private boolean edgesCompatible(int edge1, int edge2) {
E e1 = edgeList1.get(edge1);
E e2 = edgeList2.get(edge2);
boolean result = false;
// edge label must be the same
if (e1.getLabel().equals(e2.getLabel())) {
// check connecting vertex labels
L v1SourceLbl = g1.getEdgeSource(e1).getLabel(),
v1TargetLbl = g1.getEdgeTarget(e1).getLabel(),
v2SourceLbl = g2.getEdgeSource(e2).getLabel(),
v2TargetLbl = g2.getEdgeTarget(e2).getLabel();
// checks if the pair of source vertices have the same label, and checks the same for the
// target vertices
boolean sourceTargetMatch =
v1SourceLbl.equals(v2SourceLbl) && v1TargetLbl.equals(v2TargetLbl);
if (directed) {
result = sourceTargetMatch;
} else {
// checks if source1,target2 have the same label and if target1,source2 have the same label
boolean sourceTargetInverseMatch =
v1SourceLbl.equals(v2TargetLbl) && v1TargetLbl.equals(v2SourceLbl);
result = (sourceTargetMatch || sourceTargetInverseMatch);
}
}
return result;
}
private void init(Graph<V, E> g, Set<V> vertexSet, Set<E> edgeSet) {
// create a map between vertex value to its order(1st,2nd,etc)
// "CAT"=1 "DOG"=2 "RHINO"=3
this.mapVertexToOrder = new HashMap<V, Integer>(vertexSet.size());
int counter = 0;
for (V vertex : vertexSet) {
mapVertexToOrder.put(vertex, new Integer(counter));
counter++;
}
// create a friendlier representation of an edge
// by order, like 2nd->3rd instead of B->A
// use the map to convert vertex to order
// on directed graph, edge A->B must be (A,B)
// on undirected graph, edge A-B can be (A,B) or (B,A)
this.labelsEdgesSet = new HashSet<LabelsEdge>(edgeSet.size());
for (E edge : edgeSet) {
V sourceVertex = g.getEdgeSource(edge);
Integer sourceOrder = mapVertexToOrder.get(sourceVertex);
int sourceLabel = sourceOrder.intValue();
int targetLabel = (mapVertexToOrder.get(g.getEdgeTarget(edge))).intValue();
LabelsEdge lablesEdge = new LabelsEdge(sourceLabel, targetLabel);
this.labelsEdgesSet.add(lablesEdge);
if (g instanceof UndirectedGraph<?, ?>) {
LabelsEdge oppositeEdge = new LabelsEdge(targetLabel, sourceLabel);
this.labelsEdgesSet.add(oppositeEdge);
}
}
}
/**
* @param vertexNumber the number which identifies the vertex v in this order.
* @return the identifying numbers of all vertices which are connected to v by an edge incoming to
* v.
*/
public int[] getInEdges(int vertexNumber) {
if (cacheEdges && (incomingEdges[vertexNumber] != null)) {
return incomingEdges[vertexNumber];
}
V v = getVertex(vertexNumber);
Set<E> edgeSet;
if (graph instanceof DirectedGraph<?, ?>) {
edgeSet = ((DirectedGraph<V, E>) graph).incomingEdgesOf(v);
} else {
edgeSet = graph.edgesOf(v);
}
int[] vertexArray = new int[edgeSet.size()];
int i = 0;
for (E edge : edgeSet) {
V source = graph.getEdgeSource(edge), target = graph.getEdgeTarget(edge);
vertexArray[i++] = mapVertexToOrder.get(source.equals(v) ? target : source);
}
if (cacheEdges) {
incomingEdges[vertexNumber] = vertexArray;
}
return vertexArray;
}
@Override
public TraversalGraph<V, E> reconstructTraversalGraph() {
if (currentStartNode == null) {
throw new IllegalStateException(
"You must call #calculate before " + "reconstructing the traversal graph.");
}
TraversalGraph<V, E> traversalGraph =
new TraversalGraph<V, E>(graph.getEdgeFactory(), currentStartNode);
for (V v : graph.vertexSet()) {
Set<E> predEdges = (Set<E>) v.getPredecessorEdges();
for (E e : predEdges) {
V source = graph.getEdgeSource(e);
V target = graph.getEdgeTarget(e);
traversalGraph.addVertex(source);
traversalGraph.addVertex(target);
if (v.equals(source)) {
traversalGraph.addEdge(target, source).setBaseGraphEdge(e);
} else if (v.equals(target)) {
traversalGraph.addEdge(source, target).setBaseGraphEdge(e);
} else {
throw new IllegalStateException(
"A vertex has a predecessor " + "edge not ending on itself.");
}
}
}
return traversalGraph;
}
public int[] getEdgeNumbers(E e) {
V v1 = graph.getEdgeSource(e), v2 = graph.getEdgeTarget(e);
int[] edge = new int[2];
edge[0] = mapVertexToOrder.get(v1);
edge[1] = mapVertexToOrder.get(v2);
return edge;
}
/**
* Compute all vertices that have positive degree by iterating over the edges on purpose. This
* keeps the complexity to O(m) where m is the number of edges.
