T6: 0"];
-            // T7["T7: 4"];T8["T8: 0"];T9["T9: 4"];
-            // T1-->T0;T2-->T0;T3-->T2;T3-->T4;T5-->T4;T3-->T6;T7-->T6;T3-->T8;T9-->T8;
-            // ```
-            if (i == 0) {
-                depgraph.AddTransaction({1, 1});
-            } else if (i == 1) {
-                depgraph.AddTransaction({3, 1});
-                depgraph.AddDependencies(SetType::Singleton(0), 1);
-            } else if (i == 2) {
-                depgraph.AddTransaction({1, 1});
-                depgraph.AddDependencies(SetType::Singleton(0), 2);
-            } else if (i & 1) {
-                depgraph.AddTransaction({4, 1});
-                depgraph.AddDependencies(SetType::Singleton(i - 1), i);
-            } else {
-                depgraph.AddTransaction({0, 1});
-                depgraph.AddDependencies(SetType::Singleton(i), 3);
-            }
-        }
-    }
-    return depgraph;
-}
-
-/** Benchmark that does search-based candidate finding with a specified number of iterations.
- *
- * Its goal is measuring how much time every additional search iteration in linearization costs,
- * by running with a low and a high count, subtracting the results, and divided by the number
- * iterations difference.
- */
-template<typename SetType>
-void BenchLinearizeWorstCase(DepGraphIndex ntx, benchmark::Bench& bench, uint64_t iter_limit)
-{
-    const auto depgraph = MakeHardGraph<SetType>(ntx);
-    uint64_t rng_seed = 0;
-    bench.run([&] {
-        SearchCandidateFinder finder(depgraph, rng_seed++);
-        auto [candidate, iters_performed] = finder.FindCandidateSet(iter_limit, {});
-        assert(iters_performed == iter_limit);
-    });
-}
-
-/** Benchmark for linearization improvement of a trivial linear graph using just ancestor sort.
- *
- * Its goal is measuring how much time linearization may take without any search iterations.
- *
- * If P is the benchmarked per-iteration count (obtained by running BenchLinearizeWorstCase for a
- * high and a low iteration count, subtracting them, and dividing by the difference in count), and
- * N is the resulting time of BenchLinearizeNoItersWorstCase*, then an invocation of Linearize with
- * max_iterations=m should take no more than roughly N+m*P time. This may however be an
- * overestimate, as the worst cases do not coincide (the ones that are worst for linearization
- * without any search happen to be ones that do not need many search iterations).
- *
- * This benchmark exercises a worst case for AncestorCandidateFinder, but for which improvement is
- * cheap.
- */
-template<typename SetType>
-void BenchLinearizeNoItersWorstCaseAnc(DepGraphIndex ntx, benchmark::Bench& bench)
-{
-    const auto depgraph = MakeLinearGraph<SetType>(ntx);
-    uint64_t rng_seed = 0;
-    std::vector<DepGraphIndex> old_lin(ntx);
-    for (DepGraphIndex i = 0; i < ntx; ++i) old_lin[i] = i;
-    bench.run([&] {
-        Linearize(depgraph, /*max_iterations=*/0, rng_seed++, old_lin);
-    });
-}
-
-/** Benchmark for linearization improvement of a trivial wide graph using just ancestor sort.
- *
- * Its goal is measuring how much time improving a linearization may take without any search
- * iterations, similar to the previous function.
- *
- * This benchmark exercises a worst case for improving an existing linearization, but for which
- * AncestorCandidateFinder is cheap.
- */
-template<typename SetType>
-void BenchLinearizeNoItersWorstCaseLIMO(DepGraphIndex ntx, benchmark::Bench& bench)
-{
-    const auto depgraph = MakeWideGraph<SetType>(ntx);
-    uint64_t rng_seed = 0;
-    std::vector<DepGraphIndex> old_lin(ntx);
-    for (DepGraphIndex i = 0; i < ntx; ++i) old_lin[i] = i;
-    bench.run([&] {
-        Linearize(depgraph, /*max_iterations=*/0, rng_seed++, old_lin);
-    });
-}
-
 template<typename SetType>
 void BenchPostLinearizeWorstCase(DepGraphIndex ntx, benchmark::Bench& bench)
 {
@@ -189,93 +44,53 @@ void BenchPostLinearizeWorstCase(DepGraphIndex ntx, benchmark::Bench& bench)
     });
 }
 
-template<typename SetType>
+void BenchLinearizeOptimallyTotal(benchmark::Bench& bench, const std::string& name, const std::vector<std::vector<uint8_t>>& serializeds)
-void BenchMergeLinearizationsWorstCase(DepGraphIndex ntx, benchmark::Bench& bench)
 {
-    DepGraph<SetType> depgraph;
+    for (const auto& serialized : serializeds) {
-    for (DepGraphIndex i = 0; i < ntx; ++i) {
-        depgraph.AddTransaction({i, 1});
-        if (i) depgraph.AddDependencies(SetType::Singleton(0), i);
-    }
-    std::vector<DepGraphIndex> lin1;
-    std::vector<DepGraphIndex> lin2;
-    lin1.push_back(0);
-    lin2.push_back(0);
-    for (DepGraphIndex i = 1; i < ntx; ++i) {
-        lin1.push_back(i);
-        lin2.push_back(ntx - i);
-    }
-    bench.run([&] {
-        MergeLinearizations(depgraph, lin1, lin2);
-    });
-}
-
-template<size_t N>
-void BenchLinearizeOptimally(benchmark::Bench& bench, const std::array<uint8_t, N>& serialized)
-{
-    // Determine how many transactions the serialized cluster has.
-    DepGraphIndex num_tx{0};
-    {
         SpanReader reader{serialized};
-        DepGraph<BitSet<128>> depgraph;
+        DepGraph<BitSet<64>> depgraph;
         reader >> Using<DepGraphFormatter>(depgraph);
-        num_tx = depgraph.TxCount();
+        auto bench_name = strprintf("%s_%utx_%udep", name, depgraph.TxCount(), depgraph.CountDependencies());
-        assert(num_tx < 128);
-    }
 
-    SpanReader reader{serialized};
+        // Benchmark the total time to optimal.
-    auto runner_fn = [&]<typename SetType>() noexcept {
-        DepGraph<SetType> depgraph;
-        reader >> Using<DepGraphFormatter>(depgraph);
         uint64_t rng_seed = 0;
-        bench.run([&] {
+        bench.name(bench_name).run([&] {
             auto [_lin, optimal, _cost] = Linearize(depgraph, /*max_iterations=*/10000000, rng_seed++);
             assert(optimal);
         });
-    };
+    }
+}
 
-    if (num_tx <= 32) {
+void BenchLinearizeOptimallyPerCost(benchmark::Bench& bench, const std::string& name, const std::vector<std::vector<uint8_t>>& serializeds)
-        runner_fn.template operator()<BitSet<32>>();
+{
-    } else if (num_tx <= 64) {
+    for (const auto& serialized : serializeds) {
-        runner_fn.template operator()<BitSet<64>>();
+        SpanReader reader{serialized};
-    } else if (num_tx <= 96) {
+        DepGraph<BitSet<64>> depgraph;
-        runner_fn.template operator()<BitSet<96>>();
+        reader >> Using<DepGraphFormatter>(depgraph);
-    } else if (num_tx <= 128) {
+        auto bench_name = strprintf("%s_%utx_%udep", name, depgraph.TxCount(), depgraph.CountDependencies());
-        runner_fn.template operator()<BitSet<128>>();
+
-    } else {
+        // Determine the cost of 100 rng_seeds.
-        assert(false);
+        uint64_t total_cost = 0;
+        for (uint64_t iter = 0; iter < 100; ++iter) {
+            auto [_lin, optimal, cost] = Linearize(depgraph, /*max_iterations=*/10000000, /*rng_seed=*/iter);
+            total_cost += cost;
+        }
+
+        // Benchmark the time per cost.
+        bench.name(bench_name).unit("cost").batch(total_cost).run([&] {
+            uint64_t recompute_cost = 0;
+            for (uint64_t iter = 0; iter < 100; ++iter) {
+                auto [_lin, optimal, cost] = Linearize(depgraph, /*max_iterations=*/10000000, /*rng_seed=*/iter);
+                assert(optimal);
+                recompute_cost += cost;
+            }
+            assert(total_cost == recompute_cost);
+        });
     }
 }
 
 } // namespace
 
-static void Linearize16TxWorstCase20Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<16>>(16, bench, 20); }
-static void Linearize16TxWorstCase120Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<16>>(16, bench, 120); }
-static void Linearize32TxWorstCase5000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<32>>(32, bench, 5000); }
-static void Linearize32TxWorstCase15000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<32>>(32, bench, 15000); }
-static void Linearize48TxWorstCase5000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<48>>(48, bench, 5000); }
-static void Linearize48TxWorstCase15000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<48>>(48, bench, 15000); }
-static void Linearize64TxWorstCase5000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<64>>(64, bench, 5000); }
-static void Linearize64TxWorstCase15000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<64>>(64, bench, 15000); }
-static void Linearize75TxWorstCase5000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<75>>(75, bench, 5000); }
-static void Linearize75TxWorstCase15000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<75>>(75, bench, 15000); }
-static void Linearize99TxWorstCase5000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<99>>(99, bench, 5000); }
-static void Linearize99TxWorstCase15000Iters(benchmark::Bench& bench) { BenchLinearizeWorstCase<BitSet<99>>(99, bench, 15000); }
-
-static void LinearizeNoIters16TxWorstCaseAnc(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseAnc<BitSet<16>>(16, bench); }
-static void LinearizeNoIters32TxWorstCaseAnc(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseAnc<BitSet<32>>(32, bench); }
-static void LinearizeNoIters48TxWorstCaseAnc(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseAnc<BitSet<48>>(48, bench); }
-static void LinearizeNoIters64TxWorstCaseAnc(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseAnc<BitSet<64>>(64, bench); }
-static void LinearizeNoIters75TxWorstCaseAnc(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseAnc<BitSet<75>>(75, bench); }
-static void LinearizeNoIters99TxWorstCaseAnc(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseAnc<BitSet<99>>(99, bench); }
-
-static void LinearizeNoIters16TxWorstCaseLIMO(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseLIMO<BitSet<16>>(16, bench); }
-static void LinearizeNoIters32TxWorstCaseLIMO(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseLIMO<BitSet<32>>(32, bench); }
-static void LinearizeNoIters48TxWorstCaseLIMO(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseLIMO<BitSet<48>>(48, bench); }
-static void LinearizeNoIters64TxWorstCaseLIMO(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseLIMO<BitSet<64>>(64, bench); }
-static void LinearizeNoIters75TxWorstCaseLIMO(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseLIMO<BitSet<75>>(75, bench); }
-static void LinearizeNoIters99TxWorstCaseLIMO(benchmark::Bench& bench) { BenchLinearizeNoItersWorstCaseLIMO<BitSet<99>>(99, bench); }
-
 static void PostLinearize16TxWorstCase(benchmark::Bench& bench) { BenchPostLinearizeWorstCase<BitSet<16>>(16, bench); }
 static void PostLinearize32TxWorstCase(benchmark::Bench& bench) { BenchPostLinearizeWorstCase<BitSet<32>>(32, bench); }
 static void PostLinearize48TxWorstCase(benchmark::Bench& bench) { BenchPostLinearizeWorstCase<BitSet<48>>(48, bench); }
@@ -283,105 +98,57 @@ static void PostLinearize64TxWorstCase(benchmark::Bench& bench) { BenchPostLinea
 static void PostLinearize75TxWorstCase(benchmark::Bench& bench) { BenchPostLinearizeWorstCase<BitSet<75>>(75, bench); }
 static void PostLinearize99TxWorstCase(benchmark::Bench& bench) { BenchPostLinearizeWorstCase<BitSet<99>>(99, bench); }
 
-static void MergeLinearizations16TxWorstCase(benchmark::Bench& bench) { BenchMergeLinearizationsWorstCase<BitSet<16>>(16, bench); }
+// Constructed from replayed historical mempool activity, selecting for clusters that are slow
-static void MergeLinearizations32TxWorstCase(benchmark::Bench& bench) { BenchMergeLinearizationsWorstCase<BitSet<32>>(32, bench); }
+// to linearize from scratch, with increasing number of transactions (9 to 63).
-static void MergeLinearizations48TxWorstCase(benchmark::Bench& bench) { BenchMergeLinearizationsWorstCase<BitSet<48>>(48, bench); }
+static const std::vector<std::vector<uint8_t>> CLUSTERS_HISTORICAL = {
-static void MergeLinearizations64TxWorstCase(benchmark::Bench& bench) { BenchMergeLinearizationsWorstCase<BitSet<64>>(64, bench); }
+    "8540e93a008331c66a018331c66a028331c66a038331c66a048331c66a058331c66a068f1b84a1060000000000000007995e888c04010000000000000000"_hex_v_u8,
-static void MergeLinearizations75TxWorstCase(benchmark::Bench& bench) { BenchMergeLinearizationsWorstCase<BitSet<75>>(75, bench); }
+    "8e4886a46000835c819a100000835d819c000100835f819c000200837581a7200300835f819c000400835c819a1005008360819c000600836e81a3400700835f819c0008009c728d813000000000000000000000854e88df0600008e48a9c5700100835f8bfd40000183608bfd40010100"_hex_v_u8,
-static void MergeLinearizations99TxWorstCase(benchmark::Bench& bench) { BenchMergeLinearizationsWorstCase<BitSet<99>>(99, bench); }
+    "836880bf4000834c80b6600000836880bf400100834c80b6600001836880bf400101834c80b6600002836880bf400102834c80b6600003836880bf400103834c80b6600004836880bf400104834c80b6600005836880bf400105836880bf400006834c80b6600106836880bf400106834c80b6600206836880bf400107834c80b6600207823c80bf400108834c80b660020800"_hex_v_u8,
+    "81b0708db03800ef7a84a6700180c57b87c87802f24f83fc7e0381a3688ce20a04cb0d82a27205b40481887e068331965207d84384a07a0880850887b31609d57a83b62a09098865c82e0707c84083a736060009932d8098240a00058c1edf48070503f55a85fc560803058b6ddf660e0002e67d858d68090107921a81a1560d0302857cb32206148235986406149a5680e67c0b000106854cc12001118578e228001281cf6499b350120000000000108578e22801128578e228001300"_hex_v_u8,
+    "80df2a87e05c00f62883d34801f23983c02c02808e0784ca280380c35b86d64c0480956584f1080580a91b85d20c06808c4b84c27c0780b473868c4408f54983cf7c0980aa5385d9380a80b00285f4140b80804f8487100c8099308582700d80b3138683640efe1183fa640fa734849e28000000000000000000000000000000000fc82788ce48010000000000000000000000000000000fa92b84be300200000000000000000000000000000000ab3b84e1460300000000000000000000000000000000833dc93c0102833dc93c02028331c14402038540e12603038431cc3405028335c50e030a8331c7760506930880af020307833dc07605068331be0205068335be3a05078d09fb76030d842dcb6e030d00"_hex_v_u8,
+    "8368903600836890360183689036028368903603836890360483689036058368903606836890360783689036088368903609836890360a836890360b836890360c836890361b836890360e836890360f83689036228368903611836890361283689036138359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a13158359900a12148359900a12148359900a11138359900a11138359900a11138359900a1113a42281a91012000000000000000000000000000000000000002600"_hex_v_u8,
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+};
 
-// The following example clusters were constructed by replaying historical mempool activity, and
+// Randomly generated clusters, selected for slow linearization, from 28 to 64 transactions.
-// selecting for ones that take many iterations (after the introduction of some but not all
+// The first 10 are selected for long total runtime, the last 10 for high runtime per cost.
-// linearization algorithm optimizations).
+static const std::vector<std::vector<uint8_t>> CLUSTERS_SYNTHETIC = {
+    "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"_hex_v_u8,
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+    "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"_hex_v_u8,
+    "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"_hex_v_u8,
+    "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"_hex_v_u8
+};
 
-/* 2023-05-05T23:12:21Z 71, 521780, 543141,*/
+static void LinearizeOptimallyTotal(benchmark::Bench& bench)
-static constexpr auto BENCH_EXAMPLE_00 = "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"_hex_u8;
+{
-/* 2023-12-06T09:30:01Z 81, 141675, 647053,*/
+    BenchLinearizeOptimallyTotal(bench, "LinearizeOptimallyHistoricalTotal", CLUSTERS_HISTORICAL);
-static constexpr auto BENCH_EXAMPLE_01 = "b348f1fc4000f365818a9e2c01b44cf7ca0002b004f0b02003b33ef8ae3004b334f9e87005800d81c85e06b368fae26007b05ef2e14208be1a8093a50409b15cf5ee500a802c80a1420b802dea440c802ce50a0d802cdc320e802cd7220f802dd72210805380f74a118174f370126e96b32812127182c4701312817389d26414128035848c221512800e82bf3816126f81e4341712801082b228181280518af57418128040859a0019127182d0401a12803e858b641b127182c4421c126f82b3481d12811486b6301e12821d89e7281f126e8a8b421f127182d6642012806284c12021126e81d34822126e86a76222126e86d8102212805187b6542312800d82fc002412803d848e0e2512801082d27a26126e8589642612800e83a9602712800e83bd0028126e81ef1a29116e858d7228126f82db5e2912801083843c2a127181c93c2b126e85d0162b127181c5622c126e84f8262c12800f8392202d12800e82b66c2e126e81d0082f12803282d50430126e84f9003012805f84be6c3112846e88df0e2b12804080d44c340a8b31898808350a800ed760350b801083a1182b517182817e2a51800e82b6582951803583cb52420030806284cb6c204f7181d300204f82688ce0303e001d800e82bb200f488010808a182822a3289cd63041000a6fcd100a408a7caaa7024800002f803584e0741e27288f3386dd783b001000802683f27e004b8c44bcd0763f0000000000000000000100000e00"_hex_u8;
+    BenchLinearizeOptimallyTotal(bench, "LinearizeOptimallySyntheticTotal", CLUSTERS_SYNTHETIC);
-/* 2023-04-04T00:26:50Z 90, 99930, 529375,*/
+}
-static constexpr auto BENCH_EXAMPLE_02 = "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"_hex_u8;
-/* 2023-05-08T15:51:59Z 87, 76869, 505222,*/
-static constexpr auto BENCH_EXAMPLE_03 = "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"_hex_u8;
-/* 2023-05-01T19:32:10Z 35, 55747, 504128,*/
-static constexpr auto BENCH_EXAMPLE_04 = "801af95c00801af72801801af95c02873e85f2180202873e85f2180202873e85f21802028018fb2802068018fb2803068018fb2804068018fb2805068018fb2806068018fb2807068018fb2808068018fb2809068018fb280a068018fb280a058018fb280b058018fb280c058018fb280d058018fb280e058018fb280f058018fb2810058018fb2811058018fb2812058018fb2813058018fb2814058018fb2815058018fb2815048018fb2816048018fb2817048018fb2818048018fb2819048018fb281a048018fb281b04810d80d9481f00000100"_hex_u8;
-/* 2023-02-27T17:06:38Z 60, 55680, 502749,*/
-static constexpr auto BENCH_EXAMPLE_05 = "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"_hex_u8;
-/* 2023-04-20T22:25:49Z 99, 49100, 578622,*/
-static constexpr auto BENCH_EXAMPLE_06 = "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"_hex_u8;
-/* 2023-06-05T19:56:12Z 52, 44896, 540514,*/
-static constexpr auto BENCH_EXAMPLE_07 = "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"_hex_u8;
-/* 2023-12-05T23:48:44Z 69, 44283, 586734,*/
-static constexpr auto BENCH_EXAMPLE_08 = "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"_hex_u8;
-/* 2023-04-14T19:36:52Z 77, 20418, 501117,*/
-static constexpr auto BENCH_EXAMPLE_09 = "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"_hex_u8;
-/* 2023-11-07T17:59:35Z 48, 4792, 498995,*/
-static constexpr auto BENCH_EXAMPLE_10 = "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"_hex_u8;
-/* 2023-11-16T10:47:08Z 77, 473962, 486863,*/
-static constexpr auto BENCH_EXAMPLE_11 = "801980c06000801980c06001801980c06002801980c06003801980c06004801980c06005801980c06006801980c06007801980c06008801980c06009801980c0600a801980c0600b801980c0600c801980c0600d801980c0600e801980c0600f801980c060108019d12c11800f80b1601111800f80b1601111801080b1601111800f80b160100e800f80b160100f801980c060110f800f80b160140d801180b1601111801180b160100d801180b160120c801180b1600f10801180b1600f11801980c0601011800f80b160140e800f80b160110f801980c060170a801180b1601210801980c060140f800f80b1601311801980c0602005801180b1601f07800f80b1601b0c800fca7c1611812081f9601638812081f9601637812081fb001636801080b160142f801980c0600e2a801080b1600f2a801180b1600d25801980c0600e25800f80b1600d27801980c0600e27801980c0600d27801180b1600e26812080b1500c27812081f960201025812081f960200f27812081fc201d101c812081fc201d101d812081fc201d0f1f812081fc201d0f20812081f9601b1016800f80b1600a35800f80b1600a36800f80b1600e32801080b160122f812081f960280040812081fc20121d1b812081f960112713812081f960160d37812081fc20140d2b812081f960130d2d812081fc20130c2c812081fb001b0157812081fb001a0245812081fc20140030812081fc20092747812081fb000b152500"_hex_u8;
-/* 2023-10-06T20:44:09Z 40, 341438, 341438,*/
-static constexpr auto BENCH_EXAMPLE_12 = "80318f4c0080318f4c0180318f4c0280318f4c0380318f4c0480318f4c0580318f4c0680318f4c078033a57807078033a57807078033a57807078033a57807078033a57807078033a57807078033a57807078033a578070780318f4c0e0180318f4c0d0380318f4c0c0580318f4c0b078033a57803128033a57803128033a57803128033a578031280318f4c0412810b9c28140300810c9c281303028033a57802188033a57802188033a5780218810c9c280b01108033a578001c810c9c2807050f8033a578001b810c98040700158033a578001c810c98040301158033a5780019806ca1240101118033a578001300"_hex_u8;
-/* 2023-11-15T21:40:46Z 96, 23608, 138286,*/
-static constexpr auto BENCH_EXAMPLE_13 = "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"_hex_u8;
-/* 2023-12-06T09:18:20Z 93, 68130, 122830,*/
-static constexpr auto BENCH_EXAMPLE_14 = "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"_hex_u8;
-/* 2023-12-14T02:02:29Z 55, 247754, 247754,*/
-static constexpr auto BENCH_EXAMPLE_15 = "801980c06000801980c06001801980c06002801980c06003801980c06004801980c06005801980c06006801980c06007801980c06008801980c06009801980c0600a801980c0600b801980c0600c801980c0600d801980c0600e801180b1600e0e801180b1600e0e801180b1600e0e801180b1600e0e801180b1600e0e801180b1600e0e801180b1600d07801180b1600f06801180b1600c0a801180b1600f08801180b1600c0c801180b1600c0d801180b1600c0e801180b160100b801180b1601309812081fc200e2a812081fc200e29812081fc200e28812081fc200e0e18812081fc200e0e17801980c060042e812081fc200e0d07812081fc200e0d08812081fc200e0c0a812081fc200e0d0a801980c060081e812081fc200f0c0c812081fc200f0c0d812081fc200f0c0e801180b160083a801180b1600426801980c0600b20801980c0600a22812081fc200f0b30801180b160022b801180b160022b812081fc20062422812081fc2006220b812081fc200c0a1e812081fc2012041a00"_hex_u8;
-/* 2023-12-14T15:17:20Z 76, 102600, 103935,*/
-static constexpr auto BENCH_EXAMPLE_16 = "801980c06000801980c06001801980c06002801980c06003801980c06004801180b1600404801180b1600404801180b1600404801980c0600504801980c0600802801980c0600803801180b1600704801980c0600804801280b1600804812081fc200810812081fc20080f812081fc20080e801180b160080c800f80b160080d801980c060090d801180b160090e801980c0600a0e812181fc200a0c801180b1600a0d812181fd400a0c801980c0600a1c801980c0600916801180b1600719801180b160061b801980c0600d15801980c0600717812081fc200718801980c0600716801180b160072d801180b1600722801180b1600525801980c060091b801980c060071e801080b160071f801280b160061d812081fc20063a812181f960160815801280b1600525801980c0600625801180b1600626801980c0600726801980c0600536801180b160032b801980c060042b801280b160032d801980c060033e801180b160043e812181fc20100c27801080b160042f801980c0600342801180b1600442812081fc20150d25800f80b1600245812081fd40120619812081fc20040243812081fc20120c2c812081fd40120a1d812181fb00100623812081fc20030347812081fc20072126801980c0600236812081fc20040d2b812081fc20120328801980c0600237801180b1600337812081fc20052230801180b1600239812081fc2008242c812081fd4005112d812081fb00070b32812081f96011034700"_hex_u8;
-/* 2023-12-15T07:12:29Z 98, 112693, 112730,*/
-static constexpr auto BENCH_EXAMPLE_17 = "801980c06000801980c06001801980c06002801980c06003801980c06004801980c06005801980c06006801180b1600606801180b1600606801180b1600606801180b1600606801280b1600606801180b1600606801180b1600606801980c0600d00801980c0600b03801980c0600b04801980c0600f01812081fc200a16812081fc200a15812081fc200a14812081fc200a13812081fd400a12812181fc200a11812181fc200a0f801180b1600a10801180b1600a10801980c0600a10801180b1600b10801180b1600b10801980c0600621801980c0600915801980c060041b801180b160051b801980c0600f12801980c0600f13801980c0600d15801980c0600c17801980c060072e800f80b160082e812181fc200d150e801980c0600922801180b1600923801980c0600823801180b1600623801180b1600a20801180b1600e1c801180b1600b20801180b1600b21801980c0600a3e800f80b1600b3e801980c0600931801180b1600a31812181fc20140325801180b1600a30801180b160054c801180b160043b801980c0600336812181fc200253812081f960090944812081fc2007003c801980c0600339801180b1600433801980c0600453801980c0600340801980c060033d801080b160043d812081f960070854801980c060045a801180b160055a801180b1600545801980c0600643801980c0600641801280b1600739801180b1600562812081fc20121f27812181fc20210137812181fc2016112f801980c0600259801980c0600156812181fc20053a31801180b160025c801180b1600257801980c0600357812081fc200d2d1e812181fc20102444812181fc20035a801180b160035b801980c0600751812181fc2007392a812181fc20025f801980c060045e801180b1600350812081fc20070f6f801180b1600263812181fc201b1322812181fc2011283b812081fc2002442100"_hex_u8;
-/* 2023-12-16T02:25:33Z 99, 112399, 112399,*/
-static constexpr auto BENCH_EXAMPLE_18 = "801980c06000801980c06001801980c06002801980c06003801980c06004801980c06005801980c06006801980c06007801180b16008801180b16009801180b1600a801180b1600a0a801180b1600a0a801180b1600a0a801180b1600a0a801980c0600d06801180b1600b09801980c0601005801180b1600c0a801980c0600d0a801980c0601106801180b1600e0a801980c0601207801980c0601207801180b160100a812081e668100a812081e668100a812081e668100a801980c0601407801980c0601606812081fc201226812081fc201225812081fc201224812081fc201223801180b1600e21801980c0600b1e801180b1600c1e801180b1601316801980c060091b801980c0601312801980c0600a1c801180b160190e801180b1601315801180b1600e1b801180b1601713801180b1600f1c801980c0600d34801980c0600d30801980c060102e801980c060122d801980c0600b2a801980c0600b2a801980c0600b2b801180b1601122801180b1600e26801180b1601025801180b1600f26812081fc20280032812081fc20270034812081fc20250034801180b1600d4b801980c0600d457a809a000d46801980c0601044801980c0600e46801180b1600f43801180b160123f801180b160123e801180b1601130801180b1601131801180b1601131812081fc20230a36801980c0600a5a801180b1600a5b801980c0600a5b801180b1600b5b801980c0600b5a801180b1600f57801180b1600d3f801980c0600669801980c0600568801980c0600466801180b1600945801180b1600649801180b1600945812081fc2018234b812081fc20142534812081fc20142532812081fc20142530801180b160074d801180b1600a4b801180b1600a4a812081fc20221662812081fc200c0472812081fc20072e42812081fc20062c23812081fc20100572812081fc200f036c812081fc2001345100"_hex_u8;
-/* 2023-03-31T19:24:02Z 78, 90393, 152832,*/
-static constexpr auto BENCH_EXAMPLE_19 = "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"_hex_u8;
 
