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;
}
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;
}
private void markPath(V v, V child, V stem, Set<V> blossom) {
while (!contracted.get(v).equals(stem)) {
blossom.add(contracted.get(v));
blossom.add(contracted.get(match.get(v)));
path.put(v, child);
child = match.get(v);
v = path.get(match.get(v));
}
}
/** @see Graph#getEdgeWeight */
@Override
public double getEdgeWeight(E e) {
double weight;
// Always return the value from the weight map first and
// only pass the call through as a backup
if (weightMap.containsKey(e)) {
weight = weightMap.get(e);
} else {
weight = super.getEdgeWeight(e);
}
return weight;
}
/**
* Runs the algorithm on the input graph and returns the match edge set.
*
* @return set of Edges
*/
private Set<E> findMatch() {
Set<E> result = new ArrayUnenforcedSet<>();
match = new HashMap<>();
path = new HashMap<>();
contracted = new HashMap<>();
for (V i : graph.vertexSet()) {
// Any augmenting path should start with _exposed_ vertex
// (vertex may not escape match-set being added once)
if (!match.containsKey(i)) {
// Match is maximal iff graph G contains no more augmenting paths
V v = findPath(i);
while (v != null) {
V pv = path.get(v);
V ppv = match.get(pv);
match.put(v, pv);
match.put(pv, v);
v = ppv;
}
}
}
Set<V> seen = new HashSet<>();
graph
.vertexSet()
.stream()
.filter(v -> !seen.contains(v) && match.containsKey(v))
.forEach(
v -> {
seen.add(v);
seen.add(match.get(v));
result.add(graph.getEdge(v, match.get(v)));
});
return result;
}
private V lowestCommonAncestor(V a, V b) {
Set<V> seen = new HashSet<>();
for (; ; ) {
a = contracted.get(a);
seen.add(a);
if (!match.containsKey(a)) {
break;
}
a = path.get(match.get(a));
}
for (; ; ) {
b = contracted.get(b);
if (seen.contains(b)) {
return b;
}
b = path.get(match.get(b));
}
}
private IntrusiveEdge getIntrusiveEdge(E e) {
if (e instanceof IntrusiveEdge) {
return (IntrusiveEdge) e;
}
return edgeMap.get(e);
}
private V findPath(V root) {
Set<V> used = new HashSet<>();
Queue<V> q = new ArrayDeque<>();
// Expand graph back from its contracted state
path.clear();
contracted.clear();
graph.vertexSet().forEach(vertex -> contracted.put(vertex, vertex));
used.add(root);
q.add(root);
while (!q.isEmpty()) {
V v = q.remove();
for (E e : graph.edgesOf(v)) {
V to = graph.getEdgeSource(e);
if (to.equals(v)) {
to = graph.getEdgeTarget(e);
}
if ((contracted.get(v).equals(contracted.get(to))) || to.equals(match.get(v))) {
continue;
}
// Check whether we've hit a 'blossom'
if ((to.equals(root)) || ((match.containsKey(to)) && (path.containsKey(match.get(to))))) {
V stem = lowestCommonAncestor(v, to);
Set<V> blossom = new HashSet<>();
markPath(v, to, stem, blossom);
markPath(to, v, stem, blossom);
graph
.vertexSet()
.stream()
.filter(i -> contracted.containsKey(i) && blossom.contains(contracted.get(i)))
.forEach(
i -> {
contracted.put(i, stem);
if (!used.contains(i)) {
used.add(i);
q.add(i);
}
});
// Check whether we've had hit a loop (of even length (!) presumably)
} else if (!path.containsKey(to)) {
path.put(to, v);
if (!match.containsKey(to)) {
return to;
}
to = match.get(to);
used.add(to);
q.add(to);
}
}
}
return null;
}
public int getVertexNumber(V v) {
return mapVertexToOrder.get(v);
}
/**
* Access the data stored for a seen vertex.
*
* @param vertex a vertex which has already been seen.
* @return data associated with the seen vertex or <code>null</code> if no data was associated
* with the vertex. A <code>null</code> return can also indicate that the vertex was
* explicitly associated with <code>
* null</code>.
*/
protected D getSeenData(V vertex) {
return seen.get(vertex);
}
/**
* Compute the minimal triangulation of the graph. Implementation of Algorithm MCS-M+ as described
* in Berry et al. (2010), DOI:10.3390/a3020197 <a href="http://www.mdpi.com/1999-4893/3/2/197">
* http://www.mdpi.com/1999-4893/3/2/197</a>
*/
private void computeMinimalTriangulation() {
// initialize chordGraph with same vertices as graph
chordalGraph = new SimpleGraph<>(graph.getEdgeFactory());
for (V v : graph.vertexSet()) {
chordalGraph.addVertex(v);
}
// initialize g' as subgraph of graph (same vertices and edges)
final UndirectedGraph<V, E> gprime = copyAsSimpleGraph(graph);
int s = -1;
generators = new ArrayList<>();
meo = new LinkedList<>();
final Map<V, Integer> vertexLabels = new HashMap<>();
for (V v : gprime.vertexSet()) {
vertexLabels.put(v, 0);
}
for (int i = 1, n = graph.vertexSet().size(); i <= n; i++) {
V v = getMaxLabelVertex(vertexLabels);
LinkedList<V> Y = new LinkedList<>(Graphs.neighborListOf(gprime, v));
if (vertexLabels.get(v) <= s) {
generators.add(v);
}
s = vertexLabels.get(v);
// Mark x reached and all other vertices of gprime unreached
HashSet<V> reached = new HashSet<>();
reached.add(v);
// mark neighborhood of x reached and add to reach(label(y))
HashMap<Integer, HashSet<V>> reach = new HashMap<>();
// mark y reached and add y to reach
for (V y : Y) {
reached.add(y);
addToReach(vertexLabels.get(y), y, reach);
}
for (int j = 0; j < graph.vertexSet().size(); j++) {
if (!reach.containsKey(j)) {
continue;
}
while (reach.get(j).size() > 0) {
// remove a vertex y from reach(j)
V y = reach.get(j).iterator().next();
reach.get(j).remove(y);
for (V z : Graphs.neighborListOf(gprime, y)) {
if (!reached.contains(z)) {
reached.add(z);
if (vertexLabels.get(z) > j) {
Y.add(z);
E fillEdge = graph.getEdgeFactory().createEdge(v, z);
fillEdges.add(fillEdge);
addToReach(vertexLabels.get(z), z, reach);
} else {
addToReach(j, z, reach);
}
}
}
}
}
for (V y : Y) {
chordalGraph.addEdge(v, y);
vertexLabels.put(y, vertexLabels.get(y) + 1);
}
meo.addLast(v);
gprime.removeVertex(v);
vertexLabels.remove(v);
}
}