*
* @param graph the graph
* @return set of vertices with positive degree
*/
private Set<V> initVisibleVertices(Graph<V, E> graph) {
Set<V> visibleVertex = new HashSet<>();
for (E e : graph.edgeSet()) {
V s = graph.getEdgeSource(e);
V t = graph.getEdgeTarget(e);
if (!s.equals(t)) {
visibleVertex.add(s);
visibleVertex.add(t);
}
}
return visibleVertex;
}
/** Calculates the matrix of all shortest paths, but does not populate the paths map. */
private void lazyCalculateMatrix() {
if (d != null) {
// already done
return;
}
int n = vertices.size();
// init the backtrace matrix
backtrace = new int[n][n];
for (int i = 0; i < n; i++) {
Arrays.fill(backtrace[i], -1);
}
// initialize matrix, 0
d = new double[n][n];
for (int i = 0; i < n; i++) {
Arrays.fill(d[i], Double.POSITIVE_INFINITY);
}
// initialize matrix, 1
for (int i = 0; i < n; i++) {
d[i][i] = 0.0;
}
// initialize matrix, 2
Set<E> edges = graph.edgeSet();
for (E edge : edges) {
V v1 = graph.getEdgeSource(edge);
V v2 = graph.getEdgeTarget(edge);
int v_1 = vertices.indexOf(v1);
int v_2 = vertices.indexOf(v2);
d[v_1][v_2] = graph.getEdgeWeight(edge);
if (!(graph instanceof DirectedGraph<?, ?>)) {
d[v_2][v_1] = graph.getEdgeWeight(edge);
}
}
// run fw alg
for (int k = 0; k < n; k++) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
double ik_kj = d[i][k] + d[k][j];
if (ik_kj < d[i][j]) {
d[i][j] = ik_kj;
backtrace[i][j] = k;
}
}
}
}
}
public long countExternalEdges(Integer i, Set<DefaultWeightedEdge> neighborSet) {
int numberExternalEdges = 0;
// count number of external edges
for (DefaultWeightedEdge edge : neighborSet) {
// no easy way to get 'other' out of JGraph's undirected graph edge traversal... ugh!
Integer src = graph.getEdgeSource(edge);
Integer dst = graph.getEdgeTarget(edge);
Integer other = src.equals(i) ? dst : src;
if (contains(other)) {
numberExternalEdges -= 1;
} else {
numberExternalEdges += 1;
}
}
return numberExternalEdges;
}
V getEdgeTarget(E e) {
return graph.getEdgeTarget(e);
}
// the algorithm (improved with additional heuristics)
private Pair<Double, Set<E>> runWithHeuristics(Graph<V, E> graph) {
// lookup all relevant vertices
Set<V> visibleVertex = initVisibleVertices(graph);
// create solver for paths
DynamicProgrammingPathSolver pathSolver = new DynamicProgrammingPathSolver();
Set<E> matching = new HashSet<>();
double matchingWeight = 0d;
Set<V> matchedVertices = new HashSet<>();
// run algorithm
while (!visibleVertex.isEmpty()) {
// find vertex arbitrarily
V x = visibleVertex.stream().findAny().get();
// grow path from x
LinkedList<E> path = new LinkedList<>();
while (x != null) {
// first heaviest edge incident to vertex x (among visible neighbors)
double maxWeight = 0d;
E maxWeightedEdge = null;
V maxWeightedNeighbor = null;
for (E e : graph.edgesOf(x)) {
V other = Graphs.getOppositeVertex(graph, e, x);
if (visibleVertex.contains(other) && !other.equals(x)) {
double curWeight = graph.getEdgeWeight(e);
if (comparator.compare(curWeight, 0d) > 0
&& (maxWeightedEdge == null || comparator.compare(curWeight, maxWeight) > 0)) {
maxWeight = curWeight;
maxWeightedEdge = e;
maxWeightedNeighbor = other;
}
}
}
// add edge to path and remove x
if (maxWeightedEdge != null) {
path.add(maxWeightedEdge);
}
visibleVertex.remove(x);