-static void LinearizeOptimallyExample00(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_00); }
+static void LinearizeOptimallyPerCost(benchmark::Bench& bench)
-static void LinearizeOptimallyExample01(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_01); }
+{
-static void LinearizeOptimallyExample02(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_02); }
+    BenchLinearizeOptimallyPerCost(bench, "LinearizeOptimallyHistoricalPerCost", CLUSTERS_HISTORICAL);
-static void LinearizeOptimallyExample03(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_03); }
+    BenchLinearizeOptimallyPerCost(bench, "LinearizeOptimallySyntheticPerCost", CLUSTERS_SYNTHETIC);
-static void LinearizeOptimallyExample04(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_04); }
+}
-static void LinearizeOptimallyExample05(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_05); }
-static void LinearizeOptimallyExample06(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_06); }
-static void LinearizeOptimallyExample07(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_07); }
-static void LinearizeOptimallyExample08(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_08); }
-static void LinearizeOptimallyExample09(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_09); }
-static void LinearizeOptimallyExample10(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_10); }
-static void LinearizeOptimallyExample11(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_11); }
-static void LinearizeOptimallyExample12(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_12); }
-static void LinearizeOptimallyExample13(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_13); }
-static void LinearizeOptimallyExample14(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_14); }
-static void LinearizeOptimallyExample15(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_15); }
-static void LinearizeOptimallyExample16(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_16); }
-static void LinearizeOptimallyExample17(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_17); }
-static void LinearizeOptimallyExample18(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_18); }
-static void LinearizeOptimallyExample19(benchmark::Bench& bench) { BenchLinearizeOptimally(bench, BENCH_EXAMPLE_19); }
-
-BENCHMARK(Linearize16TxWorstCase20Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize16TxWorstCase120Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize32TxWorstCase5000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize32TxWorstCase15000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize48TxWorstCase5000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize48TxWorstCase15000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize64TxWorstCase5000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize64TxWorstCase15000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize75TxWorstCase5000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize75TxWorstCase15000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize99TxWorstCase5000Iters, benchmark::PriorityLevel::HIGH);
-BENCHMARK(Linearize99TxWorstCase15000Iters, benchmark::PriorityLevel::HIGH);
-
-BENCHMARK(LinearizeNoIters16TxWorstCaseAnc, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters32TxWorstCaseAnc, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters48TxWorstCaseAnc, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters64TxWorstCaseAnc, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters75TxWorstCaseAnc, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters99TxWorstCaseAnc, benchmark::PriorityLevel::HIGH);
-
-BENCHMARK(LinearizeNoIters16TxWorstCaseLIMO, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters32TxWorstCaseLIMO, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters48TxWorstCaseLIMO, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters64TxWorstCaseLIMO, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters75TxWorstCaseLIMO, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeNoIters99TxWorstCaseLIMO, benchmark::PriorityLevel::HIGH);
 
 BENCHMARK(PostLinearize16TxWorstCase, benchmark::PriorityLevel::HIGH);
 BENCHMARK(PostLinearize32TxWorstCase, benchmark::PriorityLevel::HIGH);
@@ -390,30 +157,5 @@ BENCHMARK(PostLinearize64TxWorstCase, benchmark::PriorityLevel::HIGH);
 BENCHMARK(PostLinearize75TxWorstCase, benchmark::PriorityLevel::HIGH);
 BENCHMARK(PostLinearize99TxWorstCase, benchmark::PriorityLevel::HIGH);
 
-BENCHMARK(MergeLinearizations16TxWorstCase, benchmark::PriorityLevel::HIGH);
+BENCHMARK(LinearizeOptimallyTotal, benchmark::PriorityLevel::HIGH);
-BENCHMARK(MergeLinearizations32TxWorstCase, benchmark::PriorityLevel::HIGH);
+BENCHMARK(LinearizeOptimallyPerCost, benchmark::PriorityLevel::HIGH);
-BENCHMARK(MergeLinearizations48TxWorstCase, benchmark::PriorityLevel::HIGH);
-BENCHMARK(MergeLinearizations64TxWorstCase, benchmark::PriorityLevel::HIGH);
-BENCHMARK(MergeLinearizations75TxWorstCase, benchmark::PriorityLevel::HIGH);
-BENCHMARK(MergeLinearizations99TxWorstCase, benchmark::PriorityLevel::HIGH);
-
-BENCHMARK(LinearizeOptimallyExample00, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample01, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample02, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample03, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample04, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample05, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample06, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample07, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample08, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample09, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample10, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample11, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample12, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample13, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample14, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample15, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample16, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample17, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample18, benchmark::PriorityLevel::HIGH);
-BENCHMARK(LinearizeOptimallyExample19, benchmark::PriorityLevel::HIGH);

src/test/cluster_linearize_tests.cpp

@@ -15,6 +15,7 @@
 BOOST_FIXTURE_TEST_SUITE(cluster_linearize_tests, BasicTestingSetup)
 
 using namespace cluster_linearize;
+using namespace util::hex_literals;
 
 namespace {
 
@@ -36,6 +37,7 @@ void TestDepGraphSerialization(const std::vector<std::pair<FeeFrac, SetType>>& c
         depgraph.AddDependencies(cluster[i].second, i);
     }
     depgraph.RemoveTransactions(holes);
+    SanityCheck(depgraph);
 
     // There may be multiple serializations of the same graph, but DepGraphFormatter's serializer
     // only produces one of those. Verify that hexenc matches that canonical serialization.
@@ -52,6 +54,65 @@ void TestDepGraphSerialization(const std::vector<std::pair<FeeFrac, SetType>>& c
     BOOST_CHECK(depgraph == depgraph_read);
 }
 
+void TestOptimalLinearization(const std::vector<uint8_t>& enc, const std::vector<FeeFrac>& optimal_diagram)
+{
+    DepGraphIndex tx_count = 0;
+    FastRandomContext rng;
+
+    auto test_fn = [&]<typename SetType>() {
+        DepGraph<SetType> depgraph;
+        SpanReader reader(enc);
+        reader >> Using<DepGraphFormatter>(depgraph);
+        SanityCheck(depgraph);
+        std::vector<DepGraphIndex> lin;
+        for (int iter = 0; iter < 200; ++iter) {
+            bool opt;
+            uint64_t cost{0};
+            switch (rng.randrange(3)) {
+            case 0:
+                // Use empty input linearization.
+                lin.clear();
+                break;
+            case 1:
+                // Reuse previous optimal linearization as input.
+                break;
+            case 2:
+                // Construct random input linearization.
+                std::shuffle(lin.begin(), lin.end(), rng);
+                FixLinearization(depgraph, lin);
+                break;
+            }
+            std::tie(lin, opt, cost) = Linearize(depgraph, 1000000000000, rng.rand64(), lin);
+            BOOST_CHECK(opt);
+            BOOST_CHECK(cost <= MaxOptimalLinearizationIters(depgraph.TxCount()));
+            SanityCheck(depgraph, lin);
+            auto chunking = ChunkLinearization(depgraph, lin);
+            BOOST_CHECK(std::is_eq(CompareChunks(chunking, optimal_diagram)));
+            // TODO: temporarily disabled; SFL does not guarantee minimal chunks. This will be
+            // reinstated in a future commit.
+            // // Verify that the chunks are minimal.
+            // BOOST_CHECK(chunking.size() == optimal_diagram.size());
+        }
+        tx_count = depgraph.PositionRange();
+    };
+
+    // Always run with 64-bit set types
+    // - The native one that will be used on this platform.
+    test_fn.template operator()<BitSet<64>>();
+    // - The one used on 32-bit platforms.
+    test_fn.template operator()<bitset_detail::MultiIntBitSet<uint32_t, 2>>();
+    // - An 8-bit one, which is maximally different in terms of bitset behavior.
+    test_fn.template operator()<bitset_detail::MultiIntBitSet<uint8_t, 8>>();
+
+    // Also run with 32-bit set types if the cluster doesn't use indexes above 31.
+    if (tx_count <= 32) {
+        // - The native one that will be used on this platform.
+        test_fn.template operator()<BitSet<32>>();
+        // - An 8-bit one, which is maximally different in terms of bitset behavior.
+        test_fn.template operator()<bitset_detail::MultiIntBitSet<uint8_t, 4>>();
+    }
+}
+
 } // namespace
 
 BOOST_AUTO_TEST_CASE(depgraph_ser_tests)
@@ -174,4 +235,244 @@ BOOST_AUTO_TEST_CASE(depgraph_ser_tests)
     );
 }
 
