lnrpc+autopilot: add graph diameter calculation

* adds a brute force computation of the diameter
* adds a more efficient calculation of the diameter

autopilot/simple_graph_test.go

@@ -0,0 +1,94 @@
+package autopilot
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	testShortestPathLengths = map[int]uint32{
+		0: 0,
+		1: 1,
+		2: 1,
+		3: 1,
+		4: 2,
+		5: 2,
+		6: 3,
+		7: 3,
+		8: 4,
+	}
+	testNodeEccentricities = map[int]uint32{
+		0: 4,
+		1: 5,
+		2: 4,
+		3: 3,
+		4: 3,
+		5: 3,
+		6: 4,
+		7: 4,
+		8: 5,
+	}
+)
+
+// NewTestSimpleGraph is a helper that generates a SimpleGraph from a test
+// graph description.
+// Assumes that the graph description is internally consistent, i.e. edges are
+// not repeatedly defined.
+func NewTestSimpleGraph(graph testGraphDesc) SimpleGraph {
+	// We convert the test graph description into an adjacency list.
+	adjList := make([][]int, graph.nodes)
+	for node, neighbors := range graph.edges {
+		for _, neighbor := range neighbors {
+			adjList[node] = append(adjList[node], neighbor)
+			adjList[neighbor] = append(adjList[neighbor], node)
+		}
+	}
+
+	return SimpleGraph{Adj: adjList}
+}
+
+func TestShortestPathLengths(t *testing.T) {
+	simpleGraph := NewTestSimpleGraph(centralityTestGraph)
+
+	// Test the shortest path lengths from node 0 to all other nodes.
+	shortestPathLengths := simpleGraph.shortestPathLengths(0)
+	require.Equal(t, shortestPathLengths, testShortestPathLengths)
+}
+
+func TestEccentricities(t *testing.T) {
+	simpleGraph := NewTestSimpleGraph(centralityTestGraph)
+
+	// Test the node eccentricities for all nodes.
+	nodes := make([]int, len(simpleGraph.Adj))
+	for a := range nodes {
+		nodes[a] = a
+	}
+	nodeEccentricities := simpleGraph.nodeEccentricities(nodes)
+	require.Equal(t, nodeEccentricities, testNodeEccentricities)
+}
+
+func TestDiameterExact(t *testing.T) {
+	simpleGraph := NewTestSimpleGraph(centralityTestGraph)
+
+	// Test the diameter in a brute-force manner.
+	diameter := simpleGraph.Diameter()
+	require.Equal(t, uint32(5), diameter)
+}
+
+func TestDiameterCutoff(t *testing.T) {
+	simpleGraph := NewTestSimpleGraph(centralityTestGraph)
+
+	// Test the diameter by cutting out the inside of the graph.
+	diameter := simpleGraph.DiameterRadialCutoff()
+	require.Equal(t, uint32(5), diameter)
+}
+
+func BenchmarkShortestPathOpt(b *testing.B) {
+	// TODO: a method that generates a huge graph is needed
+	simpleGraph := NewTestSimpleGraph(centralityTestGraph)
+
+	for n := 0; n < b.N; n++ {
+		_ = simpleGraph.shortestPathLengths(0)
+	}
+}