// go to next vertex
x = maxWeightedNeighbor;
}
// find maximum weight matching of path using dynamic programming
Pair<Double, Set<E>> pathMatching = pathSolver.getMaximumWeightMatching(graph, path);
// add it to result while keeping track of matched vertices
matchingWeight += pathMatching.getFirst();
for (E e : pathMatching.getSecond()) {
V s = graph.getEdgeSource(e);
V t = graph.getEdgeTarget(e);
if (!matchedVertices.add(s)) {
throw new RuntimeException("Set is not a valid matching, please submit a bug report");
}
if (!matchedVertices.add(t)) {
throw new RuntimeException("Set is not a valid matching, please submit a bug report");
}
matching.add(e);
}
}
// extend matching to maximal cardinality (out of edges with positive weight)
for (E e : graph.edgeSet()) {
double edgeWeight = graph.getEdgeWeight(e);
if (comparator.compare(edgeWeight, 0d) <= 0) {
// ignore zero or negative weight
continue;
}
V s = graph.getEdgeSource(e);
if (matchedVertices.contains(s)) {
// matched vertex, ignore
continue;
}
V t = graph.getEdgeTarget(e);
if (matchedVertices.contains(t)) {
// matched vertex, ignore
continue;
}
// add edge to matching
matching.add(e);
matchingWeight += edgeWeight;
}
// return extended matching
return Pair.of(matchingWeight, matching);
}
/**
* @param connectedOnly if true, the result will be a connected graph
* @return
*/
public Graph<V, E> toGraph() {
if (subgraph != null) return subgraph;
if (directed) {
subgraph = new DirectedMultigraph<V, E>(g2.getEdgeFactory());
} else {
subgraph = new Multigraph<V, E>(g2.getEdgeFactory());
}
E edge;
V source;
V target;
for (int x = 0; x < dimx; x++) {
for (int y = 0; y < dimy; y++) {
if (matrix[x][y]) {
edge = edgeList2.get(y);
source = g2.getEdgeSource(edge);
target = g2.getEdgeTarget(edge);
if (mappedVerticesFromG2.contains(source) && mappedVerticesFromG2.contains(target)) {
// make sure the source and target vertices have been added, then add the edge
subgraph.addVertex(source);
subgraph.addVertex(target);
subgraph.addEdge(source, target, edge);
}
}
}
}
if (connectedOnly) {
// make sure this subgraph is connected, if it is not return the largest connected part
List<Set<V>> connectedVertices = new ArrayList<Set<V>>();
for (V v : subgraph.vertexSet()) {
if (!SharedStaticMethods.containsV(connectedVertices, v)) {
connectedVertices.add(SharedStaticMethods.getConnectedVertices(subgraph, v));
}
}
// ConnectedVertices now contains Sets of connected vertices every vertex of the subgraph is
// contained exactly once in the list
// if there is more then 1 set, then this method should return the largest connected part of
// the graph
if (connectedVertices.size() > 1) {
Graph<V, E> largestResult = null;
Graph<V, E> currentGraph;
int largestSize = -1;
Set<V> currentSet;
for (int i = 0; i < connectedVertices.size(); i++) {
currentSet = connectedVertices.get(i);
/*note that 'subgraph' is the result from the Mcgregor algorithm, 'currentGraph' is an
* induced subgraph of 'subgraph'. 'currentGraph' is connected, because the vertices in
* 'currentSet' are connected with edges in 'subgraph'
*/
currentGraph = new Subgraph<V, E, Graph<V, E>>(subgraph, currentSet);
if (currentGraph.edgeSet().size() > largestSize) {
largestResult = currentGraph;
}
}
return largestResult;
}
}
return subgraph;
}