+BOOST_AUTO_TEST_CASE(depgraph_optimal_tests)
+{
+    // Compare linearizations with known-optimal chunk feerate diagrams.
+
+    // Hard clusters (according to various metrics) that appeared in replayed 2023 mempool data, ranging from 2 to 64 transactions.
+    TestOptimalLinearization("9276fa3a009c3b80cd4001a21680d85c02927bfa5403934280845404a04c80cf0805c75b82c22206a46880f532079c7e80b85608965780916a09a04a80cf080a9823809b3e0bb27b81ec0c0c8540c60e0c0c993e80c86a0d0b8540c2020c0c9352809f780c09972f80f84a080c85449900080c875da164080c875081ae54070c8335af4c071f9c6781a72a13010f99108190160e000e85419f2c07168332903c05158540819e54041216ba5183907a140000001182428d080024a25c83c11201040400010609b6668487240004060000000000"_hex_v_u8, {{47188, 8550}, {42800, 7755}, {325314, 79021}, {2070, 833}, {900, 450}, {2226, 1117}, {1664, 836}, {1118, 562}});
+    TestOptimalLinearization("850d81fd4000850e81fd400000850d81fd400000850d81fd400000850e8285000000850d8285000000850e8288600000850e8288600000850e828860000000"_hex_v_u8, {{223440, 7034}});
+    TestOptimalLinearization("818f1c8a935a0083219530000083219530010083219530020083219530030083219530040083219530050083219530060083219530070083219530080000"_hex_v_u8, {{104325, 39749}});
+    TestOptimalLinearization("836880bf4000834c80b6600000836880bf400100834c80b6600001836880bf400101834c80b6600002836880bf400102834c80b6600003836880bf400103834c80b6600004836880bf400104834c80b6600005836880bf400105836880bf400006834c80b6600106834c80b6600106836880bf400206834c80b6600008836880bf400108836880bf40000900"_hex_v_u8, {{12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {11760, 588}, {12320, 616}, {12320, 616}});
+    TestOptimalLinearization("84a22e8fce380083208c38000083208c38010083208c38020083208c38030083208c38040083208c38050083208c38060083208c38070083208c38080083208c38090000"_hex_v_u8, {{144756, 91886}});
+    TestOptimalLinearization("8361a8340084309730000000"_hex_v_u8, {{2650, 609}, {1560, 688}});
+    TestOptimalLinearization("829428f0fe20008319809604000183198096040100831980960402008319809604030083198096040400831980960405008319809604060083198096040700831980960408008319809604090083198096040a0083198096040b0083198096040c0083198096040d0083198096040e0083198096040f008319809604100083198096041100831980960412008319809604130083198096041400831980960415008319809604160083198096041700831980960418008319809604190083198096041a0000"_hex_v_u8, {{933840, 51880}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}});
+    TestOptimalLinearization("854ec47200854ec4720001854ec4720001854ec4720001854ec4720001854ec4720001854ec4720001854ec4720001854ec4720001854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec4720000854ec472000000"_hex_v_u8, {{4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}, {4473, 846}});
+    TestOptimalLinearization("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"_hex_v_u8, {{248978, 14346}, {1136423, 78068}, {270282, 20244}, {1423139, 109038}, {903617, 69567}, {106746, 10092}});
+    TestOptimalLinearization("836880ba5807845d80df200000836880ba580100845d80df200001836880bd0c0101845d80e2100002836880bf400102845d80e5000003836880bf400103845d80e5000004854e818800010300854e818800000300854e818800000200854e818800000100854e819178000000836880ed1c0000845f819b500017854e818b28001700"_hex_v_u8, {{252408, 12326}, {17172, 846}});
+    TestOptimalLinearization("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"_hex_v_u8, {{100312, 2047}, {584400, 19178}, {381780, 12556}, {363360, 11954}, {142320, 4730}});
+    TestOptimalLinearization("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"_hex_v_u8, {{9641, 616}, {2544700, 172404}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}, {10104, 685}});
+    TestOptimalLinearization("99469a2e008e638f32018e638f32028e638718038e638718048e638718058e648c44068e659002078e639340088f74873c098e6488380a8d6586340b894784240c894784240d8b56852c0ea71993100f8b6d8538108b56852c118e628b76128e638b76138e638b76148e628b76158e648b7616a06c8f78178e638b76188e628838198e638b761a8e6388381b894784241c9412894c1d8e6690521e9c538e1c05199b10f15017000400189527955a1a0000000000001a9e5d8e70120000000000000117b372993c000300000000000000000000000000001800"_hex_v_u8, {{11835, 11678}, {1129, 2022}, {1751, 3398}, {866, 2020}, {827, 2018}, {827, 2018}, {827, 2019}, {827, 2019}, {827, 2019}, {827, 2019}, {827, 2020}, {3025, 8912}, {604, 2018}, {604, 2019}, {604, 2020}, {974, 3795}, {678, 2706}, {542, 2164}, {412, 1645}, {474, 1893}, {1288, 5145}, {406, 1622}, {406, 1622}, {1084, 4332}, {3724, 14884}});
+    TestOptimalLinearization("833583380083368338000083328334000083318334000083328334000083368338000083358338000083328334000000"_hex_v_u8, {{284, 565}, {848, 1689}, {850, 1693}, {282, 562}});
+    TestOptimalLinearization("80f96f88ab2a008235839b0600008a4880b31801008604ec3c02008235a97c0300833dab7204008752d502050000"_hex_v_u8, {{140794, 37044}});
+    TestOptimalLinearization("f9718def4800823ab01c01833980c238028544848f20038478e07c04887280ef2a05823680a54e068081149ea80a07808714ac995208823680a55c0980b85cbcdc020abb759acf180b8338fe680c82359eac280c0c824280a9620d0c857cf9400e0c823ae5520a0c823590c744090c823584ef14090c847c80a32a0a0c8451808b100b0c824280a9420a0c823580a52c0b0c823586bf2c0c0c857c8186200d0c847882c63a0d0c854081cf060e0c833880b66e0f0c8338808e40100b8368809552110b8241de74130a8242c34c1608894480bc48102a851e818356050e0fad56888c401d00000000198fe81c808fc7501a0000000410933d86e120031300000a00"_hex_v_u8, {{42000, 836}, {255465, 8557}, {21507, 832}, {10670, 438}, {10663, 438}, {588686, 25096}, {389673, 16616}, {418483, 17865}, {400487, 17097}, {12508, 569}, {11767, 568}, {16848, 892}, {24863, 1366}, {83604, 4861}, {9184, 568}, {9641, 616}, {10517, 764}, {6138, 449}, {21950, 1708}, {8968, 721}, {84012, 7176}, {4390, 450}, {1184296, 275612}});
+    TestOptimalLinearization("82369e200084459e200186569e200282369e200384459e200488649e200586559e200684459e200788649e200886549e200984449e200a82369e200b9961dc600ca34b81da7800000000000000000000000000008368af4c0000869520c6dd6800008368af3800008368af3801008368af3802008368af3803008368af3804008368af3805008368af3806008368af3807008368af3808008368af3809008368af380a008368af380b008368af380c008368af380d008368af380e008368af380f0000"_hex_v_u8, {{692678, 145712}});
+    TestOptimalLinearization("8335862e008335862e00008335862e00008335862e00008335862e00008335862e00008335862e00008335862e00008331862600008335862e00008335862e00008335862e00008335862e00008335862e00008335862e0000833d863a00008335862e00008335862e00008544896a000000"_hex_v_u8, {{471, 565}, {471, 565}, {471, 565}, {471, 565}, {471, 565}, {471, 565}, {471, 565}, {471, 565}, {3293, 3951}, {1419, 1703}, {693, 836}});
+    TestOptimalLinearization("836183f20200842b84b82e00008a1089f33e0100842a849a7c00018361838f420101842b83ca680002836282f8280102842983b00c000300"_hex_v_u8, {{40129, 609}, {44631, 683}, {89375, 1424}, {42750, 682}, {33825, 609}, {37620, 683}, {32340, 610}, {35910, 681}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3098, 442}, {2883, 442}, {1070885, 209051}, {148942, 39219}, {107942, 30418}, {3136, 892}, {738, 713}, {357, 450}, {332, 442}, {624, 832}, {831, 1108}, {837, 1116}, {1011, 1348}, {627, 837}, {627, 838}, {330, 442}, {420, 566}});
+    TestOptimalLinearization("80e67480e6740080d53480d56e0180d04881bd62028f108f1c038335cb7204847ce13e0404824184240504823594990c0604823580d07c07048235a6160804857cdd4009048474f2640904823592ce5c0a04833692700b048540ad300d038608b37c0c04823583e0720d048500a9000e048239841c0f048242b70011038540cc681203833e855a13038470bf7c13048545956a16008600be000d1a8f1880990a17000d8a448a4c1600048544f63c1603018f18f1180c0d0b8600ac40041f00"_hex_v_u8, {{4921, 565}, {221979, 33050}, {185495, 29087}, {4980, 832}, {2507, 437}, {9861, 2072}, {4032, 896}, {2968, 832}, {2912, 896}, {76978, 31757}, {1272, 566}, {1461, 837}, {334, 441}, {338, 449}, {429, 574}, {1038, 2064}, {742, 1476}});
+    TestOptimalLinearization("84418c6a0080fe1d86fc00000080b97084ea50000080de1c85fc00010080ed4986b930020080a17b848a70030080d07b85c670040080a86b84a630050080e405869320060080db1185ef50070080d11b85c770080080d00185c310090000"_hex_v_u8, {{593589, 297030}});
+    TestOptimalLinearization("856ea51800856da5180000856eab080002856eab080002856dab080002856dab08000000"_hex_v_u8, {{16168, 5265}});
+    TestOptimalLinearization("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"_hex_v_u8, {{88836, 35145}});
+    TestOptimalLinearization("80886c99f50c00835df5600000835df5600100835df5600200835df5600300835df5600400835df5600500835df5600600835df5600700835df5600800835df5600900835df5600a00835df5600b00835df5600c00835df5600d00835df5600e00835df5600f00835df5601000835df5601100835df5601200835df5601300835df5601400835df5601500835df5601600835df5601700836880cd78180080895badcb740018835b80c9740018835b80c9740118835b80c9740218835b80c9740318835b80c9740418835b80c9740518835b80c9740618835b80c9740718835b80c9740818835b80c9740918835b80c9740a18835b80c9740b18835b80c9740c18835b80c9740d18835b80c9740e18835b80c9740f18835b80c9741018835b80c974111800"_hex_v_u8, {{849296, 46869}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}, {7600, 605}});
+    TestOptimalLinearization("8514d518008344be3800008514d51801008344be3800018514d51801018514d51800028344be3801028344be3801028514d51802028344be3800048514d51801048344be3800058514d51801058514d51800068344be3801068344be3801068514d51802068344be3800088514d51801088344be3800098514d51801098514d518000a00"_hex_v_u8, {{5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {4060, 580}, {5516, 788}, {5516, 788}});
+    TestOptimalLinearization("8442922e009069bd3a0000872d9c1a010083618f5e010183618f5e020183618f5e030183618f5e040183618f5e050183618f5e060183618f5e070183618f5e080183618f5e09019743a36609018442922e0a01835f8610010b835f8610020b835f8610030b835f8610040b835f8610050b835f8610060b835f8610070b835f8610080b835f8610090b835f86100a0b835f86100b0b835f86100c0b8442d82a0c0b8441e332001700"_hex_v_u8, {{16489, 3892}, {13636, 7762}, {7827, 10423}});
+    TestOptimalLinearization("9420928e2c008368f11a0000c52488dd700000834acf100000834acf100100834acf100200834acf100300834acf100400834acf100500834acf100600834acf100700834acf100800834acf100900834acf100a00834acf100b00834acf100c00834acf100d00834acf100e00834acf100f00834acf101000834acf101100834acf101200834acf101300834acf10140000"_hex_v_u8, {{156630, 2720}, {7309, 616}, {79800, 8996}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}, {5128, 586}});
+    TestOptimalLinearization("9d2c83920200856cf66200008570f7280100856bf65202008567f60c03008563f54604008572f74c0500856ef7060600856af6400700856af64008008561f52209008566f57a0a008566f57a0b008575f8000c008571f73a0d008571f73a0e00856df6740f00856df67410008565f56811008561f522120000"_hex_v_u8, {{102774, 11745}, {7569, 865}, {7569, 865}, {7604, 869}, {7674, 877}, {7674, 877}, {7709, 881}, {7709, 881}, {7744, 885}, {7665, 876}, {7700, 880}});
+    TestOptimalLinearization("854e80806600854e80806600008368e25000008462f54200008368e50601008463f8340001854e80b25c010000854e80b606000183688089400001846280a3620001854e80c00401000083688095520001846280b21c000100"_hex_v_u8, {{120967, 9647}});
+    TestOptimalLinearization("836186101483618872001583608842001584508d74001583618812011500"_hex_v_u8, {{2652, 2546}, {585, 609}});
+    TestOptimalLinearization("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"_hex_v_u8, {{450290, 291274}});
+    TestOptimalLinearization("a34c88ff6400835c80a4140000835c80a4140100835c80a4140200835c80a4140300835c80a4140400835c80a4140500835c80a4140600835c80a4140700835c80a4140800835c80a4140900835c80a4140a00835c80a4140b00835c80a4140c00835c80a4140d00835c80a4140e00835c80a4140f00835c80a414100000"_hex_v_u8, {{81970, 4684}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}, {10570, 604}});
+    TestOptimalLinearization("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"_hex_v_u8, {{82550, 6601}, {136779, 19257}, {12190, 1724}, {3399, 561}, {3390, 565}, {5567, 1109}, {2178, 437}, {2584, 573}, {27411, 6674}, {23563, 5932}, {2458, 721}, {4916, 1443}, {86513, 26559}, {1720, 529}, {2496, 768}, {4170, 1288}, {30286, 10050}, {3308, 1107}, {1466, 534}, {1455, 530}, {5420, 2104}, {1506, 670}});
+    TestOptimalLinearization("83689e4c0085599314000083689e4c0100864cc014010185599314010183689e4c0201864cc014010300"_hex_v_u8, {{2022, 616}, {2022, 616}, {2022, 616}, {5460, 1829}, {5460, 1829}});
+    TestOptimalLinearization("81c47cafb03400835bd8540000835bd8540100835bd8540200835bd8540300835bd8540400835bd8540500835bd8540600835bd8540700835bd8540800835bd8540900835bd8540a00835bd8540b00835bd8540c00835bd8540d00835bd8540e00835bd8540f00835bd8541000835bd8541100835bd8541200835bd8541300835bd8541400835bd8541500835bd8541600835bd8541700835bd8541800835bd8541900835bd8541a00835bd8541b00835bd8541c00835bd8541d00835bd8541e00835bd8541f00835bd8542000835bd8542100835bd8542200835bd8542300835bd8542400835bd8542500835bd8542600835bd8542700835bd8542800835bd8542900835bd8542a0000"_hex_v_u8, {{643112, 67653}});
+    TestOptimalLinearization("83359d2c0083359d2c000083359d2c000283359d2c000283359d2c000200"_hex_v_u8, {{1942, 565}, {1942, 565}, {1942, 565}, {1942, 565}, {1942, 565}});
+    TestOptimalLinearization("a335b4af0400832f85b3280000832f85b3280100832f85b3280200832f85b3280300832f85b3280400832f85b3280500832f85b3280600832f85b3280700832f85b3280800832f85b3280900832f85b3280a00832f85b3280b00832f85b3280c00832f85b3280d00832f85b3280e00832f85b3280f00832f85b3281000832f85b328110000"_hex_v_u8, {{1382250, 14723}});
+    TestOptimalLinearization("833284fd3a00833581fc3801823684d50e02833181fb500383358695480480d77881b6f12005857c89bf7c0681a21d82999c300780d81d81b3ec6808844581a474098332899a7e0909833185bb04090984398190380809823587ae06070982358ddc1e080982368688220909823585cb000a09823586b3120b09823687aa6e0a0982359bf34a0b09823592ed040b09860880af480f05833286e0460b1d833185ba620b1c833288e64a0b1a833188a270022a833186bb5e0228833e89976a0225833186eb0a012b8332898512012783358a9130012d823986ff5a012883358a8f00012fed4996937e04020b000000000000000100"_hex_v_u8, {{272375, 2247}, {438299, 3939}, {46471, 438}, {353620, 3397}, {58788, 565}, {2916860, 29954}, {86078, 892}, {3665780, 38152}, {2692854, 28242}, {18810, 709}, {189759, 14153}, {11300, 904}});
+    TestOptimalLinearization("883180ae7800a37a81cc480001a37a81cc480100a37a81cc480204835aaa160101835aaa160102835aaa160301835aaa160401835aaa160501835aaa160601835aaa160602835aaa160900835aaa160901835aaa160a01835aaa160b01835aaa160c01835aaa160c02835aaa160e01835aaa160f01835aaa160f02835aaa161101835aaa161201835aaa161301835aaa161401835aaa161600835aaa161700835aaa161800835aaa161702835aaa161802835aaa161902835aaa161c00835aaa161b02835aaa161e0000"_hex_v_u8, {{11260, 1201}, {62793, 13760}, {43452, 9546}, {37926, 8342}});
+    TestOptimalLinearization("a25c81b56200832fa5000000832fa5000100832fa5000200832fa5000300832fa5000400832fa5000500832fa5000600832fa5000700832fa5000800832fa5000900832fa5000a00832fa5000b00832fa5000c00832fa5000d00832fa5000e00832fa5000f00832fa5001000832fa5001100832fa5001200832fa5001300832fa500140000"_hex_v_u8, {{70961, 16311}});
+    TestOptimalLinearization("8368d63c00b273aaf80001842dec5e0101854e829f0201018f6681fb320103854e828b060300019e228ea20a0202835aea780206835aea780306835aea780406835aea780506835aea780606835aea780706835aea780806835aea780906835aea780a06842dec720a05836281a96a0a04836281a96a0b04836281a96a0c04836281a96a0d04836281a96a0e04836281a96a0f04836281a96a1004836281a96a1104836281a96a1204836281a96a1304836281a96a1404836281a96a1504836281a96a1604836281a96a1704836281a96a1804836281a96a1904836281a96a1a04836281a96a1b04836281a96a1c049d1e84a95e132200"_hex_v_u8, {{360000, 6643}, {26625, 846}, {488500, 15592}, {30945, 1462}, {93540, 8253}, {50728, 4555}});
+    TestOptimalLinearization("80de6ebba3280081a442d1976601990e86a22a02996686ba6a0381cb6bdcce060480e358beea3205823590802e0506847480cb6c06058241e47a0705845280a22e0805824180ab2c09058241e5120a05854580fd100b05833580b34e0b058235919c180c05833280b8080d05823593c3700b0586048189660c05906383fd600d0582358db5100d0582358087700e05823a8088400f058242e47a10058241eb4016008235ec001304874f81ec4a1701860881896608198a77829b761700000e900f83e20e160002000300"_hex_v_u8, {{644225, 29540}, {935163, 43040}, {822655, 38007}, {641121, 29709}, {23397, 1103}, {11844, 562}, {11559, 565}, {8760, 437}, {8800, 442}, {16264, 837}, {17075, 900}, {17075, 904}, {40880, 2275}, {39111, 2191}, {59605, 3342}, {61173, 3430}, {13110, 756}, {26427, 1527}, {6976, 437}, {6944, 449}, {6537, 449}, {6525, 449}, {6525, 450}, {10455, 722}});
+    TestOptimalLinearization("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"_hex_v_u8, {{96480, 4675}, {48240, 2338}, {48240, 2338}, {482080, 23373}, {12400, 609}, {12400, 610}, {12400, 610}});
+    TestOptimalLinearization("818e6ca18c5000834fc8700001834fc8700100834fc8700200834fc8700300834fc8700400834fc8700500834fc8700600834fc8700700834fc8700800834fc8700900834fc8700a00834fc8700b00834fc8700c00834fc8700d00834fc8700e00834fc8700f00834fc8701000834fc8701100834fc8701200834fc8701300834fc8701400834fc8701500834fc8701600834fc8701700834fc8701800834fc8701900834fc8701a00834fc8701b00834fc8701c00834fc8701d00834fc8701e00834fc8701f00834fc8702000834fc8702100834fc8702200834fc8702300834fc8702400834fc8702500834fc8702600834fc8702700834fc870280000"_hex_v_u8, {{279400, 34796}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}});
+    TestOptimalLinearization("8442872600c61981fd680000835a8c420000835a8c420100835a8c420200835a8c420300835a8c420400835a8c420500835a8c420600835a8c420700835a8c420800835a8c420900835a8c420a00835a8c420b00835a8c420c00835a8c420d00835a8c420e00835a8c420f00835a8c421000835a8c421100835a8c421200835a8c421300835a8c421400835a8c421500835a8c421600835a8c421700835a8c42180000"_hex_v_u8, {{25031, 9819}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}, {865, 602}});
+    TestOptimalLinearization("8540e74000833180831801875dd14e00000000"_hex_v_u8, {{8460, 561}, {6688, 832}, {5287, 1117}});
+    TestOptimalLinearization("808a5292d06800835ad3780000835ad3780100835ad3780200835ad3780300835ad3780400835ad3780500835ad3780600835ad3780700835ad3780800835ad3780900835ad3780a00835ad3780b00835ad3780c00835ad3780d00835ad3780e00835ad3780f00835ad3781000835ad3781100835ad3781200835ad3781300835ad3781400835ad3781500835ad3781600835ad3781700835ad3781800835ad3781900835ad3781a00835ad3781b00835ad3781c0000"_hex_v_u8, {{318528, 35332}});
+    TestOptimalLinearization("8a0d8a54008368843000008a0d8a5401008368843000018a0d8a54010000836884300001996cc3320100008a449d1e00018d20a37e01000000"_hex_v_u8, {{11949, 12847}});
+    TestOptimalLinearization("80ba1386a6640080c14d86cc1001809b10858b500280927684e2580380e9458893680480b6538695240580bb2086ac2006942981e1240000000000000000900e819b3a0100000000000000e2528bf6420200000000000000854dca54020200"_hex_v_u8, {{565214, 183924}});
+    TestOptimalLinearization("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"_hex_v_u8, {{920592, 51098}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2460632, 356111}, {9539, 1398}, {2999, 561}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {4869, 1076}, {1555, 616}, {1555, 616}, {42540, 16995}, {39460, 15765}});
+    TestOptimalLinearization("854887862000854887862000008548878a0000008548878a0000008548878d6000008548879520000000"_hex_v_u8, {{397920, 5040}});
+    TestOptimalLinearization("8331f924008336fa1400008331f70e00008335f56200008331ee3000008336ef1600008335e17c00008335df62000000"_hex_v_u8, {{7826, 561}, {7882, 566}, {7687, 561}, {7601, 565}, {7128, 561}, {7179, 566}, {6334, 565}, {6193, 565}});
+    TestOptimalLinearization("808962829f2c0083628d2c000183628d2c010183628d2c020083628d2c030083628d2c040083628d2c050083628d2c060083628d2c070083628d2c080083628d2c090083628d2c0a0083628d2c0b0083628d2c0c0083628d2c0d0083628d2c0e0083628d2c0f0083628d2c100083628d2c110083628d2c120083628d2c130083628d2c140083628d2c150083628d2c160083628d2c170083628d2c180083628d2c190083628d2c1a0083628d2c1b0083628d2c1c0083628d2c1d0083628d2c1e0083628d2c1f0083628d2c200083628d2c210083628d2c220083628d2c230083628d2c240083628d2c250083628d2c260000"_hex_v_u8, {{62448, 41552}});
+    TestOptimalLinearization("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"_hex_v_u8, {{22491, 574}, {83836, 9123}, {72635, 9291}, {6944, 892}, {74024, 9613}, {77864, 10309}, {57207, 7689}, {51363, 6931}, {50808, 6964}, {41279, 5818}, {42972, 6497}, {8845, 1395}, {2825, 449}, {17265, 2817}, {4843, 845}, {4843, 845}, {3966, 710}, {4588, 836}, {4588, 838}, {5954, 1139}, {166740, 33283}, {4170, 837}, {2800, 574}, {7749, 1700}, {2613, 574}, {32469, 7383}, {2790, 764}, {1953, 561}, {714, 574}, {586, 752}, {633, 846}, {623, 834}});
+    TestOptimalLinearization("a25c82906c00835fb17e0000835fb17e0100835fb17e0200835fb17e0300835fb17e0400835fb17e0500835fb17e0600835fb17e0700835fb17e0800835fb17e0900835fb17e0a00835fb17e0b00835fb17e0c00835fb17e0d00835fb17e0e00835fb17e0f00835fb17e1000835fb17e1100835fb17e1200835fb17e1300835fb17e140000"_hex_v_u8, {{25718, 4572}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}, {3263, 607}});
+    TestOptimalLinearization("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"_hex_v_u8, {{26297, 1728}, {26297, 1736}, {139807, 9456}, {8990, 610}, {68514, 4674}, {35240, 2406}, {26660, 1828}, {8835, 610}, {8294, 578}, {8151, 578}, {8008, 577}, {8008, 578}, {8008, 579}, {8008, 582}, {8008, 583}, {8370, 610}, {8008, 587}, {7722, 578}});
+    TestOptimalLinearization("a44d9db27a00824081e92c0000824081e92c0100824081e92c0200824081e92c0300824081e92c0400824081e92c0500824081e92c0600824081e92c070000"_hex_v_u8, {{434605, 8397}});
+    TestOptimalLinearization("880180cf2200829428c7e9180000831ce0040000831ce0040100831ce0040200831ce0040300831ce004040000"_hex_v_u8, {{13329, 1153}, {596620, 51880}, {6210, 540}, {6210, 540}, {6210, 540}, {6210, 540}, {6210, 540}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2320269, 40741}, {38964, 764}, {21137, 438}, {20152, 438}, {19600, 437}, {18447, 438}, {18191, 437}, {31228, 764}, {129164, 3167}, {17678, 437}, {17678, 438}, {28281, 752}, {27925, 768}, {27648, 768}, {31149, 888}, {51562, 1476}, {31149, 896}, {51562, 1484}, {15481, 449}, {30551, 888}, {30688, 892}, {30962, 900}, {42756, 1245}, {27226, 802}, {27744, 904}, {2466, 437}});
+    TestOptimalLinearization("8361a17a008430a138000000"_hex_v_u8, {{2237, 609}, {2204, 688}});
+    TestOptimalLinearization("fc7d88962000f93b87f516018a50809c6401018235a10402018235f65203018236cd1004018a4c80bb6405018235956e06018604de2c07018332fc480801847cdc0009018336fc700a018a50809e340b0182418c540c01831dcf020d01893c809f400d018470df300e018474dc640f01857cdd4010018802c83811018608dc00120183159a0a14008578dc0015008600dc001501823acf7c0e15857cf12412128336b6760a14926881943019000400"_hex_v_u8, {{171970, 27015}, {134824, 24317}, {2178, 437}, {4700, 1154}, {1463, 437}, {1733, 533}, {874, 449}});
+    TestOptimalLinearization("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"_hex_v_u8, {{933840, 51880}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}, {9666, 537}});
+    TestOptimalLinearization("870180db6e00841580832400008416808d5400008416eb7800008416808d54000000"_hex_v_u8, {{14135, 1025}, {17596, 1323}, {16102, 1324}});
+    TestOptimalLinearization("818f1c85840c0083208b08000083208b08010083208b08020083208b08030083208b08040083208b08050083208b08060083208b08070083208b08080083208b08090083208b080a0083208b080b0083208b080c0083208b080d0083208b080e0083208b080f0083208b08100083208b08110083208b08120083208b08130083208b08140083208b08150083208b08160000"_hex_v_u8, {{49478, 34844}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}, {772, 544}});
+    TestOptimalLinearization("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"_hex_v_u8, {{1406632, 29465}, {1934192, 40603}, {1338143, 28094}, {1360813, 28571}, {1479376, 31139}, {1261329, 26621}, {19665, 437}, {241164, 5561}, {18572, 442}, {22861, 562}, {16988, 442}, {54538, 1431}, {31485, 837}, {26700, 710}, {26317, 712}, {38797, 1075}, {15863, 449}, {24695, 721}, {65610, 1936}, {30260, 905}, {14896, 449}, {16038, 485}, {14702, 450}, {14689, 450}, {18701, 574}, {18439, 566}, {82250, 2648}, {40755, 1410}, {12019, 438}, {12250, 449}, {26939, 1007}, {35776, 1380}, {11457, 442}, {11519, 449}, {11475, 450}, {28383, 1117}, {14226, 562}, {11138, 449}, {40677, 1784}, {121204, 6276}});
+    TestOptimalLinearization("80ba43afe456008b358582100180c16cb587240280d261c0c11a0380d924bbc75c04833180ad5805900e84e9260682359b9b5c060782398087040706823598f2560606823599eb60050684788199680606823594a33c0805823580a95e0905854081f70c0d02824183c8280e028eb06183c190480b00058a7183aa0c0a000400ad428fc3340d000000000800"_hex_v_u8, {{49352, 1589}, {692467, 25721}, {711083, 27542}, {655101, 25377}, {716126, 28377}, {10927, 437}, {18100, 760}, {135450, 5954}, {94469, 4272}, {8706, 441}, {4736100, 252129}});
+    TestOptimalLinearization("a25c86f87e008362808722000083628087220100836280872202008362808722030083628087220400836280872205008362808722060083628087220700836280872208008362808722090083628087220a0083628087220b0083628087220c0083628087220d0083628087220e0083628087220f008362808722100083628087221100836280872212008362808722130000"_hex_v_u8, {{239571, 16772}});
+    TestOptimalLinearization("864a828f7a008b6384a51401854181d76c02833180e754038431819c3a04892a87a42205894587ba5c06853981d44607861c81ca2c0107857881bb3a010785008193000306823582ee280505854e81ec5a0a000a853581e22c0014896183d36c0007000007833e80f734000e860481c37000098642829e5c0106078a588398500108854181e744010f9659899c24000707843a81ac70000e857881b50e010c860481fb26020788358393240210833180f7420012843e81b51a0011874082e014000807853581ea0a000f853681ea0a000f833e80fc66000e833580f924000e833580fe4c000d00"_hex_v_u8, {{99621, 1759}, {69358, 1349}, {594899, 21560}, {24339, 900}, {20792, 900}, {17664, 768}, {34408, 1496}, {21206, 924}, {20253, 888}, {19847, 888}});
+    TestOptimalLinearization("818e6ca18c5000834fc8700001834fc8700100834fc8700200834fc8700300834fc8700400834fc8700500834fc8700600834fc8700700834fc8700800834fc8700900834fc8700a00834fc8700b00834fc8700c00834fc8700d00834fc8700e00834fc8700f00834fc8701000834fc8701100834fc8701200834fc8701300834fc8701400834fc8701500834fc8701600834fc8701700834fc8701800834fc8701900834fc8701a00834fc8701b00834fc8701c00834fc8701d00834fc8701e00834fc8701f00834fc8702000834fc8702100834fc8702200834fc8702300834fc8702400834fc8702500834fc8702600834fc870270000"_hex_v_u8, {{279400, 34796}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}, {4728, 591}});
+    TestOptimalLinearization("c7128ac61a00837ae46e0000837ae46e0100837ae46e0200837ae46e0300837ae46e0400837ae46e0500837ae46e0600837ae46e0700837ae46e0800837ae46e0900837ae46e0a00837ae46e0b00837ae46e0c00837ae46e0d00837ae46e0e00837ae46e0f00837ae46e1000837ae46e1100837ae46e1200837ae46e1300837ae46e1400837ae46e1500837ae46e1600837ae46e1700837ae46e1800837ae46e1900837ae46e1a00837ae46e1b00837ae46e1c00837ae46e1d00837ae46e1e0000"_hex_v_u8, {{296758, 28888}});
+    TestOptimalLinearization("8440881a0084408c5e000000"_hex_v_u8, {{1468, 1408}});
+    TestOptimalLinearization("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"_hex_v_u8, {{1006076, 56244}});
+    TestOptimalLinearization("8472e52e008473e52e018473e52e028473e52e038472e52e048472f85c058472e77405058472e52e05058473e52e05058473e52e05058473e52e05058472fe0005058472ef1e050f8473809e14050e8473e874050d8239ad42060d8473809e14060c8472e874060b8472fb58060a847280b024061a847280837406188473e674061684738083740514847280b91405128473fb580424847380cd24031e8472fb58031a8472f85c03178473fb58032b8473f85c03238472f85c031e847380ab14031a8472f85c03318472f85c03288473fe0003228473fb58031d8472f85c03378473f85c011d8473f85c031c8472808028023c8472f85c021e8473f85c021f8473f85c01208473f85c00218e0b81d3280a03010514901a8089000c000502020800"_hex_v_u8, {{50602, 4526}, {196414, 18533}, {7980, 755}, {23898, 2262}, {15918, 1509}, {23856, 2262}, {15580, 1509}, {7790, 755}, {7790, 755}, {7790, 755}, {7790, 755}, {2977, 441}, {8832, 2202}});
+    TestOptimalLinearization("8361c74a0084a108cec45c0000831cbe5e0000831cbe5e0100831cbe5e0200831cbe5e0300831cbe5e0400831cbe5e0500831cbe5e0600831cbe5e0700831cbe5e0800831cbe5e0900831cbe5e0a00831cbe5e0b00831cbe5e0c00831cbe5e0d00831cbe5e0e00831cbe5e0f00831cbe5e1000831cbe5e1100831cbe5e1200831cbe5e1300831cbe5e1400831cbe5e1500831cbe5e1600831cbe5e1700831cbe5e1800831cbe5e1900831cbe5e1a00831cbe5e1b00831cbe5e1c00831cbe5e1d00831cbe5e1e00831cbe5e1f00831cbe5e2000831cbe5e2100831cbe5e2200831cbe5e2300831cbe5e2400831cbe5e2500831cbe5e2600831cbe5e270000"_hex_v_u8, {{4645, 609}, {814790, 107880}});
+    TestOptimalLinearization("8431e564008369a158018369a15c028369a162038550ae20048369a17a058501a94a068501a946078430e72e088369a178098500a93a0a842fe5640b8502a9360c8501a8740d83699f5a0e8431e5640f8431e564108369a144118550ae2211118737ba280a118369a178081183699f5a051183699e4605118374b1601204891ec536060b0682199b70021582199b70041482199b7006138540ab7c031a853fab76001db6219ddc1007000000000100000000000000000000001e00"_hex_v_u8, {{327699, 22688}, {3248, 628}, {1848, 409}, {1848, 409}, {1848, 409}, {2210, 617}, {10260, 2973}});
+    TestOptimalLinearization("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"_hex_v_u8, {{133936, 1817}, {876600, 19178}, {627930, 13760}, {545040, 11954}, {213480, 4730}});
+    TestOptimalLinearization("836884c43c00a30da899200000847285dd280000856c86e6180100853586aa700200846085c6400300853586aa70040085168686300500853a86af38060085238694080700844f85b4200800853b86af380900850985f8580a00850185ef480b00853d86b4000c00853c86af380d00855d86d8400e00853e86b4000f00845985c1781000846485cb081100844c85af581200853e86b4001300845085b420140000"_hex_v_u8, {{45406, 616}, {1043316, 14258}, {52560, 719}, {58692, 803}, {60444, 827}, {52268, 716}, {52560, 720}, {53728, 736}, {54020, 740}, {60444, 828}, {63948, 876}});
+    TestOptimalLinearization("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"_hex_v_u8, {{25744, 6035}, {2422, 601}, {61527, 21962}, {43202, 25453}, {899, 2420}, {205, 617}, {205, 617}, {205, 617}});
+    TestOptimalLinearization("8089328682520083329b52000083329b52010083329b52020083329b52030083329b52040083329b52050083329b52060083329b52070083329b52080083329b52090083329b520a0083329b520b0083329b520c0083329b520d0083329b520e0083329b520f0083329b52100083329b52110083329b52120083329b52130083329b52140083329b52150083329b52160083329b52170083329b52180083329b52190083329b521a0083329b521b0083329b521c0083329b521d0083329b521e0000"_hex_v_u8, {{114400, 35136}});
+    TestOptimalLinearization("872d8f58009928c064000089509a400000895d99700100860d90680200860a905e03008655921c0400872b936e0500857f904006008603904a07008608905408008602904a0900861f91100a00862591240b0000"_hex_v_u8, {{20428, 16489}});
+    TestOptimalLinearization("8472cf14008472cf14018472cf14028473cf1402028473cf1401028472cf1403018472cf1401098472cf1403068473cf1402048473cf1402058473cf1402068472cf1402068472cf1402078472cf1402088473cf1402088472cf1402098473cf14020a8472cf14020a8472cf14010d8473cf14030b8473cf14020cb42181bf200d00010e8473cf14020e8472cf14040d8472cf14030e8472cf1402108473cf1402118473cf1402118473cf1402128472cf1402138472cf140213886f80845e090b01148473cf1402158472cf1404148472cf1403158472cf1402188472cf1402178473cf1402188472cf14021b8473cf14001b00"_hex_v_u8, {{5130, 754}, {5130, 754}, {5130, 754}, {5130, 754}, {25650, 3772}, {61560, 9053}, {46170, 6790}, {30780, 4527}, {5130, 755}, {5130, 755}, {29055, 8080}});
+    TestOptimalLinearization("808967889a74008367a77400018367a77401008367a77402008367a77403008367a77404008367a77405008367a77406008367a77407008367a77408008367a77409008367a7740a008367a7740b008367a7740c008367a7740d008367a7740e008367a7740f008367a77410008367a77411008367a77412008367a77413008367a77414008367a77415008367a77416008367a77417008367a77418008367a77419008367a7741a008367a7741b008367a7741c008367a7741d0000"_hex_v_u8, {{154054, 36217}});
+    TestOptimalLinearization("8335b816008335c44c00008335c44c00008331c40c00008335c44c00008335c44c00008335c44c00008335c44c0000833dc54800008335c44c00008331c40c00008335c44c00008335c44c00008335c44c00008335c44c00008335c44c0000833dc54800008331c40c00008331c40c00008335c44c00008335c44c00008335c44c00008335c44c000000"_hex_v_u8, {{101643, 12995}});
+    TestOptimalLinearization("89c0788087d818008448c72800008448c72801008448c72802008448c72803008448c72804008448c72805008448c72806008448c72807008448c72808008448c72809008448c7280a008448c7280b008448c7280c008448c7280d008448c7280e008448c7280f008448c72810008448c72811008448c72812008448c72813008448c72814008448c72815008448c72816008448c72817008448c72818008448c72819008448c7281a008448c7281b008448c7281c008448c7281d008448c7281e008448c7281f008448c72820008448c72821008448c72822008448c728230000"_hex_v_u8, {{1119820, 172280}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}, {4628, 712}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2075276, 38979}, {2283550, 42896}, {1937047, 36390}, {1473556, 27686}, {23320, 441}, {22996, 449}, {34161, 708}, {21037, 437}, {21037, 438}, {52893, 1107}, {20492, 437}, {20492, 437}, {20492, 438}, {20492, 438}, {20492, 438}, {32490, 721}, {21489, 485}, {37048, 845}, {28811, 708}, {17527, 441}, {16970, 442}, {16988, 450}, {21456, 574}, {15963, 441}, {27152, 764}, {15413, 449}, {135287, 4031}, {59862, 1792}, {14960, 449}, {35776, 1123}, {121446, 3848}, {28198, 896}, {26313, 844}, {17469, 562}, {27798, 900}, {25020, 837}, {16890, 566}, {21450, 720}, {107879, 3689}, {19648, 721}, {45100, 1662}, {24408, 904}, {29835, 1107}, {23968, 892}, {12950, 548}, {33576, 1553}, {77700, 5974}});
+    TestOptimalLinearization("8368aa5e008368aa5e018368aa5e028368aa5e038368aa5e0483689726058368aa5e05058368aa5e05058368aa5e05058368aa5e05058368aa5e05058368aa5e05058368972608038368aa5e010b854ea024080005a35780b638020ba35780b638010e83679708010d83679708020d83679708030d83679708040d83679708050d83679708060d83679708070d83679708080d83679708090d836797080a0d836797080b0d836797080c0d836797080d0d836797080e0d854eba7414001c836797080f1d83679708101d83679708111d83679708121d83679708131d83679708141d83679708151d83679708161d83679708171d83679708181d83679708191d836797081a1d836797081b1d836797081c1d836797081d1d836797081e1d836797081f1d83679708201d83679708211d8734cb0a2a0000308734cf280013112600"_hex_v_u8, {{2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {2799, 616}, {3834, 846}, {4869, 1076}, {12293, 2924}, {1555, 616}, {2130, 846}, {41000, 16380}, {33300, 13305}});
+    TestOptimalLinearization("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"_hex_v_u8, {{263296, 19845}, {267965, 20479}, {7293, 577}, {7293, 577}, {7293, 577}, {7293, 578}, {7293, 579}, {7293, 579}, {7150, 577}, {7150, 579}, {6578, 577}, {6578, 578}, {6578, 582}});
+    TestOptimalLinearization("80de1a89c02e0080dd1c8aac460180d10789b70202b04282ee2803854da96204833da30005ae0e82d6200682429268078608ac7408833e973a09b4558397700a823589e10e0a0a8331b54c0b0a8335a0000c0a823588ec180c0a8544ac400d0a8242bd000d0a8235899b7e0e0a8546ac500f0a8544ac5011098242974e12098545d03a110a8331a42215058241974015068545d35c140883319d5017068578b37c130a8541d3261408f43185ba60120a82429b001607833282b6161a048235ac5a140a8336b87219068331b54c14288f1c81a34020001a8751bb1e2000178540ac341f001483359d6611228241cc781024833db67c101a8b708099280d1dbf3a85a62a2301021483319d4a0634833d9e1e0633dd3884c704230000108a58d654120f0a9e65829c580438880ff5100010208474e9700030894880bd1002013200"_hex_v_u8, {{59807, 6900}, {10201, 1286}, {5422, 837}, {173248, 27774}, {454202, 73978}, {39260, 7429}, {5967, 1134}, {13266, 2536}, {37285, 7306}, {61944, 14794}, {1792, 450}, {68941, 17522}, {5610, 1496}, {2112, 565}, {1575, 450}, {1960, 561}, {2920, 836}, {1568, 449}, {3855, 1105}, {1971, 565}, {1957, 561}, {2920, 838}, {2912, 836}, {7642, 2250}});
+    TestOptimalLinearization("81903fc9ee3800819170cfe6520180d334bef35002819540d0d4480380da6ebdd94a0482359094100405823580a7120504823589bd760504847c819d100504823585f11c060482358d8d6a0604823589c62e0604823580b5520704a51586dd5008000000000000"_hex_v_u8, {{784665, 36085}, {764717, 35881}, {611877, 29016}, {598334, 28389}, {747940, 35621}, {63400, 4885}});
+    TestOptimalLinearization("808963829f2c0083638d2c000183638d2c010083638d2c020083638d2c030083638d2c040083638d2c050083638d2c060083638d2c070083638d2c080083638d2c090083638d2c0a0083638d2c0b0083638d2c0c0083638d2c0d0083638d2c0e0083638d2c0f0083638d2c100083638d2c110083638d2c120083638d2c130083638d2c140083638d2c150083638d2c160083638d2c170083638d2c180083638d2c190083638d2c1a0083638d2c1b0083638d2c1c0083638d2c1d0083638d2c1e0083638d2c1f0083638d2c200083638d2c210083638d2c220000"_hex_v_u8, {{58776, 39148}});
+    TestOptimalLinearization("8d29889718008368809064018368809064028d1386db10020292618bd5080302846380ac380301846380ac38030283688090640307854e80c6580500038360b8540403824182812a0503844682b6300603846380ac38040e8368809064050e8368809064050b846380ac38060a842ebf400609846380ac38031683688090640415846380ac380410846380ac38011a854e80c65802030b846380ac3800108368809064010e846280ac38000f8368809064010d846280ac38000e8368809064010e846380ac38000f00"_hex_v_u8, {{203813, 4811}, {28120, 710}, {63240, 1811}, {9330, 616}, {9330, 616}, {9330, 616}, {9330, 616}, {9330, 616}, {62880, 4156}, {11100, 738}, {11100, 738}, {11100, 739}, {11100, 739}, {11100, 739}, {11100, 739}, {11100, 739}, {11100, 739}, {11100, 739}, {11100, 739}, {11100, 739}, {3690, 608}, {4128, 686}});
+    TestOptimalLinearization("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"_hex_v_u8, {{248259, 59175}, {180475, 43031}, {27624, 6624}, {167256, 41844}, {116449, 30424}, {3113, 832}, {1547, 441}, {4029, 1155}, {1540, 442}, {1957, 562}, {1756, 565}, {2260, 904}, {6555, 5133}});
+    TestOptimalLinearization("c554baaa4600835c82fa220000835c82fa220100835c82fa220200835c82fa220300835c82fa220400835c82fa220500835c82fa220600835c82fa220700835c82fa220800835c82fa220900835c82fa220a0000"_hex_v_u8, {{486115, 9044}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}, {32465, 604}});
+    TestOptimalLinearization("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"_hex_v_u8, {{188460, 36250}, {175929, 34601}, {161920, 31928}, {182991, 36239}, {179050, 35516}, {176697, 35119}, {179744, 35778}, {194089, 38639}, {169428, 33733}, {7480, 1492}, {19140, 3821}, {4170, 836}, {4150, 832}, {2795, 562}, {2090, 442}, {3400, 760}, {5913, 1950}, {1778, 789}, {765, 438}, {438, 438}, {563, 565}, {1130, 1135}, {392, 442}, {375, 437}, {370, 437}, {1122, 1360}, {14637, 19470}, {532, 708}, {576, 768}, {624, 833}, {1317, 1759}});
+    TestOptimalLinearization("836880ed0e00d724a0e46400008430818630000084308186300100842c81846c02008430818630030084308186300400842c81846c0500842c81846c060084308186300700842c81846c080084308186300900842c81846c0a0084308186300b0084308186300c0084308186300d00842c81846c0e00842c81846c0f0084308186301000842c81846c11008430818630120000"_hex_v_u8, {{15239, 616}, {276850, 11300}, {16758, 684}, {16758, 684}, {16758, 684}, {16758, 684}, {16758, 684}, {16758, 684}, {16758, 684}, {16758, 684}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}, {16856, 688}});
+    TestOptimalLinearization("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"_hex_v_u8, {{119706, 15443}, {6467, 892}, {178169, 24786}, {6244, 888}, {6328, 904}, {10202, 1480}, {10202, 1480}, {2947, 438}, {8112, 1352}, {2306, 438}, {90860, 18386}, {7194, 1484}, {3512, 834}, {5610, 1488}, {3272, 1003}, {1281, 437}, {1025, 438}, {1025, 449}, {1756, 832}, {2019, 966}, {926, 530}, {10968, 7073}});
+    TestOptimalLinearization("80896681da040083668b04000183668b04010083668b04020083668b04030083668b04040083668b04050083668b04060083668b04070083668b04080083668b04090083668b040a0083668b040b0083668b040c0083668b040d0083668b040e0083668b040f0083668b04100083668b04110083668b04120083668b04130083668b04140083668b04150083668b04160083668b04170083668b04180083668b04190083668b041a0083668b041b0083668b041c0083668b041d0083668b041e0083668b041f0083668b04200083668b04210083668b04220083668b04230083668b04240083668b04250083668b04260083668b04270083668b04280083668b04290083668b042a0083668b042b0000"_hex_v_u8, {{56090, 44782}});
+    TestOptimalLinearization("80ea55a1fc3c0080e47da4dc2c0180e159a1c3340280e411a4ca500380d35ba1f20c04823586f77404048a5080b00405048265994a0604823a994a07048242c90a08048500e91a0904823680830e0904850081884e0a0482358397480b048474d8080c0485208194460d048542bf6c0e04854dc40a0f048239c92010048335ad181203823585e33a1104853f80871812048474e80613048236e47a1304823582a2261404823582894414048241c86a1504854cc40a17038658d0301704854dc0641804865fc4601c00138546c3361c0109833eb00a041c8452ba141c0004875c80c2541e0002833ead6c032900"_hex_v_u8, {{386635, 31880}, {338487, 29454}, {351640, 30602}, {341304, 30204}, {311144, 27664}, {12522, 1116}, {4752, 441}, {4741, 450}, {4725, 449}, {8716, 831}, {6723, 756}, {6797, 768}, {11330, 1488}, {5700, 756}, {7562, 1418}, {5208, 984}, {3786, 722}, {4421, 845}, {2956, 565}, {4379, 838}, {2998, 574}, {4210, 845}, {4150, 834}, {4464, 991}, {1701, 442}, {1701, 485}});
+    TestOptimalLinearization("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"_hex_v_u8, {{29924, 7517}, {1617, 609}, {25754, 20468}, {754, 1062}, {546, 1107}, {1036, 2126}, {7609, 17367}, {1180, 3530}, {2634, 8297}, {172, 617}, {172, 617}});
+    TestOptimalLinearization("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"_hex_v_u8, {{96480, 4675}, {48240, 2338}, {48240, 2338}, {482080, 23373}, {12400, 609}});
+    TestOptimalLinearization("836880bf4000834c80b6600000836880bf400100834c80b6600001836880bf400101834c80b6600002836880bf400102834c80b6600003836880bf400103834c80b6600004836880bf400104834c80b6600005836880bf400105834c80b6600006836880bf400106834c80b6600007836880bf400107834c80b6600008836881b768010800"_hex_v_u8, {{130900, 6160}, {11760, 588}, {11760, 588}, {11760, 588}, {11760, 588}, {11760, 588}, {11760, 588}, {11760, 588}, {11760, 588}, {11760, 588}});
+    TestOptimalLinearization("8369817400885084460183698174028369817403842482760485028244058501824406836981740783698174088550827609866883460a836981740b836981740c850282440d836981740e836981740f8550827610836983261183698326128550846613836983261483698326158501841c168501841c1783698326188550846619836981741a836983261b836983261c836983261d842486681e836983261f83698326208501841c2185508276228550827647850182442483698174258550827626836981742783698174288369817429836981742a866783462b836981742c836981742d836981742e836981742e2f956f9220152f873786240e2f8667855c142a8b0589240f23823d897c0453bc50d70c06000000000000000000000024bf66db78061e00000000000000000000000000000035c30085961a0200020b000000000000000000000000000000003500"_hex_v_u8, {{59283, 28013}, {7894, 15440}, {9513, 20143}, {466, 1079}, {430, 999}});
+    TestOptimalLinearization("cc1b8ae36800d6628bd74401912d81d342028368d406038e54819144048f7481a73405af7687b42806d35e8aa12c078416ab0c088f4781d31609a42e85905a0909b53087da7c07098459e30a0809cc4789cd7e0709912881db4405098422de500509a84b8693220e000d901e828d56050f823cce0e030f9017828c2201158608809b340807000d901e81d8420116925282b97c080600020a901c81d8420117901f81d8420012ca088ab75202010102020200"_hex_v_u8, {{68948, 6262}, {127805, 11981}, {21771, 2119}, {44226, 4410}, {22113, 2207}, {146849, 14665}, {162611, 16557}, {31803, 3253}, {151865, 16609}, {6120, 674}, {216238, 23904}, {6405, 729}});
+    TestOptimalLinearization("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"_hex_v_u8, {{16424, 2763}, {9568, 1720}, {54506, 9812}, {11635, 2160}, {45440, 8447}, {20893, 4158}, {4150, 833}, {5505, 1105}, {7182, 1503}, {68976, 14854}, {1967, 437}, {11126, 2482}, {24695, 5526}, {13379, 3279}, {10034, 2836}, {2496, 828}});
+    TestOptimalLinearization("80884d94bf40008349db4000018349db4001008349db4002008349db4003008349db4004008349db4005008349db4006008349db4007008349db4008008349db4009008349db400a008349db400b008349db400c008349db400d008349db400e008349db400f008349db4010008349db4011008349db4012008349db4013008349db4014008349db4015008349db4016008349db4017008349db4018008349db4019008349db401a008349db401b008349db401c008349db401d008349db401e008349db401f008349db4020008349db4021008349db4022008349db4023008349db4024008349db4025008349db4026008349db4027008349db4028008349db4029008349db402a008349db402b008349db402c008349db402d008349db402e008349db402f0000"_hex_v_u8, {{460320, 45693}});
+    TestOptimalLinearization("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"_hex_v_u8, {{5859, 759}, {4364, 566}, {76038, 10164}, {9434, 1266}, {187130, 27709}, {3774, 561}, {3774, 561}, {172985, 27560}, {4457, 713}, {209015, 34252}, {3408, 565}, {3118, 529}, {3275, 565}, {3275, 565}, {4393, 760}, {4347, 756}, {4370, 760}, {5152, 896}, {3840, 764}, {3704, 929}, {2115, 561}, {9990, 3884}, {1264, 845}, {845, 565}, {10371, 8037}});
+    TestOptimalLinearization("cf0884cf6c008324a54400008324a54401008324a54402008324a54403008324a54404008324a54405008324a54406008324a54407008324a54408008324a54409008324a5440a008324a5440b008324a5440c008324a5440d008324a5440e0000"_hex_v_u8, {{46134, 10248}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}, {2466, 548}});
+    TestOptimalLinearization("8474ad70008474ad70018470ad70028470ad70038470ad70048470ad70058470ad70068474ad70078474ad70088470ad70098474ad700a8474ad700b8474ad700c8470ad700d8474ad700e8474ad700fb83285d734000000000000000000000000000000000f00"_hex_v_u8, {{102810, 19414}});
+    TestOptimalLinearization("a408f07c00832c8c320000832c8c320100832c8c320200832c8c320300832c8c320400832c8c320500832c8c320600832c8c320700832c8c320800832c8c32090083308c3e0a0083308c3e0b0083308c3e0c0083308c3e0d00832f8c3a0e00832f8c3a0f00832f8c3a1000832f8c3a1100832f8c3a1200832d8c341300832d8c341400832d8c341500832d8c34160000"_hex_v_u8, {{27053, 17567}});
+    TestOptimalLinearization("8362861c00da64e1740000832a83460000832a83460100832e834a02008331834e0300832a83460400832a83460500832a83460600832a83460700832a83460800832a83460900832a83460a00832a83460b00832a83460c00832a83460d0000"_hex_v_u8, {{462, 610}, {6330, 11748}, {295, 561}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {291, 554}, {293, 558}});
+    TestOptimalLinearization("80df4cacb754009e3d87e13a0180f36aac8350028541808e5803833180867004833180ce0a05971285db6206ab6d8bbe0407854180f21608841280c278099a2e86ce3c0a83328086700ba81f8abc700c857c80ef360d860080fb000e8331809e140f857881922210ad498bfa16118331808e1a1281c806d98a341380d468ad813a148235a4fa741415824180a40015148239d05c1614823ad22017148236d1101714847480bc561714823980804018148235ace32819148331e7681a138236e35c1d11833580d5681e11854480c66a19148236f9301614833280a23e1c0d8331808612181285788187681514857c81a01a1414846681882e1414823a809620151482359ec46414148335f12e151482359392721514854480a5161614847c80f9502b008241e252191382358082122b02833df27e1130857c818b260b338578818b260b31854d80aa041d1105857c819222013d857881aa5403358a7581d40e3100000029857c81aa540133c92091aa5e2a0000000000000000011e823580a6480035a10988bb460103010b0e000000000d00"_hex_v_u8, {{13253, 561}, {707608, 30199}, {996428, 42555}, {743996, 31775}, {16040, 764}, {36126, 1780}, {88603, 4456}, {34788, 1780}, {542102, 27805}, {8393, 437}, {12540, 658}, {8288, 441}, {15563, 833}, {10463, 562}, {132850, 7145}, {10186, 561}, {70262, 3940}, {71837, 4029}, {55089, 3090}, {102338, 5741}, {94072, 5279}, {15387, 892}, {265139, 15986}, {12139, 756}, {8649, 561}, {12789, 836}, {6446, 438}, {6377, 449}, {31027, 2358}, {7319, 565}, {10946, 845}, {10635, 836}, {14131, 1134}, {5328, 442}, {5256, 438}, {5230, 441}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3956, 750}, {3956, 750}, {3956, 750}, {3956, 750}, {3956, 750}, {4377, 832}, {4377, 832}, {6968, 1582}, {17006, 4078}, {10111, 2496}, {20807, 5971}, {2591, 750}, {2591, 750}, {2729, 791}, {2729, 791}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}, {2867, 832}});
+    TestOptimalLinearization("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"_hex_v_u8, {{316363, 12974}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}, {13320, 588}});
+    TestOptimalLinearization("808934829e280083348c28000183348c28010083348c28020083348c28030083348c28040083348c28050083348c28060083348c28070083348c28080083348c28090083348c280a0083348c280b0083348c280c0083348c280d0083348c280e0083348c280f0083348c28100083348c28110083348c28120083348c28130083348c28140083348c28150083348c28160083348c28170083348c28180083348c28190083348c281a0083348c281b0083348c281c0083348c281d0083348c281e0083348c281f0083348c28200083348c28210083348c28220083348c28230083348c28240083348c28250083348c28260083348c28270083348c28280083348c28290083348c282a0000"_hex_v_u8, {{63216, 41968}});
+    TestOptimalLinearization("80af1a838c0a0080b37b82af76018335854e028335a64e03867cb2760483358a0c0580cd6485e13206854c8f3a0606823586e37207068241894608068750901a0906857cf2400a06823aab020b06824194060c068541bc500d068608f3440e068241a2000e06854ebd420f06823588b41610068500e13e11068241a2501206894480c21413068500905a1406854d8f3a150683368766160683358a0c1306823a983a1306823586bd7e140685458f261506833da17616068242a0341321854dc0641d000a83318a02061d854dc064120d8751901a0124b524808a58091200000000000200"_hex_v_u8, {{128151, 26614}, {4001, 846}, {127437, 27752}, {2535, 565}, {116824, 26905}, {2235, 573}, {1629, 442}, {3323, 1020}, {1347, 449}, {3239, 1554}, {675, 449}, {1133, 768}, {2125, 1691}, {1053, 844}, {9363, 7513}, {1053, 845}, {1043, 837}, {1101, 1105}, {563, 566}});
+    TestOptimalLinearization("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"_hex_v_u8, {{1073483, 28599}, {974262, 25978}, {28500, 760}, {1176771, 31491}, {1583595, 42433}, {1276412, 34206}, {1159437, 31072}, {998800, 26825}, {1208196, 32597}, {16080, 437}, {35960, 992}, {25776, 713}, {39912, 1105}, {62800, 1784}, {26220, 760}, {15039, 437}, {26030, 760}, {24300, 721}, {32931, 993}, {14203, 438}, {91071, 2829}, {22489, 720}, {13950, 449}, {17453, 565}, {17329, 561}, {42904, 1389}, {953801, 38788}, {8296, 442}, {4883, 441}, {5070, 1352}});
+    TestOptimalLinearization("a91cb4e81c00fc20809ebc6801a454aef86e02ad6cbad74c03e044fba04e04c020d2950605a004a9893e06a004a9893e07a454aef86e089b38a39a1009a928b4e81c0a8d4c91cc040b8d4c91cc040c81940681dfa368000000000000000000000000000000"_hex_v_u8, {{440910, 5404}, {681347, 8352}, {152386, 1868}, {152386, 1868}, {488998, 5996}, {1017959, 12484}, {344735, 4228}, {344735, 4228}, {392823, 4820}, {392823, 4820}, {296648, 3640}, {1306484, 16032}, {440910, 5416}, {2885940, 35462}});
+    TestOptimalLinearization("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"_hex_v_u8, {{124474, 1810}, {827900, 17978}, {540855, 11884}, {462570, 10222}, {201620, 4682}});
+    TestOptimalLinearization("921a84f92a008312809d6801841280c870028b7082891803945985e91004997e87ad7c0580b815ada40006941185c61807974d86cf62089f0a88f80209926d85932e0a963686a0560b945a85dc400c8d2183b53c0d9c5288972a0e9b4e87ee380f943585d12c108e1183d818119625869b5a128f3184896213911a84d154149305859a6415914284de0816980986e22e17920d84f54e18841280c2061818875c82817a1918854d818c5c1518823583bf4c1518861c818d101717857080d7481718866081cc2017188235fe2c1618866281d13e1518847880e9441518857880eb781318894c82b7781218850df5601018847c80ed601018854d80e51e0f18847480ed601018854280a71e1018850081a50002298d7f84983828000025dd44a5ec3425000025823980ac38014e866081f670022726ac7cc3fd5016000000000000000000000000000000000001042900"_hex_v_u8, {{1679688, 62029}, {24765, 1116}, {21663, 994}, {76772, 3548}, {21328, 992}, {28220, 1356}, {33551, 1613}, {17262, 845}, {790344, 39015}, {15280, 756}, {15280, 764}, {15010, 760}, {12483, 658}, {17288, 924}, {49284, 2640}, {8150, 437}, {15164, 888}, {13860, 880}, {10767, 834}, {7600, 781}});
+    TestOptimalLinearization("836880832c00850d80a738000000"_hex_v_u8, {{19250, 1397}});
+    TestOptimalLinearization("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"_hex_v_u8, {{38835, 23106}, {40075, 24533}, {37668, 23160}, {110289, 72339}, {1062, 705}, {1062, 705}, {1062, 706}, {1062, 706}, {1062, 706}, {33045, 22510}, {30667, 21592}, {31176, 22039}, {26458, 22359}});
+    TestOptimalLinearization("8a4481f65e008f7783dc7c00008f7783c70801008f6f83c70801008f7083c7080100008f7783bf620100008f7783bf620100008f7783bf620100008f7783c70801019b1686e862000200"_hex_v_u8, {{313375, 18069}, {36913, 2167}, {36913, 2167}});
+    TestOptimalLinearization("dd5096a94c00db479a8f2201de64999944028236809310020285008082080302847c8083020402857c80830205028a5480d9140602847080f950070285008083020802857cfc38090283318c9b520a02823686d3220a02824187b83c0b02823680ad120c028236e65c0d028478fd180e028239c5640f028a5480d91410028a4880d60811028544e5301202854588ba341302847c8082641402823a87f5101402823687ab7e1502823680a1121602823580ad121702823680a7121802833e80c05e1902823ae9161a028241e1381b02850080966c1c0284788083361d028500fe641e02857c8083021f028a4480d9142002847cee0021028578ff7622028a4480d32423028500eb0024028a4c80cf582502833dc52826028a4c80d914280016824185df5e1128823a80ad1211288a4480cf582a000100"_hex_v_u8, {{431706, 13571}, {421921, 14027}, {11145, 437}, {11145, 438}, {11145, 442}, {10761, 438}, {299471, 12673}, {9480, 438}, {12399, 574}, {16040, 752}, {6795, 442}, {6638, 438}, {6300, 449}, {9718, 768}, {8475, 760}, {8449, 764}, {8434, 764}, {8449, 768}, {8388, 768}, {8178, 768}, {8076, 760}, {4530, 441}, {8449, 892}, {8449, 892}, {13962, 1476}, {13962, 1484}, {13962, 1492}, {13962, 1492}, {13764, 1480}, {7104, 764}, {8251, 888}, {13586, 1476}, {13356, 1476}, {6912, 768}, {8028, 892}, {13356, 1484}, {4500, 573}, {6552, 836}});
+    TestOptimalLinearization("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"_hex_v_u8, {{91200, 4576}, {48195, 6111}, {29525, 3762}, {28266, 5337}, {79016, 15147}, {68868, 16192}, {4752, 1196}, {1582, 437}, {56602, 16222}, {53282, 15911}, {49862, 15150}, {44115, 13578}, {7082, 2217}, {1410, 449}, {5655, 1833}, {6949, 2253}, {5902, 1914}, {5531, 2337}, {1094, 485}, {891, 437}, {2224, 1110}, {891, 450}, {37218, 20378}, {1497, 834}, {43233, 26724}, {41499, 25699}});
+    TestOptimalLinearization("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"_hex_v_u8, {{1360002, 282751}, {2975, 662}, {1887, 441}, {1808, 449}, {2464, 721}, {1463, 449}, {2344, 720}, {1463, 450}, {2344, 721}, {1856, 574}, {1830, 566}, {2304, 764}, {1689, 565}, {1592, 561}, {1226, 449}, {1000, 533}, {1000, 533}, {1000, 534}, {300, 534}});
+
+    // Hard clusters (according to various metrics) in synthetically generated clusters, with 26-64 transactions.
+    TestOptimalLinearization("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"_hex_v_u8, {{3672, 493}, {9871, 2079}, {7901, 1719}, {3172, 732}, {1434, 591}, {1470, 1295}, {734, 715}, {-3533, 9003}, {-3439, 2406}, {-1059, 680}, {-15211, 8262}, {-2491, 993}, {-1297, 351}, {-11899, 3148}, {-1868, 453}});
+    TestOptimalLinearization("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"_hex_v_u8, {{9571, 3032}, {9352, 6065}, {1318, 1023}, {633, 568}, {729, 671}, {7060, 11184}, {-8300, 1641}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2315, 321}, {4683, 667}, {1002, 144}, {4179, 613}, {1369, 254}, {2847, 541}, {2534, 489}, {4242, 963}, {1944, 760}, {832, 472}, {577, 475}, {828, 920}, {643, 967}, {82, 142}, {3527, 21301}, {-455, 904}, {-396, 651}, {-677, 781}, {-381, 398}, {-849, 765}, {-1920, 892}, {-2336, 737}, {-3443, 676}, {-5589, 801}, {-4948, 678}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3748, 674}, {3078, 561}, {3671, 967}, {3017, 805}, {2769, 994}, {2386, 934}, {546, 277}, {1739, 1038}, {188, 452}, {-35, 365}, {-443, 326}, {-27524, 18833}, {-1152, 664}, {-1098, 632}, {-572, 309}, {-1831, 774}, {-1990, 539}, {-1002, 254}, {-4841, 995}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2334, 348}, {5939, 894}, {2743, 415}, {4266, 664}, {2106, 334}, {826, 134}, {4006, 904}, {1321, 331}, {1948, 647}, {22824, 14732}, {793, 816}, {-91, 203}, {-997, 1014}, {-634, 638}, {-930, 902}, {-358, 312}, {-1224, 242}, {-790, 149}, {-2869, 513}, {-6412, 1076}, {-4189, 664}});
+    TestOptimalLinearization("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"_hex_v_u8, {{4112, 1539}, {2265, 900}, {8705, 4603}, {2414, 2781}, {76, 1413}, {-1707, 2591}, {-854, 375}, {-4513, 1397}, {-3611, 740}});
+    TestOptimalLinearization("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"_hex_v_u8, {{4584, 725}, {4364, 762}, {1750, 317}, {4185, 1078}, {1232, 326}, {683, 183}, {408, 114}, {1745, 1029}, {198, 189}, {18555, 18373}, {188, 267}, {96, 292}, {68, 257}, {-196, 469}, {-630, 604}, {-774, 712}, {-203, 165}, {-1478, 974}, {-291, 180}, {-1945, 470}, {-738, 172}, {-3548, 702}, {-755, 134}, {-2029, 359}, {-1206, 186}, {-1582, 220}, {-3524, 460}});
+    TestOptimalLinearization("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"_hex_v_u8, {{774, 136}, {1738, 317}, {4071, 843}, {945, 217}, {3564, 835}, {1059, 281}, {3413, 951}, {3429, 958}, {1999, 578}, {786, 469}, {907, 609}, {681, 463}, {385, 352}, {-79, 114}, {-14191, 11733}, {-1185, 252}, {-1319, 269}});
+    TestOptimalLinearization("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"_hex_v_u8, {{6043, 1305}, {2111, 1592}, {16829, 16660}, {2522, 3629}, {-232, 292}, {-1546, 885}, {-4578, 1405}, {-1409, 389}});
+    TestOptimalLinearization("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"_hex_v_u8, {{6398, 1068}, {3769, 1008}, {1511, 511}, {6, 7736}, {-2660, 6557}, {-1198, 1987}, {-717, 747}, {-2735, 921}, {-2555, 645}, {-2677, 584}, {-9778, 2011}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2372, 409}, {1851, 334}, {3742, 728}, {832, 179}, {1198, 375}, {1873, 654}, {2459, 983}, {2589, 1067}, {791, 441}, {382, 266}, {184, 167}, {6046, 9350}, {268, 510}, {263, 828}, {-7, 288}, {-158, 471}, {-428, 1037}, {-388, 339}, {-1690, 900}, {-1270, 568}, {-916, 278}, {-642, 182}, {-3042, 844}, {-3819, 1016}, {-3826, 816}, {-2475, 516}, {-3102, 621}, {-3131, 592}});
+    TestOptimalLinearization("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"_hex_v_u8, {{7128, 1003}, {1584, 223}, {4155, 641}, {4115, 666}, {4415, 919}, {797, 210}, {3016, 970}, {677, 355}, {1212, 857}, {878, 867}, {327, 975}, {111, 369}, {-1440, 17399}, {-303, 893}, {-339, 488}, {-586, 825}, {-1001, 633}, {-1284, 732}, {-510, 281}, {-438, 203}, {-745, 340}, {-2403, 806}, {-925, 266}, {-4294, 1052}, {-4252, 993}, {-4536, 885}, {-5353, 964}, {-7198, 1072}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3137, 724}, {1966, 694}, {2184, 1015}, {1077, 671}, {-56, 417}, {-4305, 19152}, {-424, 603}, {-2200, 861}, {-6216, 1876}});
+    TestOptimalLinearization("8711d24400834a8e460180458b4302841fbf3200028025883800068672d2640104841fc210020104856fbd3001078039820e050000018175930b03038174915d070000008469864b011086248a4004098475a8040701000a844e925c080000000d8157a0540302108442c13504020f8162895105020685169902050401128559c2360101020b81568a5207000300028427c340060500001180118d520400000204137a835c0901010001118318ad6606010204000a847c8f39050805835da52600248455cb19050206048400b27b010c048604b97b0302080a842695560024835f96790002158530bc2f030703038365a02f012d807481580800040003001c801e851e01218631a40503050004218535c7030405000413800e82080202040602846ec55f09020002000000000017831fb37904020104000000001f85588150030005010101000885449c3d0600010400000f872e8f3f080101000100000e804a825106000100011e81619a5c03010200000c80118b1301010102002c00"_hex_v_u8, {{5346, 1041}, {12977, 2549}, {3992, 879}, {604, 165}, {9466, 2925}, {10459, 5394}, {1398, 1369}, {-5465, 2673}, {-3270, 1378}, {-25877, 8528}, {-4167, 688}});
+    TestOptimalLinearization("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"_hex_v_u8, {{7621, 1016}, {3067, 429}, {5953, 838}, {3365, 481}, {1165, 177}, {4390, 676}, {4241, 770}, {3694, 826}, {880, 197}, {1746, 492}, {2419, 699}, {2891, 1040}, {2540, 1008}, {32264, 19146}, {945, 606}, {202, 989}, {-244, 394}, {-556, 703}, {-1018, 1057}, {-566, 469}, {-1564, 1000}, {-2434, 921}, {-2446, 631}, {-2401, 588}, {-6088, 956}, {-3397, 515}, {-6952, 1035}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3577, 877}, {2923, 769}, {2435, 709}, {783, 480}, {-1399, 8615}, {-337, 909}, {-477, 582}, {-642, 725}, {-1406, 752}, {-804, 388}, {-3142, 915}, {-4096, 1038}, {-2364, 552}, {-4347, 954}, {-1558, 299}, {-805, 153}});
+    TestOptimalLinearization("8327982d0080608f67000085299d2a0100847b8207020082769438030082479f0b0202822a996a01000887298a350100098432a61f010883029b5b04000006870ec96a03048172812b03010008824d916f010102000c833aa8040110801a847f0402000002832c862104000000000a873d9c060202010383208e7803010110815d1101041268870f050001851254010e8124804a020411822c9028060001000e866d8a77030105836ba27e001a8503890804030116857b8f620110850ba7510008188704b103010201001c857cc54f000001000000"_hex_v_u8, {{8000, 4089}, {-935, 11933}, {-3202, 1028}, {-2601, 779}, {-4520, 892}});
+    TestOptimalLinearization("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"_hex_v_u8, {{497, 327}, {-4592, 24583}, {-360, 1076}, {-2707, 644}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3548, 898}, {3266, 836}, {2613, 693}, {3334, 973}, {21647, 16912}, {849, 990}, {285, 521}, {-52, 125}, {-328, 605}, {-222, 380}, {-423, 128}, {-1353, 345}, {-864, 213}, {-1961, 481}, {-3970, 927}, {-3551, 709}});
+    TestOptimalLinearization("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"_hex_v_u8, {{943, 154}, {4543, 1004}, {1208, 271}, {2086, 484}, {1022, 264}, {549, 156}, {1308, 547}, {1277, 953}, {1026, 778}, {12943, 11680}, {486, 863}, {366, 811}, {445, 1094}, {-55, 479}, {-240, 165}, {-304, 139}, {-1110, 337}, {-3876, 1007}, {-1479, 368}, {-1935, 438}, {-4883, 952}, {-5262, 979}, {-1626, 256}, {-3959, 622}});
+    TestOptimalLinearization("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"_hex_v_u8, {{4709, 1055}, {2513, 620}, {2218, 909}, {6605, 3186}, {6218, 3702}, {703, 1507}, {20, 886}, {-2372, 6067}, {-10262, 12450}});
+    TestOptimalLinearization("803a8f330086548209018265ac21028521bf2e0104800b844d02018321a05d0006835e933e040003835792230400048047865703068201a07d04068662a16d0308865ad476000e8431bb620200020b8264841503010c8625ba5704000209837d9d52021686378e68020e837b8174020e840e80590301060383329a4007020100118262885c0305010a834d8d2a02128133964d0600040d8437ac2a0503040005816b810705020419840cb2440d00000100000b865ad07005030003118419ae21060201030586748076060005000c80068a0e050103030006870dc31208020000020010863bc91f060100020301000a80218b4f0400020d817c8e6f080100020201000880108c4f010d1b834db0320607000017841ca15c0500040000020478853200020100000000001300"_hex_v_u8, {{3922, 1781}, {3529, 2772}, {16566, 14073}, {579, 1338}, {-1016, 380}, {-7368, 1740}, {-808, 161}, {-872, 144}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2085, 516}, {-1, 2091}, {-214, 2450}, {-2803, 3167}, {-16800, 11295}});
+    TestOptimalLinearization("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"_hex_v_u8, {{9901, 20654}, {1369, 3124}, {-656, 773}});
+    TestOptimalLinearization("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"_hex_v_u8, {{5480, 1030}, {4602, 881}, {2811, 551}, {4043, 853}, {3062, 687}, {3415, 878}, {1536, 414}, {698, 231}, {797, 438}, {518, 311}, {661, 424}, {568, 442}, {1004, 794}, {504, 592}, {367, 592}, {221, 672}, {67, 271}, {34, 177}, {-526, 14670}, {-108, 541}, {-616, 849}, {-663, 863}, {-769, 956}, {-1245, 990}, {-2033, 1010}, {-1105, 495}, {-1916, 678}, {-2491, 745}, {-3117, 877}, {-980, 263}, {-3333, 680}, {-3790, 536}});
+    TestOptimalLinearization("82549265008464d27c01866ab47902837da12a0380368f74048738dc4d05842e8b3b06853dc84a078661ab22088454a16b09865f957f0a8279ab2b0b837b84050c837dc31a0d837db5180e7b816f0f8346ac4310800b883d1180148709128349a63c1380629800148638ae3f15802c8b59168223ae4117801d8e1718812f893319853bdc3b1a841caa5b1b8354aa55000000000000000000000000000000000000000000000000000000001c870abd4d010000000000000000000000000000000000000000000000000000001b85768103020000000000000000000000000000000000000000000000000000001a801c8861030000000000000000000000000000000000000000000000000000001980658e150400000000000000000000000000000000000000000000000000000019826da47005000000000000000000000000000000000000000000000000000000198100884506000000000000000000000000000000000000000000000000000000188528d056070000000000000000000000000000000000000000000000000000001880718a5d08000000000000000000000000000000000000000000000000000000178677ba060900000000000000000000000000000000000000000000000000000017815889110a00000000000000000000000000000000000000000000000000000016813187200b00000000000000000000000000000000000000000000000000000015804a800a0c00000000000000000000000000000000000000000000000000000015847a81550d0000000000000000000000000000000000000000000000000000001486799e420e00000000000000000000000000000000000000000000000000000013835cb8120f00000000000000000000000000000000000000000000000000000012865ff84910000000000000000000000000000000000000000000000000000000118403ac6111000000000000000000000000000000000000000000000000000000108656db361200000000000000000000000000000000000000000000000000000010815da06013000000000000000000000000000000000000000000000000000000108740f30c1400000000000000000000000000000000000000000000000000000010843ad1361500000000000000000000000000000000000000000000000000000010806a92421600000000000000000000000000000000000000000000000000000010874acc3017000000000000000000000000000000000000000000000000000000108001897218000000000000000000000000000000000000000000000000000000108213a100190000000000000000000000000000000000000000000000000000001085159f141a0000000000000000000000000000000000000000000000000000000e806288681b0000000000000000000000000000000000000000000000000000000c842d86401c0000000000000000000000000000000000000000000000000000000b860bb3081d00000000000000000000000000000000000000000000000000000008814ca17f1e0000000000000000000000000000000000000000000000000000000680418c4e1f00000000000000000000000000000000000000000000000000000006820e98212000000000000000000000000000000000000000000000000000000006856db851210000000000000000000000000000000000000000000000000000000300"_hex_v_u8, {{5374, 740}, {1600, 226}, {4365, 637}, {1082, 182}, {4709, 829}, {3468, 637}, {2526, 585}, {2197, 637}, {2833, 993}, {14949, 22604}, {69, 202}, {-130, 886}, {-171, 762}, {-649, 344}, {-611, 256}, {-751, 241}, {-4007, 1034}, {-625, 156}, {-1617, 398}, {-3689, 877}, {-971, 229}, {-2929, 643}, {-2795, 596}, {-2240, 332}, {-7781, 991}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3242, 1160}, {9343, 4022}, {7247, 25626}, {-574, 1753}, {-2604, 5019}, {-2887, 1089}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2932, 731}, {1341, 504}, {3541, 2737}, {492, 640}, {40, 106}, {72, 211}, {-779, 2654}, {-2914, 8443}, {-359, 577}, {-2424, 572}});
+    TestOptimalLinearization("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"_hex_v_u8, {{6122, 1002}, {7354, 1720}, {2575, 735}, {1254, 454}, {1609, 1061}, {302, 747}, {-6224, 20869}});
+    TestOptimalLinearization("8677a44400823d9b1101847c893e0102831ea2130201865b944502028560ac640301856cc01101088644cc2c0302867ea77d0008843d8949040202843a9d0307000081528f5707000005804e8c5b0403000585169c7e06000201834e8e0d0503000d835e96250500000f8628a9550104078018847d0302000201821f90780301000002000681648442030103028433976b070000000000000e844a9116040202000d82349016000880158b240600010100108006831101060001850bb04e0101010100088723835a010002010c830593360203000003811a8e150400000000001c7f8168010000001300"_hex_v_u8, {{2402, 1015}, {2700, 1506}, {671, 764}, {1129, 1309}, {-7302, 12461}, {-1410, 818}, {-971, 282}});
+    TestOptimalLinearization("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"_hex_v_u8, {{7322, 1810}, {2404, 2903}, {8842, 11211}, {4511, 6807}, {764, 2139}, {-1680, 551}, {-4367, 1277}, {-10769, 2999}, {-2074, 527}});
+    TestOptimalLinearization("82159935008379b66e01830bae7202803d87690203826ea53b0302821a993303038408b52a0502864de64005028326bc7b050106827a9b050508842ace1c010f836f966204020865810a080106816ba5640703018270844306010301851f8e69050201000d8500866c0505000b8357ac7d040500098542881e040109822f8451050303048257985708010400028555bd29020e8116875e0603010211865c9f0906010408846db41b0206050786259654050503000011855ac662080300010100068655c91b020910830bb7540d0000020000000d8563da4d0e0000010000001481148d1f0e010000010012831193360a000004010a860ece440807000100068402b614060404020e8712da6e06080001028377997c070401040000018224a23c040800041e805f976e0c0201000200018655e22305060501088656a83c0801000401011e8248a140010a02002385633903010703011c80528207080302000200002780038e130c01000300000000268421330701020103010b800682590a0102020000001f863ca66005050202012b831fb146070300000202000024834c9f5d060003000100010d840dc01a040201010319857a8a2606010101000001000009824f814701040301136e876d05000202010000000c871cad4d0107002c803d884203000402008446cd4e0000010000000d00"_hex_v_u8, {{10199, 1606}, {3065, 523}, {1786, 1053}, {1089, 913}, {792, 773}, {1104, 1232}, {13868, 19409}, {-4512, 8170}, {-567, 110}});
+    TestOptimalLinearization("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"_hex_v_u8, {{1532, 222}, {2915, 429}, {697, 126}, {3528, 696}, {4357, 912}, {4628, 1011}, {1679, 380}, {1411, 343}, {4387, 1081}, {415, 106}, {2696, 766}, {3104, 890}, {3306, 1007}, {672, 389}, {411, 244}, {296, 219}, {906, 713}, {134, 132}, {-227, 896}, {-3629, 13571}, {-188, 691}, {-356, 844}, {-500, 1083}, {-468, 910}, {-1696, 1065}, {-899, 558}, {-330, 161}, {-2614, 797}, {-3343, 867}, {-3385, 863}, {-3047, 706}, {-2051, 404}, {-2043, 324}, {-2980, 458}});
+    TestOptimalLinearization("8063850a0084718e1f018627d96c028369c06503842ec7070480158a0505853fbf200683719c3e07806f906a088611df4e09816fa0570a863e94760b800485030c8307b4590d8642e7400e8459bf1d0f803461108259aa03118671ad171280708651138257907e14821986091582203b168527c013178315aa081880558e67198664c5511a872afc330000000000000000000000000000000000000000000000000000001b863b8d480100000000000000000000000000000000000000000000000000001b847f81610200000000000000000000000000000000000000000000000000001b8526852d03000000000000000000000000000000000000000000000000000018857d901b0400000000000000000000000000000000000000000000000000001884238e240500000000000000000000000000000000000000000000000000001885049c610600000000000000000000000000000000000000000000000000001880401a070000000000000000000000000000000000000000000000000000168349a2100800000000000000000000000000000000000000000000000000001581539c5f09000000000000000000000000000000000000000000000000000015810f96030a0000000000000000000000000000000000000000000000000000148406b8190b0000000000000000000000000000000000000000000000000000138005801a0c000000000000000000000000000000000000000000000000000013863c99570d000000000000000000000000000000000000000000000000000013842ea1130e000000000000000000000000000000000000000000000000000012810b8a5e0f000000000000000000000000000000000000000000000000000011861c8474100000000000000000000000000000000000000000000000000000118117903911000000000000000000000000000000000000000000000000000010850b981d12000000000000000000000000000000000000000000000000000010822d9d73130000000000000000000000000000000000000000000000000000108655c73614000000000000000000000000000000000000000000000000000010862baf0c15000000000000000000000000000000000000000000000000000010758c001600000000000000000000000000000000000000000000000000000f80739a7f1700000000000000000000000000000000000000000000000000000f8070856b1800000000000000000000000000000000000000000000000000000f837c8d4e1900000000000000000000000000000000000000000000000000000e806888691a00000000000000000000000000000000000000000000000000000b8570de661b0000000000000000000000000000000000000000000000000000098332bb0b1c0000000000000000000000000000000000000000000000000000098240ae6b1d000000000000000000000000000000000000000000000000000008861599711e000000000000000000000000000000000000000000000000000006821da71e1f0000000000000000000000000000000000000000000000000000038334af692000000000000000000000000000000000000000000000000000000200"_hex_v_u8, {{6688, 962}, {6183, 913}, {5814, 935}, {2756, 533}, {4112, 831}, {1141, 239}, {1887, 625}, {1151, 471}, {389, 227}, {1403, 958}, {-30, 416}, {-49, 180}, {-13972, 17369}, {-1102, 893}, {-1708, 956}, {-438, 240}, {-1721, 917}, {-1615, 779}, {-1905, 772}, {-629, 232}, {-2186, 686}, {-1117, 279}, {-1978, 429}, {-1474, 271}, {-3125, 564}, {-1904, 339}, {-3661, 646}, {-3062, 448}, {-3846, 562}, {-1792, 243}, {-8026, 1066}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2562, 604}, {2588, 663}, {982, 316}, {2708, 904}, {8802, 12587}, {-198, 177}, {-961, 544}, {-1534, 843}, {-3237, 835}, {-704, 168}, {-2842, 568}, {-3479, 682}, {-4244, 721}});
+    TestOptimalLinearization("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"_hex_v_u8, {{3156, 563}, {1594, 1161}, {3115, 10582}, {-3684, 5344}, {-423, 547}, {-4401, 3628}, {-1634, 871}});
+    TestOptimalLinearization("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"_hex_v_u8, {{588, 201}, {3571, 2051}, {6111, 4552}, {5853, 5439}, {4559, 5181}, {-800, 860}, {-4457, 3265}, {-2115, 528}, {-5784, 1063}});
+    TestOptimalLinearization("850c8f35008651ce2f0165807a028725d844038227a4150481378e1c058729b702068279a853076f8878088239a3380981228d300a805c85710b86559b420c8653a67a0d860eac270e823d8c0a0f82539142000000000000000000000000000000000f80068543010000000000000000000000000000000f825f8156020000000000000000000000000000000d83459166030000000000000000000000000000000b84209c0a040000000000000000000000000000000b807e9509050000000000000000000000000000000a80709452060000000000000000000000000000000a70823d070000000000000000000000000000000a8301a000080000000000000000000000000000000a8168806c090000000000000000000000000000000a8120865e0a00000000000000000000000000000009801583190b00000000000000000000000000000009857ed1480c00000000000000000000000000000006806082300d00000000000000000000000000000004801f89590e000000000000000000000000000000038103965a0f00000000000000000000000000000003801d822d10000000000000000000000000000000038459a3031100000000000000000000000000000002872eaf7f1200000000000000000000000000000002854b9658130000000000000000000000000000000100"_hex_v_u8, {{636, 111}, {5730, 1061}, {2332, 441}, {3585, 1065}, {920, 290}, {974, 311}, {2557, 979}, {837, 445}, {1825, 981}, {125, 101}, {2546, 9635}, {-215, 157}, {-269, 149}, {-223, 112}, {-3136, 1070}, {-418, 134}, {-2306, 729}, {-685, 159}, {-1413, 254}});
+    TestOptimalLinearization("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"_hex_v_u8, {{5282, 945}, {4698, 957}, {3874, 805}, {692, 155}, {14104, 3949}, {6151, 2252}, {345, 908}, {-589, 2663}, {-696, 870}, {-892, 981}, {-1375, 1112}, {-32657, 11825}});
+    TestOptimalLinearization("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"_hex_v_u8, {{5265, 1000}, {4404, 894}, {4377, 896}, {3553, 734}, {3692, 969}, {969, 459}, {456, 220}, {1443, 945}, {-64, 246}, {-80, 297}, {-448, 791}, {-4017, 6631}, {-664, 505}, {-577, 294}, {-1610, 603}, {-1713, 556}, {-2810, 884}, {-585, 164}, {-1038, 230}, {-4873, 1056}, {-3019, 597}, {-1209, 235}});
+    TestOptimalLinearization("866db148008305944a018340810400038721c963010282528f4802028532a1260301852e954c030685778653050002668530010c806a4a020c8451aa0f030102866c8e250202000b812e9071060000000009852f875105010000000d834e98750400020003814b8b63040000020007840fa646050000020001812c891d0203021082428c7606000001000d822e875d01118502bf170701000006840a8e6c050002010a820c9b1c0204107c871f030100031682259a480401000300188676815a0107128034845b03030002138458a24205000000000013861ca528050000000001048560b41e0200000101000e80618757020200001300"_hex_v_u8, {{3236, 1005}, {3576, 1335}, {1060, 466}, {1984, 1492}, {37, 234}, {-3095, 13613}, {-556, 225}});
+    TestOptimalLinearization("8260991f008662892d0001837fa91b01008401a85d0001870cad1f0101810c8658010681356a0206846b824c0400058661c47805000183058c7104028609914d06000a864fc143070004852fb7020601078132943c03040008845eb202040201048626a67f02000682358c18040004000384249049050000030781428c4c02020c8361962f030204028078873307000001010008821b986c0205010005853b8a0e070001000000000c8260956c0301040c862ca078030000010200186b825d010401000c807d930100040101821196590500000000000000088235880e020000001300"_hex_v_u8, {{1910, 8479}, {-3111, 8308}, {-1517, 401}, {-1281, 253}});
+    TestOptimalLinearization("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"_hex_v_u8, {{6469, 1056}, {1595, 782}, {12744, 6989}, {-189, 1663}, {-1826, 9149}, {-470, 674}, {-615, 650}, {-8266, 5425}, {-5939, 1093}});
+    TestOptimalLinearization("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"_hex_v_u8, {{2465, 343}, {4765, 718}, {5953, 921}, {5398, 856}, {1618, 270}, {556, 110}, {3443, 695}, {2145, 528}, {1404, 385}, {3699, 1070}, {3096, 1010}, {1791, 650}, {575, 251}, {17859, 10290}, {151, 109}, {168, 122}, {756, 564}, {587, 956}, {286, 586}, {224, 1089}, {178, 867}, {-255, 295}, {-1136, 1080}, {-1971, 962}, {-1790, 668}, {-1239, 436}, {-494, 147}, {-2508, 619}, {-653, 151}, {-4079, 880}, {-4722, 971}, {-1127, 223}, {-2079, 407}, {-4927, 880}, {-4775, 753}, {-4198, 645}});
+    TestOptimalLinearization("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"_hex_v_u8, {{6971, 990}, {2555, 380}, {2543, 416}, {1011, 182}, {9375, 2190}, {3834, 926}, {7100, 2111}, {24543, 8471}, {999, 354}, {948, 782}, {3401, 2813}, {599, 974}, {-2440, 4852}, {-946, 474}, {-9312, 3117}, {-3594, 1125}, {-1603, 393}, {-4641, 790}});
+    TestOptimalLinearization("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"_hex_v_u8, {{1344, 184}, {14532, 3445}, {2929, 1712}, {19, 378}, {-2610, 2705}, {-19575, 18795}, {-12674, 4996}, {-2889, 974}, {-4804, 1026}, {-1466, 236}, {-3905, 578}, {-4401, 592}});
+    TestOptimalLinearization("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"_hex_v_u8, {{4804, 1029}, {1721, 433}, {-813, 15413}, {-1617, 12598}, {-7653, 3678}});
+    TestOptimalLinearization("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"_hex_v_u8, {{4594, 602}, {1855, 249}, {1121, 151}, {5310, 719}, {7657, 1052}, {5449, 1012}, {2001, 416}, {2550, 1090}, {18542, 18063}, {240, 241}, {198, 209}, {187, 758}, {-92, 337}, {-238, 831}, {-132, 262}, {-570, 447}, {-1294, 753}, {-1293, 585}, {-2195, 868}, {-1374, 498}, {-1902, 649}, {-2493, 710}, {-1277, 262}, {-3037, 614}, {-759, 120}, {-3684, 573}, {-2233, 336}, {-1498, 215}});
+
+    // Clusters which admit repeated states in SFL.
+    TestOptimalLinearization("862ea341008713833c018745817502827a814f0382528b6704813381280581308548010005815a8e7a0100010684019f0005000003802783720500000009856cae0005000001028601ac0e050000000475811a0601000000008135834c070000000000088007863e0800000000000284299b710900000000000200"_hex_v_u8, {{7533, 8149}, {-1849, 681}});
+    TestOptimalLinearization("82759235008069896c0186438e3d028244912600000003851ba405010000038214845c0200000183018a4b03000001807f841f00000000078573823a0100000007820f8a65020000000164805703000000018622ab5804000000018412936600000000000c82749c04010000000008832b977602000000000700"_hex_v_u8, {{694, 233}, {2856, 7908}});
+    TestOptimalLinearization("85478e3b00823c904101820c893f0283179c5903814c893104854282530583429f140100000103830d8509010001000284409a70020100000181168c190300000001088718b06a0400000001058553ac2c0500000000000b8506a22e060000000000008552803a0000000008800f861e020000010008817c844802000100010700"_hex_v_u8, {{6613, 7335}, {-322, 2176}});
+    TestOptimalLinearization("8146845100804b890d0186768b55028406a32f03863ca23104832f8e3b05810a892b0680358253078502ac5d08872d96700983718004000100000002018273952801010001000100097b3c02020000000100058562a14203010000000000010d8718817804000000010000000c862f956c050000000000000000000900"_hex_v_u8, {{1528, 1069}, {-5842, 9025}});
+    TestOptimalLinearization("8460992400872dbd1901867fb07f02852a817d00000003852d87540100000181348f60020000018435942b03000000837f8943000000000681608e730100000005857da67f0200000005843794080300000004658217040000000086628a1500000000000b8708805401000000000a847fa32402000000000700"_hex_v_u8, {{1682, 736}, {-8507, 10189}});
+    TestOptimalLinearization("81668e3500804e844f018435927302861f9d5f03846ea342010000018261897a010000018165831102000100863e895003000000078232985e04000000018606823f000001000986318a570200000009804300020100000981408323040000000885179a260400000000068510af7800000000000b8360966f01000000000000"_hex_v_u8, {{4144, 9101}, {-1528, 608}});
+    TestOptimalLinearization("861e862e00851aa57f018060816b02831ba009038628b818048576b3010580072a068478911d07854fa8600003000007816d86560200000000048576b11403000000010009850aa7100300000100010782178f040400010000010280758a22050100000000000d860eb344060000000000010c8501975a070000000001000500"_hex_v_u8, {{3660, 936}, {6832, 9471}});
+    TestOptimalLinearization("802e7300824b95370000821c8a5e0002827a89580102813185560201867ba17f0301810e83580000000000835d9a0c010000000087218c1602000000008458905a03000000008319937d00000000068216900801000000068677ab2a0200000005826f91710300000004864f4404000000038702ac3c00000000000900"_hex_v_u8, {{6067, 6956}, {392, 3033}});
+    TestOptimalLinearization("8151801500823e835201842ba81902837b881e038674b461048676897a058369894306873e8511078514a802010001010001833a8f51010001000100078236885502000101000003872cab780300000101000381035605000000000000038123825305010000000000018152847106000000000000000100"_hex_v_u8, {{5948, 5991}, {-8330, 3591}});
+    TestOptimalLinearization("6f845f008472960a01842084330286779f7903800786310481588d0505865994390683449e480100000000000387218e3a02000000000000811d22020000000100008500812a0300000000000003825e970e04000000000000028436815a05000000000000027c812e060000000000000000"_hex_v_u8, {{1477, 754}, {-526, 7248}});
+    TestOptimalLinearization("83419a7b00860e9172000183289a1901018157824f020183209e53030085398e5a040081458e2d00010000068334a04c010000000005840d8f1d02000000000281398b70030000000000872f8f5a040000000000816a8070010000000b843ba5140100000109823a91680200000000078267903303000000000700"_hex_v_u8, {{2212, 8180}, {-1114, 487}});
+    TestOptimalLinearization("867e816800827e9a7101811c8f470000018613905501000080708c0e020000865c963a030000873a834e0400008267921900000000000486238a5a0100000000028614914a020000000002823083560300000000008652993e040000000000813c8e03010000000a803c817601010000028507990402000000000a00"_hex_v_u8, {{3395, 9748}, {-962, 316}});
+    TestOptimalLinearization("856d9d530083029d1d0186429d3f02866b927b038234947a000201835389400101028460895c0201000582128f5303000100803183290400000184358f790500010082779924060000000682416d0700000006867b9a4003000000000a83149b200100010100000482488f62020100000000000b00"_hex_v_u8, {{-524, 9354}});
+    TestOptimalLinearization("8748865d0082558d3d01825d8f7a0281678623000003815e8b750100000277831e02000001873d8f3a03000000805b841f0001000682548f0b010000018376891e0200000007826d8320030000000482288b71040000000282078b0c000000000d82288e26010000000d872994040200010009800e800a03000000000b00"_hex_v_u8, {{1085, 477}, {513, 7734}});
+    TestOptimalLinearization("817b8f1100832c965701811b8a4400000281418f16010002804f86370200028573941d0300028179820f04000280238743000000000006845291470100000000037f826c0200000000018602a563030000000001850d902000000000058652826301000000058673a03602000000028379970d030000000200"_hex_v_u8, {{-3780, 7686}, {-1543, 633}});
+    TestOptimalLinearization("85179c690081659269018635831a02866289680385438d3704867eae70058726b035068009856307816e926001000100048742b83801000000010a822190360201000001098721b05603000000000108861db2580401000001000080758a30050000010000000d8354a334060100000000000d8629a87c070000010000000a00"_hex_v_u8, {{3064, 1022}, {11548, 10758}});
+    TestOptimalLinearization("813d894b008263966701802d827f028375997a00000003861891180100000387219a68020000018462827503000001821a924504000001833a9d16000000000003810e8d2d01000000000284299632020000000001820993160300000000008656b4780000000009845c8f03010000000300"_hex_v_u8, {{7961, 7623}, {-1026, 732}});
+    TestOptimalLinearization("86639b0b0084139655018156830f000002872895040100028567862f02000280468504030001830c8427040000870b987900000000000680527801000000000280148635020000000001860c952a0300000000018216867600000000098426a04c010000000481658d55020000000100"_hex_v_u8, {{-583, 8038}, {-939, 357}});
+    TestOptimalLinearization("8718a9310084369903018666a2270000018207936e0100018470800102000084609c240300008324985c04000086418d2100000000000285708d7c0100000000028362875802000000000182519504030000000001854fa01a000000000b851fa3120100000008834d8b47020000000300"_hex_v_u8, {{4600, 9729}, {-804, 589}});
+
+    // Clusters which have lots of potential SFL states/transitions.
+    TestOptimalLinearization("84559211008539851b01825098430285268d1e00010181008e700100028425a22e02000005860a9c1403000005830b924004000005810d87040500000483768808060000038731854007000003862b9066000001010a83799a540100020104850c9a5702010000020482098c0003000002000002826897580400010000010000"_hex_v_u8, {{10878, 9607}, {-1772, 780}});
+    TestOptimalLinearization("8657833900865d887e018043894b0287338377038624880100010001851fa82401000000038421990e02000000038723af560300000003866dae0a04000000028265860005000000028031863800000001088353a12c0101000000088630b51a02000000000003866ba1650300000000000300"_hex_v_u8, {{15815, 9911}, {-2227, 1003}});
+    TestOptimalLinearization("852a9d7d008350920901825193330280691201000181428c25010001823d8d1f020000018355460300000182448c0f040000008608994d05000000843ea14a01000100078511a07001000200058737ad5802000200058569ae3f04010000026e80520401000000058509ac7605000000010400"_hex_v_u8, {{1641, 8273}, {-3040, 873}});
+    TestOptimalLinearization("803a88570078825101806a88390282048777038430920a000003811b841f010000038003801c0200000006822092420300000002821a96380400000001820280110500000001806d8834000001000006871aaf2b01000000000003806a8a2a02000000000001864c9e600300000000000100"_hex_v_u8, {{4968, 4685}, {-3094, 1050}});
+    TestOptimalLinearization("8437801e00845d833f01816b907800000286438821010002867cac720200028202895e030000861db23d00000000068419a47301000000048404966b0200000002812a817c000000058438824b01000004822c980e0200000286168f4c03000002860c8a5b040000008542997a00000000000a8247815101000000000800"_hex_v_u8, {{4563, 3197}, {-4405, 7734}});
+    TestOptimalLinearization("8556877f0081658a7b01803865028412813e03810e816d048743b56e0581398d070680378048010100000001812e85280100000100000780018226020001000000078370891403000000000100824a994a05000000000000822c835a050000000000000980608376060000000000000100"_hex_v_u8, {{3511, 1091}, {1365, 4984}});
+    TestOptimalLinearization("66844f008651aa61018409810902816f814d03823084080000000004843b8144010000000483528d16020000000082758c5403000000008342927f000000000886780c01000000088656802302000000088637b649000004855f8f4001000009815a8c5002000009814b8d240300000900"_hex_v_u8, {{292, 8437}, {-3557, 951}});
+    TestOptimalLinearization("825d842900824a800401864bb0360281598d13038039835f04834a80310585568663068555862e00000000000000078552935e010000000000000785738c5c02000000000000058163864403000000000000058069837e040000000000000480708610050000000000000000"_hex_v_u8, {{3163, 971}, {1861, 6319}});
+    TestOptimalLinearization("83249365008149926b01817a925202874bba1f038631ab2b0484788e55058613992d06857aa671078367883600000100000001844f916e010100010000008179867002000100000100847a90600300000000000007842c902a0500000000000004825e856b0500000000000000068016831206000000000000000200"_hex_v_u8, {{1257, 378}, {-10088, 9271}});
+    TestOptimalLinearization("802488410085669221018528aa5b02800a8539038278921601000382338719010103802b8744030102842b8404050002857b886a040102864d9317050100088267920006000001806b813407000100863a5d080000000182529b23000000010000010884259254010000010100000781739540030000000000000600"_hex_v_u8, {{-125, 8361}, {-1810, 466}});
+    TestOptimalLinearization("81528b45008715a71201834c8c090102802f85320202866a89320301812985680001068120817301010005837a836a020000000581448a060300000005846e6b0400000001814c9355000100000582758c5a0101000002833b872d02000000000884539c000300000000068459a140000000000b83098f5a010000000300"_hex_v_u8, {{2569, 1045}, {4798, 7773}});
+    TestOptimalLinearization("8635a94d00866f9a5901847ea66802821c81640203856694370101018713b00d030001813b8b3603000000811980480400000086108960000100000881068b4301000001028033866202000001008556b22f030000000003835ba028040000000001815789540100000006823d903e01010000058629b01202000000000500"_hex_v_u8, {{2548, 766}, {-3769, 9412}});
+    TestOptimalLinearization("81188d5500822c855b01821c3a02863a9117038425930d048207906f057243068235804f07853f8b16000002000108822a8a5601000100010880738e07020001000008850d8c4605010000000681038c2205010000010681628b4a050001000007840a8d440600000002000a8538986a070000000001000000"_hex_v_u8, {{1557, 7818}, {-964, 243}});
+    TestOptimalLinearization("8522934b00812a8b15018610b44e0285789a1f0386509173048233901705840f914906857a924f07831d8e58020000000107860b806502000000010380328724030200000000824b5f0301010000000181518964040000010000000c816e8b24060000000000000b853f45070000000000000400"_hex_v_u8, {{3431, 912}, {-5784, 8563}});
+    TestOptimalLinearization("832f8f59008730831a018022822b02801239038275987b048520a0590582448b6506826398500001010007854b971a0100020000088105894c0201000001068737992603000101000387249424040001010003815b82220500000001028706934a0600000100000d8602ae3d0701000000000c844789560801000000000100"_hex_v_u8, {{3440, 9506}, {-3039, 898}});
+    TestOptimalLinearization("8458a65900850aac29018201855f02854fab75038461877504821e86330584328d3706861b8d7107844e9d2808847c9250000000030004836d8d3e040000000000098179916402020000010005825b95700400000100000000867dae5e04000000000001000a8162941e05000000000100000682628a4e06000000010000000600"_hex_v_u8, {{1940, 718}, {-1665, 9596}});
+    TestOptimalLinearization("8147814100805389410185059d29028045833103850834048073883f05803580330000000106832b9f6c0101000105821c0b020000000000068519a8600300000000000484759a66010000018339a07201000001854ea048020000018730ba160400000086409d3c040000000c00"_hex_v_u8, {{12873, 8672}});
+    TestOptimalLinearization("8219866f008118842f01854ba30b0283058a1f038614921b04866a807005840f9b140000000000000584339d1601000000000004834d925402000000000004811d8b3403000000000003844f8552040000000000038217821e0500000000000100"_hex_v_u8, {{1429, 7313}});
+    TestOptimalLinearization("8177892100831b9b490181418f05027d803603872c8040048438837805852ea30200000000000006871e956c01000000000005824c9036020000000000018471972203000000000001865d8e28040000000000008566a4100500000000000000"_hex_v_u8, {{6781, 8064}});
+    TestOptimalLinearization("8534a80f008374901f018379995e000002807a8c4201000285438d340200028019856403000282178b22040001830b930605000080608b06000000000000048621ad3601000000000001842ba10a02000000000000825494320300000000000000"_hex_v_u8, {{9556, 6553}});
+    TestOptimalLinearization("81398a1700805f84750183639f61028032835f0387498f1b048526992b0581688f4e0000000000000480028348010000000000038005821c02000000000003864fad6803000000000003816c9156040000000000038715b5320500000000000000"_hex_v_u8, {{3013, 6235}});
+    TestOptimalLinearization("83799c23008671ad4901815c896b02854fab3303810481680000000004803181130100000003845f8743020000000383258862030000000381658f6d0400000002802384590000000000058318876701000000000380758d020000038618951201000366812a02000200"_hex_v_u8, {{-7815, 6881}});
+    TestOptimalLinearization("8225945300815931018413962f02836a9635038720b46d04842b840f058659974a0000000000000587179118010000000000058710a5540200000000000187169242030000000000018620ac6c04000000000001844182700500000000000000"_hex_v_u8, {{1461, 9533}});
+    TestOptimalLinearization("806e801500871ca421018125845d02841a9c3703845da477048528997d058510a820000000000000068745946e01000000000004840f9b1202000000000004822d8e280300000000000484599f0004000000000004807d81050500000000000200"_hex_v_u8, {{2, 7480}, {-131, 253}});
+    TestOptimalLinearization("84098a0d008000811f01812f831902867a843a038124890f04821e821905870b9e4400000000000004840aa00601000000000002852e97020200000000000284769b18030000000000018042847604000000000001853290160500000000000100"_hex_v_u8, {{7324, 7073}});
+    TestOptimalLinearization("834a9b5f00820a89790180598b3f0273815703816e807004805683370580308062068417a42c0000000000000002865098610100000000000000831a93590200000000000000801981000000000a856eb5520100000786409000020000058336903803000005836b9a020400000583599c0c0500000500"_hex_v_u8, {{5272, 8022}});
+    TestOptimalLinearization("85268b4c0082748120018068802102807986310381428d770480268659058340994e00000000000004806b8a3e01000000000004811f8c3c02000000000002840a8d6c030000000000018608af5604000000000001822492100500000000000000"_hex_v_u8, {{7536, 5347}});
+    TestOptimalLinearization("83718f5300862d9663018700ae190281338d3303825c865104832c916705851b9c64000000000000068419a256010000000000028510a35802000000000001816b861a030000000000018564ad6804000000000001832e85480500000000000100"_hex_v_u8, {{2190, 7962}});
+    TestOptimalLinearization("842a980f008356951f01805c82570282308f4303802d8317048415a13705863e51000000000000058530a15201000000000004827c865402000000000004845e93260300000000000281638e68040000000000028121832e0500000000000100"_hex_v_u8, {{-1542, 6426}});
+    TestOptimalLinearization("855f8024008024816501807c81020284629b030383078631048044895c000002048078100100000000068315856a020000000004800784130300000000028167800c04000000000281758a14010000000885249a1a0100010004852ca63e020000010300"_hex_v_u8, {{3618, 5996}});
+    TestOptimalLinearization("855f97230080678a4f018210925d02856113038105892b04854e996105805a8a480000000000000283028b7a01000000000002846d9f080200000000000283189656030000000000018277862e0400000000000185508d200500000000000000"_hex_v_u8, {{573, 6834}});
+    TestOptimalLinearization("866faa23008646b71501851f96130282588f1103804d851c0000000003822097600100000003850a8f310200000003856e9201000000038656935f01000003855b8f5f020000018743923a0000000a812b810b010000098403a328020000068712970203000005833e98400400000200"_hex_v_u8, {{-4960, 11011}});
+}
+
 BOOST_AUTO_TEST_SUITE_END()

src/test/fuzz/cluster_linearize.cpp

@@ -24,29 +24,22 @@
  *          possibly by comparison with other implementations (at the end of the line ->).
  *   <<---: The right side is implemented using the left side.
  *
- *   +-----------------------+
+ *   +---------------------+                        +-----------+
- *   | SearchCandidateFinder | <<---------------------\
+ *   | SpanningForestState | <<-------------------- | Linearize |
- *   +-----------------------+                        |
+ *   +---------------------+                        +-----------+
- *     |                                            +-----------+
+ *               |                                       |
- *     |                                            | Linearize |
+ *               |                                       |        ^^  PRODUCTION CODE
- *     |                                            +-----------+
+ *               |                                       |        ||
- *     |        +-------------------------+           |  |
- *     |        | AncestorCandidateFinder | <<--------/  |
- *     |        +-------------------------+              |
- *     |          |                     ^                |        ^^  PRODUCTION CODE
- *     |          |                     |                |        ||
  *  ==============================================================================================
- *     |          |                     |                |        ||
+ *               |                                       |        ||
- *     | clusterlin_ancestor_finder*    |                |        vv  TEST CODE
+ *               |-clusterlin_sfl*                       |        vv  TEST CODE
- *     |                                |                |
+ *               |                                       |
- *     |-clusterlin_search_finder*      |                |-clusterlin_linearize*
+ *               \------------------------------------\  |-clusterlin_linearize*
- *     |                                |                |
+ *                                                    |  |
- *     v                                |                v
+ *                                                    v  v
- *   +-----------------------+          |           +-----------------+
+ *   +-----------------------+                      +-----------------+
  *   | SimpleCandidateFinder | <<-------------------| SimpleLinearize |
- *   +-----------------------+          |           +-----------------+
+ *   +-----------------------+                      +-----------------+
- *                  |                   |                |
- *                  +-------------------/                |
  *                  |                                    |
  *                  |-clusterlin_simple_finder*          |-clusterlin_simple_linearize*
  *                  v                                    v
@@ -59,15 +52,12 @@
  *   - clusterlin_depgraph_sim
  *   - clusterlin_depgraph_serialization
  *   - clusterlin_components
- * - ChunkLinearization and LinearizationChunking tests:
+ * - ChunkLinearization and ChunkLinearizationInfo tests:
  *   - clusterlin_chunking
- *   - clusterlin_linearization_chunking
  * - PostLinearize tests:
  *   - clusterlin_postlinearize
  *   - clusterlin_postlinearize_tree
  *   - clusterlin_postlinearize_moved_leaf
- * - MergeLinearization tests:
- *   - clusterlin_merge
  * - FixLinearization tests:
  *   - clusterlin_fix_linearization
  * - MakeConnected tests (a test-only function):
@@ -78,11 +68,8 @@ using namespace cluster_linearize;
 
 namespace {
 
-/** A simple finder class for candidate sets.
+/** A simple finder class for candidate sets (topologically-valid subsets with high feerate), only
- *
+ *  used by SimpleLinearize below. */
- * This class matches SearchCandidateFinder in interface and behavior, though with fewer
- * optimizations.
- */
 template<typename SetType>
 class SimpleCandidateFinder
 {
@@ -153,7 +140,8 @@ public:
 /** A very simple finder class for optimal candidate sets, which tries every subset.
  *
  * It is even simpler than SimpleCandidateFinder, and exists just to help test the correctness of
- * SimpleCandidateFinder, which is then used to test the correctness of SearchCandidateFinder.
+ * SimpleCandidateFinder, so that it can be used in SimpleLinearize, which is then used to test the
+ * correctness of Linearize.
  */
 template<typename SetType>
 class ExhaustiveCandidateFinder
@@ -204,8 +192,8 @@ public:
 /** A simple linearization algorithm.
  *
  * This matches Linearize() in interface and behavior, though with fewer optimizations, lacking
- * the ability to pass in an existing linearization, and using just SimpleCandidateFinder rather
+ * the ability to pass in an existing linearization, and linearizing by simply finding the
- * than AncestorCandidateFinder and SearchCandidateFinder.
+ * consecutive remaining highest-feerate topological subset using SimpleCandidateFinder.
  */
 template<typename SetType>
 std::pair<std::vector<DepGraphIndex>, bool> SimpleLinearize(const DepGraph<SetType>& depgraph, uint64_t max_iterations)
@@ -328,18 +316,24 @@ SetType ReadTopologicalSet(const DepGraph<SetType>& depgraph, const SetType& tod
 
 /** Given a dependency graph, construct any valid linearization for it, reading from a SpanReader. */
 template<typename BS>
-std::vector<DepGraphIndex> ReadLinearization(const DepGraph<BS>& depgraph, SpanReader& reader)
+std::vector<DepGraphIndex> ReadLinearization(const DepGraph<BS>& depgraph, SpanReader& reader, bool topological=true)
 {
     std::vector<DepGraphIndex> linearization;
     TestBitSet todo = depgraph.Positions();
-    // In every iteration one topologically-valid transaction is appended to linearization.
+    // In every iteration one transaction is appended to linearization.
     while (todo.Any()) {
-        // Compute the set of transactions with no not-yet-included ancestors.
+        // Compute the set of transactions to select from.
         TestBitSet potential_next;
-        for (auto j : todo) {
+        if (topological) {
-            if ((depgraph.Ancestors(j) & todo) == TestBitSet::Singleton(j)) {
+            // Find all transactions with no not-yet-included ancestors.
-                potential_next.Set(j);
+            for (auto j : todo) {
+                if ((depgraph.Ancestors(j) & todo) == TestBitSet::Singleton(j)) {
+                    potential_next.Set(j);
+                }
             }
+        } else {
+            // Allow any element to be selected next, regardless of topology.
+            potential_next = todo;
         }
         // There must always be one (otherwise there is a cycle in the graph).
         assert(potential_next.Any());
@@ -732,8 +726,16 @@ FUZZ_TARGET(clusterlin_chunking)
     // Read a valid linearization for depgraph.
     auto linearization = ReadLinearization(depgraph, reader);
 
-    // Invoke the chunking function.
+    // Invoke the chunking functions.
     auto chunking = ChunkLinearization(depgraph, linearization);
+    auto chunking_info = ChunkLinearizationInfo(depgraph, linearization);
+
+    // Verify consistency between the two functions.
+    assert(chunking.size() == chunking_info.size());
+    for (size_t i = 0; i < chunking.size(); ++i) {
+        assert(chunking[i] == chunking_info[i].feerate);
+        assert(SetInfo(depgraph, chunking_info[i].transactions) == chunking_info[i]);
+    }
 
     // Verify that chunk feerates are monotonically non-increasing.
     for (size_t i = 1; i < chunking.size(); ++i) {
@@ -742,7 +744,7 @@ FUZZ_TARGET(clusterlin_chunking)
 
     // Naively recompute the chunks (each is the highest-feerate prefix of what remains).
     auto todo = depgraph.Positions();
-    for (const auto& chunk_feerate : chunking) {
+    for (const auto& [chunk_set, chunk_feerate] : chunking_info) {
         assert(todo.Any());
         SetInfo<TestBitSet> accumulator, best;
         for (DepGraphIndex idx : linearization) {
@@ -754,74 +756,24 @@ FUZZ_TARGET(clusterlin_chunking)
             }
         }
         assert(chunk_feerate == best.feerate);
+        assert(chunk_set == best.transactions);
         assert(best.transactions.IsSubsetOf(todo));
         todo -= best.transactions;
     }
     assert(todo.None());
 }
 
-FUZZ_TARGET(clusterlin_ancestor_finder)
-{
-    // Verify that AncestorCandidateFinder works as expected.
-
-    // Retrieve a depgraph from the fuzz input.
-    SpanReader reader(buffer);
-    DepGraph<TestBitSet> depgraph;
-    try {
-        reader >> Using<DepGraphFormatter>(depgraph);
-    } catch (const std::ios_base::failure&) {}
-
-    AncestorCandidateFinder anc_finder(depgraph);
-    auto todo = depgraph.Positions();
-    while (todo.Any()) {
-        // Call the ancestor finder's FindCandidateSet for what remains of the graph.
-        assert(!anc_finder.AllDone());
-        assert(todo.Count() == anc_finder.NumRemaining());
-        auto best_anc = anc_finder.FindCandidateSet();
-        // Sanity check the result.
-        assert(best_anc.transactions.Any());
-        assert(best_anc.transactions.IsSubsetOf(todo));
-        assert(depgraph.FeeRate(best_anc.transactions) == best_anc.feerate);
-        assert(depgraph.IsConnected(best_anc.transactions));
-        // Check that it is topologically valid.
-        for (auto i : best_anc.transactions) {
-            assert((depgraph.Ancestors(i) & todo).IsSubsetOf(best_anc.transactions));
-        }
-
-        // Compute all remaining ancestor sets.
-        std::optional<SetInfo<TestBitSet>> real_best_anc;
-        for (auto i : todo) {
-            SetInfo info(depgraph, todo & depgraph.Ancestors(i));
-            if (!real_best_anc.has_value() || info.feerate > real_best_anc->feerate) {
-                real_best_anc = info;
-            }
-        }
-        // The set returned by anc_finder must equal the real best ancestor sets.
-        assert(real_best_anc.has_value());
-        assert(*real_best_anc == best_anc);
-
-        // Find a non-empty topologically valid subset of transactions to remove from the graph.
-        // Using an empty set would mean the next iteration is identical to the current one, and
-        // could cause an infinite loop.
-        auto del_set = ReadTopologicalSet(depgraph, todo, reader, /*non_empty=*/true);
-        todo -= del_set;
-        anc_finder.MarkDone(del_set);
-    }
-    assert(anc_finder.AllDone());
-    assert(anc_finder.NumRemaining() == 0);
-}
-
 static constexpr auto MAX_SIMPLE_ITERATIONS = 300000;
 
 FUZZ_TARGET(clusterlin_simple_finder)
 {
     // Verify that SimpleCandidateFinder works as expected by sanity checking the results
     // and comparing them (if claimed to be optimal) against the sets found by
-    // ExhaustiveCandidateFinder and AncestorCandidateFinder.
+    // ExhaustiveCandidateFinder.
     //
     // Note that SimpleCandidateFinder is only used in tests; the purpose of this fuzz test is to
-    // establish confidence in SimpleCandidateFinder, so that it can be used to test
+    // establish confidence in SimpleCandidateFinder, so that it can be used in SimpleLinearize,
-    // SearchCandidateFinder below.
+    // which is then used to test Linearize below.
 
     // Retrieve a depgraph from the fuzz input.
     SpanReader reader(buffer);
@@ -830,18 +782,15 @@ FUZZ_TARGET(clusterlin_simple_finder)
         reader >> Using<DepGraphFormatter>(depgraph);
     } catch (const std::ios_base::failure&) {}
 
-    // Instantiate the SimpleCandidateFinder to be tested, and the ExhaustiveCandidateFinder and
+    // Instantiate the SimpleCandidateFinder to be tested, and the ExhaustiveCandidateFinder it is
-    // AncestorCandidateFinder it is being tested against.
+    // being tested against.
     SimpleCandidateFinder smp_finder(depgraph);
     ExhaustiveCandidateFinder exh_finder(depgraph);
-    AncestorCandidateFinder anc_finder(depgraph);
 
     auto todo = depgraph.Positions();
     while (todo.Any()) {
         assert(!smp_finder.AllDone());
         assert(!exh_finder.AllDone());
-        assert(!anc_finder.AllDone());
-        assert(anc_finder.NumRemaining() == todo.Count());
 
         // Call SimpleCandidateFinder.
         auto [found, iterations_done] = smp_finder.FindCandidateSet(MAX_SIMPLE_ITERATIONS);
@@ -868,10 +817,6 @@ FUZZ_TARGET(clusterlin_simple_finder)
 
         // Perform further quality checks only if SimpleCandidateFinder claims an optimal result.
         if (optimal) {
-            // Compare with AncestorCandidateFinder.
-            auto anc = anc_finder.FindCandidateSet();
-            assert(anc.feerate <= found.feerate);
-
             if (todo.Count() <= 12) {
                 // Compare with ExhaustiveCandidateFinder. This quickly gets computationally
                 // expensive for large clusters (O(2^n)), so only do it for sufficiently small ones.
@@ -892,234 +837,10 @@ FUZZ_TARGET(clusterlin_simple_finder)
         todo -= del_set;
         smp_finder.MarkDone(del_set);
         exh_finder.MarkDone(del_set);
-        anc_finder.MarkDone(del_set);
     }
 
     assert(smp_finder.AllDone());
     assert(exh_finder.AllDone());
-    assert(anc_finder.AllDone());
-    assert(anc_finder.NumRemaining() == 0);
-}
-
-FUZZ_TARGET(clusterlin_search_finder)
-{
-    // Verify that SearchCandidateFinder works as expected by sanity checking the results
-    // and comparing with the results from SimpleCandidateFinder and AncestorCandidateFinder,
-    // if the result is claimed to be optimal.
-
-    // Retrieve an RNG seed, a depgraph, and whether to make it connected, from the fuzz input.
-    SpanReader reader(buffer);
-    DepGraph<TestBitSet> depgraph;
-    uint64_t rng_seed{0};
-    uint8_t make_connected{1};
-    try {
-        reader >> Using<DepGraphFormatter>(depgraph) >> rng_seed >> make_connected;
-    } catch (const std::ios_base::failure&) {}
-    // The most complicated graphs are connected ones (other ones just split up). Optionally force
-    // the graph to be connected.
-    if (make_connected) MakeConnected(depgraph);
-
-    // Instantiate the candidate finders.
-    SearchCandidateFinder src_finder(depgraph, rng_seed);
-    SimpleCandidateFinder smp_finder(depgraph);
-    AncestorCandidateFinder anc_finder(depgraph);
-
-    auto todo = depgraph.Positions();
-    while (todo.Any()) {
-        assert(!src_finder.AllDone());
-        assert(!smp_finder.AllDone());
-        assert(!anc_finder.AllDone());
-        assert(anc_finder.NumRemaining() == todo.Count());
-
-        // For each iteration, read an iteration count limit from the fuzz input.
-        uint64_t max_iterations = 1;
-        try {
-            reader >> VARINT(max_iterations);
-        } catch (const std::ios_base::failure&) {}
-        max_iterations &= 0xfffff;
-
-        // Read an initial subset from the fuzz input (allowed to be empty).
-        auto init_set = ReadTopologicalSet(depgraph, todo, reader, /*non_empty=*/false);
-        SetInfo init_best(depgraph, init_set);
-
-        // Call the search finder's FindCandidateSet for what remains of the graph.
-        auto [found, iterations_done] = src_finder.FindCandidateSet(max_iterations, init_best);
-        bool optimal = iterations_done < max_iterations;
-
-        // Sanity check the result.
-        assert(iterations_done <= max_iterations);
-        assert(found.transactions.Any());
-        assert(found.transactions.IsSubsetOf(todo));
-        assert(depgraph.FeeRate(found.transactions) == found.feerate);
-        if (!init_best.feerate.IsEmpty()) assert(found.feerate >= init_best.feerate);
-        // Check that it is topologically valid.
-        for (auto i : found.transactions) {
-            assert(found.transactions.IsSupersetOf(depgraph.Ancestors(i) & todo));
-        }
-
-        // At most 2^(N-1) iterations can be required: the maximum number of non-empty topological
-        // subsets a (connected) cluster with N transactions can have. Even when the cluster is no
-        // longer connected after removing certain transactions, this holds, because the connected
-        // components are searched separately.
-        assert(iterations_done <= (uint64_t{1} << (todo.Count() - 1)));
-        // Additionally, test that no more than sqrt(2^N)+1 iterations are required. This is just
-        // an empirical bound that seems to hold, without proof. Still, add a test for it so we
-        // can learn about counterexamples if they exist.
-        if (iterations_done >= 1 && todo.Count() <= 63) {
-            Assume((iterations_done - 1) * (iterations_done - 1) <= uint64_t{1} << todo.Count());
-        }
-
-        // Perform quality checks only if SearchCandidateFinder claims an optimal result.
-        if (optimal) {
-            // Optimal sets are always connected.
-            assert(depgraph.IsConnected(found.transactions));
-
-            // Compare with SimpleCandidateFinder.
-            auto [simple, simple_iters] = smp_finder.FindCandidateSet(MAX_SIMPLE_ITERATIONS);
-            assert(found.feerate >= simple.feerate);
-            if (simple_iters < MAX_SIMPLE_ITERATIONS) {
-                assert(found.feerate == simple.feerate);
-            }
-
-            // Compare with AncestorCandidateFinder;
-            auto anc = anc_finder.FindCandidateSet();
-            assert(found.feerate >= anc.feerate);
-
-            // Compare with a non-empty topological set read from the fuzz input (comparing with an
-            // empty set is not interesting).
-            auto read_topo = ReadTopologicalSet(depgraph, todo, reader, /*non_empty=*/true);
-            assert(found.feerate >= depgraph.FeeRate(read_topo));
-        }
-
-        // Find a non-empty topologically valid subset of transactions to remove from the graph.
-        // Using an empty set would mean the next iteration is identical to the current one, and
-        // could cause an infinite loop.
-        auto del_set = ReadTopologicalSet(depgraph, todo, reader, /*non_empty=*/true);
-        todo -= del_set;
-        src_finder.MarkDone(del_set);
-        smp_finder.MarkDone(del_set);
-        anc_finder.MarkDone(del_set);
-    }
-
-    assert(src_finder.AllDone());
-    assert(smp_finder.AllDone());
-    assert(anc_finder.AllDone());
-    assert(anc_finder.NumRemaining() == 0);
-}
-
-FUZZ_TARGET(clusterlin_linearization_chunking)
-{
-    // Verify the behavior of LinearizationChunking.
-
-    // Retrieve a depgraph from the fuzz input.
-    SpanReader reader(buffer);
-    DepGraph<TestBitSet> depgraph;
-    try {
-        reader >> Using<DepGraphFormatter>(depgraph);
-    } catch (const std::ios_base::failure&) {}
-
-    // Retrieve a topologically-valid subset of depgraph (allowed to be empty, because the argument
-    // to LinearizationChunking::Intersect is allowed to be empty).
-    auto todo = depgraph.Positions();
-    auto subset = SetInfo(depgraph, ReadTopologicalSet(depgraph, todo, reader, /*non_empty=*/false));
-
-    // Retrieve a valid linearization for depgraph.
-    auto linearization = ReadLinearization(depgraph, reader);
-
-    // Construct a LinearizationChunking object, initially for the whole linearization.
-    LinearizationChunking chunking(depgraph, linearization);
-
-    // Incrementally remove transactions from the chunking object, and check various properties at
-    // every step.
-    while (todo.Any()) {
-        assert(chunking.NumChunksLeft() > 0);
-
-        // Construct linearization with just todo.
-        std::vector<DepGraphIndex> linearization_left;
-        for (auto i : linearization) {
-            if (todo[i]) linearization_left.push_back(i);
-        }
-
-        // Compute the chunking for linearization_left.
-        auto chunking_left = ChunkLinearization(depgraph, linearization_left);
-
-        // Verify that it matches the feerates of the chunks of chunking.
-        assert(chunking.NumChunksLeft() == chunking_left.size());
-        for (DepGraphIndex i = 0; i < chunking.NumChunksLeft(); ++i) {
-            assert(chunking.GetChunk(i).feerate == chunking_left[i]);
-        }
-
-        // Check consistency of chunking.
-        TestBitSet combined;
-        for (DepGraphIndex i = 0; i < chunking.NumChunksLeft(); ++i) {
-            const auto& chunk_info = chunking.GetChunk(i);
-            // Chunks must be non-empty.
-            assert(chunk_info.transactions.Any());
-            // Chunk feerates must be monotonically non-increasing.
-            if (i > 0) assert(!(chunk_info.feerate >> chunking.GetChunk(i - 1).feerate));
-            // Chunks must be a subset of what is left of the linearization.
-            assert(chunk_info.transactions.IsSubsetOf(todo));
-            // Chunks' claimed feerates must match their transactions' aggregate feerate.
-            assert(depgraph.FeeRate(chunk_info.transactions) == chunk_info.feerate);
-            // Chunks must be the highest-feerate remaining prefix.
-            SetInfo<TestBitSet> accumulator, best;
-            for (auto j : linearization) {
-                if (todo[j] && !combined[j]) {
-                    accumulator.Set(depgraph, j);
-                    if (best.feerate.IsEmpty() || accumulator.feerate > best.feerate) {
-                        best = accumulator;
-                    }
-                }
-            }
-            assert(best.transactions == chunk_info.transactions);
-            assert(best.feerate == chunk_info.feerate);
-            // Chunks cannot overlap.
-            assert(!chunk_info.transactions.Overlaps(combined));
-            combined |= chunk_info.transactions;
-            // Chunks must be topological.
-            for (auto idx : chunk_info.transactions) {
-                assert((depgraph.Ancestors(idx) & todo).IsSubsetOf(combined));
-            }
-        }
-        assert(combined == todo);
-
-        // Verify the expected properties of LinearizationChunking::IntersectPrefixes:
-        auto intersect = chunking.IntersectPrefixes(subset);
-        // - Intersecting again doesn't change the result.
-        assert(chunking.IntersectPrefixes(intersect) == intersect);
-        // - The intersection is topological.
-        TestBitSet intersect_anc;
-        for (auto idx : intersect.transactions) {
-            intersect_anc |= (depgraph.Ancestors(idx) & todo);
-        }
-        assert(intersect.transactions == intersect_anc);
-        // - The claimed intersection feerate matches its transactions.
-        assert(intersect.feerate == depgraph.FeeRate(intersect.transactions));
-        // - The intersection may only be empty if its input is empty.
-        assert(intersect.transactions.Any() == subset.transactions.Any());
-        // - The intersection feerate must be as high as the input.
-        assert(intersect.feerate >= subset.feerate);
-        // - No non-empty intersection between the intersection and a prefix of the chunks of the
-        //   remainder of the linearization may be better than the intersection.
-        TestBitSet prefix;
-        for (DepGraphIndex i = 0; i < chunking.NumChunksLeft(); ++i) {
-            prefix |= chunking.GetChunk(i).transactions;
-            auto reintersect = SetInfo(depgraph, prefix & intersect.transactions);
-            if (!reintersect.feerate.IsEmpty()) {
-                assert(reintersect.feerate <= intersect.feerate);
-            }
-        }
-
-        // Find a non-empty topologically valid subset of transactions to remove from the graph.
-        // Using an empty set would mean the next iteration is identical to the current one, and
-        // could cause an infinite loop.
-        auto done = ReadTopologicalSet(depgraph, todo, reader, /*non_empty=*/true);
-        todo -= done;
-        chunking.MarkDone(done);
-        subset = SetInfo(depgraph, subset.transactions - done);
-    }
-
-    assert(chunking.NumChunksLeft() == 0);
 }
 
 FUZZ_TARGET(clusterlin_simple_linearize)
@@ -1169,6 +890,104 @@ FUZZ_TARGET(clusterlin_simple_linearize)
     }
 }
 
+FUZZ_TARGET(clusterlin_sfl)
+{
+    // Verify the individual steps of the SFL algorithm.
+
+    SpanReader reader(buffer);
+    DepGraph<TestBitSet> depgraph;
+    uint8_t flags{1};
+    uint64_t rng_seed{0};
+    try {
+        reader >> rng_seed >> flags >> Using<DepGraphFormatter>(depgraph);
+    } catch (const std::ios_base::failure&) {}
+    if (depgraph.TxCount() <= 1) return;
+    InsecureRandomContext rng(rng_seed);
+    /** Whether to make the depgraph connected. */
+    const bool make_connected = flags & 1;
+    /** Whether to load some input linearization into the state. */
+    const bool load_linearization = flags & 2;
+    /** Whether that input linearization is topological. */
+    const bool load_topological = load_linearization && (flags & 4);
+
+    // Initialize SFL state.
+    if (make_connected) MakeConnected(depgraph);
+    SpanningForestState sfl(depgraph, rng.rand64());
+
+    // Function to test the state.
+    std::vector<FeeFrac> last_diagram;
+    auto test_fn = [&](bool is_optimal = false) {
+        if (rng.randbits(4) == 0) {
+            // Perform sanity checks from time to time (too computationally expensive to do after
+            // every step).
+            sfl.SanityCheck(depgraph);
+        }
+        auto diagram = sfl.GetDiagram();
+        if (rng.randbits(4) == 0) {
+            // Verify that the diagram of GetLinearization() is at least as good as GetDiagram(),
+            // from time to time.
+            auto lin = sfl.GetLinearization();
+            auto lin_diagram = ChunkLinearization(depgraph, lin);
+            auto cmp_lin = CompareChunks(lin_diagram, diagram);
+            assert(cmp_lin >= 0);
+            // If we're in an allegedly optimal state, they must match.
+            if (is_optimal) assert(cmp_lin == 0);
+        }
+        // Verify that subsequent calls to GetDiagram() never get worse/incomparable.
+        if (!last_diagram.empty()) {
+            auto cmp = CompareChunks(diagram, last_diagram);
+            assert(cmp >= 0);
+        }
+        last_diagram = std::move(diagram);
+    };
+
+    if (load_linearization) {
+        auto input_lin = ReadLinearization(depgraph, reader, load_topological);
+        sfl.LoadLinearization(input_lin);
+        if (load_topological) {
+            // The diagram of the loaded linearization forms an initial lower bound on future
+            // diagrams.
+            last_diagram = ChunkLinearization(depgraph, input_lin);
+        } else {
+            // The input linearization may have been non-topological, so invoke MakeTopological to
+            // fix it still.
+            sfl.MakeTopological();
+        }
+    } else {
+        // Invoke MakeTopological to create an initial from-scratch topological state.
+        sfl.MakeTopological();
+    }
+
+    // Loop until optimal.
+    test_fn();
+    sfl.StartOptimizing();
+    while (true) {
+        test_fn();
+        if (!sfl.OptimizeStep()) break;
+    }
+    test_fn(/*is_optimal=*/true);
+
+    // Verify that optimality is reached within an expected amount of work. This protects against
+    // hypothetical bugs that hugely increase the amount of work needed to reach optimality.
+    assert(sfl.GetCost() <= MaxOptimalLinearizationIters(depgraph.TxCount()));
+
+    // The result must be as good as SimpleLinearize.
+    auto [simple_linearization, simple_optimal] = SimpleLinearize(depgraph, MAX_SIMPLE_ITERATIONS / 10);
+    auto simple_diagram = ChunkLinearization(depgraph, simple_linearization);
+    auto simple_cmp = CompareChunks(last_diagram, simple_diagram);
+    assert(simple_cmp >= 0);
+    if (simple_optimal) assert(simple_cmp == 0);
+
+    // We can compare with any arbitrary linearization, and the diagram must be at least as good as
+    // each.
+    for (int i = 0; i < 10; ++i) {
+        auto read_lin = ReadLinearization(depgraph, reader);
+        auto read_diagram = ChunkLinearization(depgraph, read_lin);
+        auto cmp = CompareChunks(last_diagram, read_diagram);
+        assert(cmp >= 0);
+    }
+}
+
 FUZZ_TARGET(clusterlin_linearize)
 {
     // Verify the behavior of Linearize().
@@ -1203,7 +1022,6 @@ FUZZ_TARGET(clusterlin_linearize)
     // Invoke Linearize().
     iter_count &= 0x7ffff;
     auto [linearization, optimal, cost] = Linearize(depgraph, iter_count, rng_seed, old_linearization);
-    assert(cost <= iter_count);
     SanityCheck(depgraph, linearization);
     auto chunking = ChunkLinearization(depgraph, linearization);
 
@@ -1215,7 +1033,7 @@ FUZZ_TARGET(clusterlin_linearize)
     }
 
     // If the iteration count is sufficiently high, an optimal linearization must be found.
-    if (iter_count >= MaxOptimalLinearizationIters(depgraph.TxCount())) {
+    if (iter_count > MaxOptimalLinearizationIters(depgraph.TxCount())) {
         assert(optimal);
     }
 
@@ -1230,9 +1048,13 @@ FUZZ_TARGET(clusterlin_linearize)
         // If SimpleLinearize finds the optimal result too, they must be equal (if not,
         // SimpleLinearize is broken).
         if (simple_optimal) assert(cmp == 0);
-        // If simple_chunking is diagram-optimal, it cannot have more chunks than chunking (as
+
-        // chunking is claimed to be optimal, which implies minimal chunks).
+        // Temporarily disabled, as Linearize() currently does not guarantee minimal chunks, even
-        if (cmp == 0) assert(chunking.size() >= simple_chunking.size());
+        // when it reports an optimal result. This will be re-introduced in a later commit.
+        //
+        // // If simple_chunking is diagram-optimal, it cannot have more chunks than chunking (as
+        // // chunking is claimed to be optimal, which implies minimal chunks).
+        // if (cmp == 0) assert(chunking.size() >= simple_chunking.size());
 
         // Compare with a linearization read from the fuzz input.
         auto read = ReadLinearization(depgraph, reader);
@@ -1278,10 +1100,9 @@ FUZZ_TARGET(clusterlin_postlinearize)
     assert(cmp >= 0);
 
     // The chunks that come out of postlinearizing are always connected.
-    LinearizationChunking linchunking(depgraph, post_linearization);
+    auto linchunking = ChunkLinearizationInfo(depgraph, post_linearization);
-    while (linchunking.NumChunksLeft()) {
+    for (const auto& [chunk_set, _chunk_feerate] : linchunking) {
-        assert(depgraph.IsConnected(linchunking.GetChunk(0).transactions));
+        assert(depgraph.IsConnected(chunk_set));
-        linchunking.MarkDone(linchunking.GetChunk(0).transactions);
     }
 }
 
@@ -1377,32 +1198,6 @@ FUZZ_TARGET(clusterlin_postlinearize_moved_leaf)
     assert(cmp >= 0);
 }
 
-FUZZ_TARGET(clusterlin_merge)
-{
-    // Construct an arbitrary graph from the fuzz input.
-    SpanReader reader(buffer);
-    DepGraph<TestBitSet> depgraph;
-    try {
-        reader >> Using<DepGraphFormatter>(depgraph);
-    } catch (const std::ios_base::failure&) {}
-
-    // Retrieve two linearizations from the fuzz input.
-    auto lin1 = ReadLinearization(depgraph, reader);
-    auto lin2 = ReadLinearization(depgraph, reader);
-
-    // Merge the two.
-    auto lin_merged = MergeLinearizations(depgraph, lin1, lin2);
-
-    // Compute chunkings and compare.
-    auto chunking1 = ChunkLinearization(depgraph, lin1);
-    auto chunking2 = ChunkLinearization(depgraph, lin2);
-    auto chunking_merged = ChunkLinearization(depgraph, lin_merged);
-    auto cmp1 = CompareChunks(chunking_merged, chunking1);
-    assert(cmp1 >= 0);
-    auto cmp2 = CompareChunks(chunking_merged, chunking2);
-    assert(cmp2 >= 0);
-}
-
 FUZZ_TARGET(clusterlin_fix_linearization)
 {
     // Verify expected properties of FixLinearization() on arbitrary linearizations.
@@ -1415,33 +1210,14 @@ FUZZ_TARGET(clusterlin_fix_linearization)
     } catch (const std::ios_base::failure&) {}
 
     // Construct an arbitrary linearization (not necessarily topological for depgraph).
-    std::vector<DepGraphIndex> linearization;
+    std::vector<DepGraphIndex> linearization = ReadLinearization(depgraph, reader, /*topological=*/false);
-    /** Which transactions of depgraph are yet to be included in linearization. */
-    TestBitSet todo = depgraph.Positions();
-    while (todo.Any()) {
-        // Read a number from the fuzz input in range [0, todo.Count()).
-        uint64_t val{0};
-        try {
-            reader >> VARINT(val);
-        } catch (const std::ios_base::failure&) {}
-        val %= todo.Count();
-        // Find the val'th element in todo, remove it from todo, and append it to linearization.
-        for (auto idx : todo) {
-            if (val == 0) {
-                linearization.push_back(idx);
-                todo.Reset(idx);
-                break;
-            }
-            --val;
-        }
-    }
     assert(linearization.size() == depgraph.TxCount());
 
     // Determine what prefix of linearization is topological, i.e., the position of the first entry
     // in linearization which corresponds to a transaction that is not preceded by all its
     // ancestors.
     size_t topo_prefix = 0;
-    todo = depgraph.Positions();
+    auto todo = depgraph.Positions();
     while (topo_prefix < linearization.size()) {
         DepGraphIndex idx = linearization[topo_prefix];
         todo.Reset(idx);

src/test/fuzz/txgraph.cpp

@@ -1230,10 +1230,9 @@ FUZZ_TARGET(txgraph)
                     // Construct a chunking object for the simulated graph, using the reported cluster
                     // linearization as ordering, and compare it against the reported chunk feerates.
                     if (sims.size() == 1 || level == TxGraph::Level::MAIN) {
-                        cluster_linearize::LinearizationChunking simlinchunk(sim.graph, simlin);
+                        auto simlinchunk = ChunkLinearizationInfo(sim.graph, simlin);
                         DepGraphIndex idx{0};
-                        for (unsigned chunknum = 0; chunknum < simlinchunk.NumChunksLeft(); ++chunknum) {
+                        for (auto& chunk : simlinchunk) {
-                            auto chunk = simlinchunk.GetChunk(chunknum);
                             // Require that the chunks of cluster linearizations are connected (this must
                             // be the case as all linearizations inside are PostLinearized).
                             assert(sim.graph.IsConnected(chunk.transactions));

src/test/util/cluster_linearize.h

@@ -331,7 +331,7 @@ void SanityCheck(const DepGraph<SetType>& depgraph)
         VectorWriter writer(ser, 0);
         writer << Using<DepGraphFormatter>(depgraph);
         SpanReader reader(ser);
-        DepGraph<TestBitSet> decoded_depgraph;
+        DepGraph<SetType> decoded_depgraph;
         reader >> Using<DepGraphFormatter>(decoded_depgraph);
         assert(depgraph == decoded_depgraph);
         assert(reader.empty());
@@ -384,37 +384,36 @@ void SanityCheck(const DepGraph<SetType>& depgraph, std::span<const DepGraphInde
 {
     // Check completeness.
     assert(linearization.size() == depgraph.TxCount());
-    TestBitSet done;
+    SetType done;
     for (auto i : linearization) {
         // Check transaction position is in range.
         assert(depgraph.Positions()[i]);
         // Check topology and lack of duplicates.
-        assert((depgraph.Ancestors(i) - done) == TestBitSet::Singleton(i));
+        assert((depgraph.Ancestors(i) - done) == SetType::Singleton(i));
         done.Set(i);
     }
 }
 
 inline uint64_t MaxOptimalLinearizationIters(DepGraphIndex cluster_count)
 {
-    // We assume sqrt(2^k)+1 candidate-finding iterations per candidate to be found, plus ceil(k/4)
+    // These are the largest numbers seen returned as cost by Linearize(), in a large randomized
-    // startup cost when up to k unlinearization transactions remain, plus ceil(n^2/64) overall
+    // trial. There exist almost certainly far worse cases, but they are unlikely to be
-    // startup cost in Linearize. Thus, we can compute the upper bound for a whole linearization
+    // encountered in randomized tests. The purpose of these numbers is guaranteeing that for
-    // (summing for k=1..n) using the Python expression:
+    // *some* reasonable cost bound, optimal linearizations are always found.
-    //
+    static constexpr uint64_t ITERS[65] = {
-    //   [sum((k+3)//4 + math.isqrt(2**k) + 1 for k in range(1, n + 1)) + (n**2 + 63) // 64 for n in range(0, 65)]
+        0,
-    //
+        0, 2, 8, 21, 51, 96, 162, 200,
-    // Note that these are just assumptions, as the proven upper bound grows with 2^k, not
+        273, 323, 413, 506, 602, 788, 883, 948,
-    // sqrt(2^k).
+        1153, 1187, 1367, 1619, 1854, 2271, 2257, 2707,
-    static constexpr uint64_t MAX_OPTIMAL_ITERS[65] = {
+        2904, 3275, 3342, 4209, 4648, 4146, 4273, 4905,
-        0, 4, 8, 12, 18, 26, 37, 51, 70, 97, 133, 182, 251, 346, 480, 666, 927, 1296, 1815, 2545,
+        5358, 5767, 5977, 6777, 7812, 7689, 8478, 8425,
-        3576, 5031, 7087, 9991, 14094, 19895, 28096, 39690, 56083, 79263, 112041, 158391, 223936,
+        9561, 11765, 10743, 11806, 12812, 12838, 15421, 16778,
-        316629, 447712, 633086, 895241, 1265980, 1790280, 2531747, 3580335, 5063259, 7160424,
+        16661, 19393, 17995, 23947, 23314, 24564, 26209, 29267,
-        10126257, 14320575, 20252230, 28640853, 40504150, 57281380, 81007962, 114562410, 162015557,
+        24719, 31065, 31794, 29185, 32465, 35432, 39986, 36865
-        229124437, 324030718, 458248463, 648061011, 916496483, 1296121563, 1832992493, 2592242635,
-        3665984477, 5184484745, 7331968412, 10368968930, 14663936244
     };
-    assert(cluster_count < sizeof(MAX_OPTIMAL_ITERS) / sizeof(MAX_OPTIMAL_ITERS[0]));
+    assert(cluster_count < std::size(ITERS));
-    return MAX_OPTIMAL_ITERS[cluster_count];
+    // Multiply the table number by two, to account for the fact that they are not absolutes.
+    return ITERS[cluster_count] * 2;
 }
 
 } // namespace

src/txgraph.cpp

@@ -1013,11 +1013,11 @@ void GenericClusterImpl::Updated(TxGraphImpl& graph, int level) noexcept
     // ACCEPTABLE, so it is pointless to compute these if we haven't reached that quality level
     // yet.
     if (level == 0 && IsAcceptable()) {
-        const LinearizationChunking chunking(m_depgraph, m_linearization);
+        auto chunking = ChunkLinearizationInfo(m_depgraph, m_linearization);
         LinearizationIndex lin_idx{0};
         // Iterate over the chunks.
-        for (unsigned chunk_idx = 0; chunk_idx < chunking.NumChunksLeft(); ++chunk_idx) {
+        for (unsigned chunk_idx = 0; chunk_idx < chunking.size(); ++chunk_idx) {
-            auto chunk = chunking.GetChunk(chunk_idx);
+            auto& chunk = chunking[chunk_idx];
             auto chunk_count = chunk.transactions.Count();
             Assume(chunk_count > 0);
             // Iterate over the transactions in the linearization, which must match those in chunk.
@@ -1031,7 +1031,7 @@ void GenericClusterImpl::Updated(TxGraphImpl& graph, int level) noexcept
                 chunk.transactions.Reset(idx);
                 if (chunk.transactions.None()) {
                     // Last transaction in the chunk.
-                    if (chunk_count == 1 && chunk_idx + 1 == chunking.NumChunksLeft()) {
+                    if (chunk_count == 1 && chunk_idx + 1 == chunking.size()) {
                         // If this is the final chunk of the cluster, and it contains just a single
                         // transaction (which will always be true for the very common singleton
                         // clusters), store the special value -1 as chunk count.
@@ -1311,13 +1311,12 @@ void SingletonClusterImpl::AppendChunkFeerates(std::vector<FeeFrac>& ret) const
 
 uint64_t GenericClusterImpl::AppendTrimData(std::vector<TrimTxData>& ret, std::vector<std::pair<GraphIndex, GraphIndex>>& deps) const noexcept
 {
-    const LinearizationChunking linchunking(m_depgraph, m_linearization);
+    auto linchunking = ChunkLinearizationInfo(m_depgraph, m_linearization);
     LinearizationIndex pos{0};
     uint64_t size{0};
     auto prev_index = GraphIndex(-1);
     // Iterate over the chunks of this cluster's linearization.
-    for (unsigned i = 0; i < linchunking.NumChunksLeft(); ++i) {
+    for (const auto& [chunk, chunk_feerate] : linchunking) {
-        const auto& [chunk, chunk_feerate] = linchunking.GetChunk(i);
         // Iterate over the transactions of that chunk, in linearization order.
         auto chunk_tx_count = chunk.Count();
         for (unsigned j = 0; j < chunk_tx_count; ++j) {
@@ -2091,9 +2090,10 @@ std::pair<uint64_t, bool> GenericClusterImpl::Relinearize(TxGraphImpl& graph, in
     // Invoke the actual linearization algorithm (passing in the existing one).
     uint64_t rng_seed = graph.m_rng.rand64();
     auto [linearization, optimal, cost] = Linearize(m_depgraph, max_iters, rng_seed, m_linearization);
-    // Postlinearize if the result isn't optimal already. This guarantees (among other things)
+    // Postlinearize to undo some of the non-determinism caused by randomizing the linearization.
-    // that the chunks of the resulting linearization are all connected.
+    // This also guarantees that all chunks are connected (which is not guaranteed by SFL
-    if (!optimal) PostLinearize(m_depgraph, linearization);
+    // currently, even when optimal).
+    PostLinearize(m_depgraph, linearization);
     // Update the linearization.
     m_linearization = std::move(linearization);
     // Update the Cluster's quality.
@@ -2758,7 +2758,8 @@ void GenericClusterImpl::SanityCheck(const TxGraphImpl& graph, int level) const
     }
 
     // Compute the chunking of m_linearization.
-    LinearizationChunking linchunking(m_depgraph, m_linearization);
+    auto linchunking = ChunkLinearizationInfo(m_depgraph, m_linearization);
+    unsigned chunk_num{0};
 
     // Verify m_linearization.
     SetType m_done;
@@ -2778,14 +2779,14 @@ void GenericClusterImpl::SanityCheck(const TxGraphImpl& graph, int level) const
         if (level == 0 && IsAcceptable()) {
             assert(entry.m_main_lin_index == linindex);
             ++linindex;
-            if (!linchunking.GetChunk(0).transactions[lin_pos]) {
+            if (!linchunking[chunk_num].transactions[lin_pos]) {
-                linchunking.MarkDone(linchunking.GetChunk(0).transactions);
+                ++chunk_num;
                 chunk_pos = 0;
             }
-            assert(entry.m_main_chunk_feerate == linchunking.GetChunk(0).feerate);
+            assert(entry.m_main_chunk_feerate == linchunking[chunk_num].feerate);
             // Verify that an entry in the chunk index exists for every chunk-ending transaction.
             ++chunk_pos;
-            bool is_chunk_end = (chunk_pos == linchunking.GetChunk(0).transactions.Count());
+            bool is_chunk_end = (chunk_pos == linchunking[chunk_num].transactions.Count());
             assert((entry.m_main_chunkindex_iterator != graph.m_main_chunkindex.end()) == is_chunk_end);
             if (is_chunk_end) {
                 auto& chunk_data = *entry.m_main_chunkindex_iterator;
@@ -2796,7 +2797,7 @@ void GenericClusterImpl::SanityCheck(const TxGraphImpl& graph, int level) const
                 }
             }
             // If this Cluster has an acceptable quality level, its chunks must be connected.
-            assert(m_depgraph.IsConnected(linchunking.GetChunk(0).transactions));
+            assert(m_depgraph.IsConnected(linchunking[chunk_num].transactions));
         }
     }
     // Verify that each element of m_depgraph occurred in m_linearization.

test/functional/mempool_packages.py

@@ -239,8 +239,9 @@ class MempoolPackagesTest(BitcoinTestFramework):
         self.generate(self.nodes[0], 1)
         self.trigger_reorg(fork_blocks, self.nodes[0])
 
-        # Check if the txs are returned to the mempool
+        # Check if the txs are returned to the mempool (though the transaction ordering may
-        assert_equal(self.nodes[0].getrawmempool(), mempool0)
+        # change as it is non-deterministic).
+        assert_equal(set(self.nodes[0].getrawmempool()), set(mempool0))
 
         # Clean-up the mempool
         self.generate(self.nodes[0], 1)