/**
* Returns a List with unique elements,
*
* @param v1 vertex from g1
* @return
*/
public List<V> getPrioritySubset(V v1) {
// The resulting list
List<V> result = new ArrayList<V>();
// list of already mapped vertices that neighbour v1
List<V> v1Others = new ArrayList<V>();
V v1other;
V v2other;
for (E e1 : g1.edgesOf(v1)) {
v1other = Graphs.getOppositeVertex(g1, e1, v1);
if (mappedVerticesFromG1.contains(v1other)) {
v1Others.add(v1other);
}
}
for (V v2 : g2.vertexSet()) {
// if v2's label is the same of v1's label and v2 has not been mapped yet
if (v1.getLabel().equals(v2.getLabel()) && !mappedVerticesFromG2.contains(v2)) {
// test if there is an edge to a vertex which has already been mapped
for (E e2 : g2.edgesOf(v2)) {
v2other = Graphs.getOppositeVertex(g2, e2, v2);
// if the vertex v2other has already been mapped
if (mappedVerticesFromG2.contains(v2other)) {
// labels are not checked, this is done at a later stage anyway and doing it twice is
// not needed and takes too much time
result.add(v2);
break;
}
}
}
}
return result;
}
/**
* @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 static Set outgoingEdgesOf(Graph g, Object node) {
if (g instanceof DirectedGraph) {
return ((DirectedGraph) g).outgoingEdgesOf(node);
} else {
return g.edgesOf(node);
}
}
@Override
public boolean add(Integer i) {
// maintain unweighted volume
Set<DefaultWeightedEdge> neighborSet = graph.edgesOf(i);
volume += neighborSet.size();
// maintain correct denominator to compute conductance with
denominator = Math.min(volume, totalVolume - volume);
// count how many external edges this node has with the community
external_edges += countExternalEdges(i, neighborSet);
conductance = external_edges / (double) denominator;
return super.add(i);
}
@Override
public boolean remove(Object o) {
Integer i = (Integer) o;
// maintain unweighted volume
Set<DefaultWeightedEdge> neighborSet = graph.edgesOf(i);
volume -= neighborSet.size();
// maintain correct denominator to compute conductance with
denominator = Math.min(volume, totalVolume - volume);
boolean retValue = super.remove(i);
// count how many external edges this node has with the community, and remove them (opposite of
// add)
external_edges -= countExternalEdges(i, neighborSet);
conductance = external_edges / (double) denominator;
return retValue;
}
/**
* Return the change in conductance which would occur from adding a particular vertex to the set.
* This is linear in the degree of the vertex. ie., O(degree(toAdd))
*/
@Override
public double getDeltaConductance(Integer vertex, boolean add) {
Set<DefaultWeightedEdge> neighborSet = graph.edgesOf(vertex);
int degree_U = neighborSet.size();
long delta_E = 0;
delta_E = countExternalEdges(vertex, neighborSet);
if (!add) {
delta_E = -1 * delta_E;
degree_U = -1 * degree_U;
}
long new_volume = volume + degree_U;
long new_denom = Math.min(new_volume, totalVolume - new_volume);
double rescaled_conductance = ((denominator) / (double) (new_denom)) * conductance;
double final_conductance = rescaled_conductance + (delta_E) / (double) (new_denom);
// this is the change in conductance if one were to add node u
return final_conductance - conductance;
}
Set<E> edgesOf(V vertex) {
return graph.edgesOf(vertex);
}
// 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);
}
// the algorithm (no heuristics)
private Pair<Double, Set<E>> run(Graph<V, E> graph) {
// lookup all relevant vertices
Set<V> visibleVertex = initVisibleVertices(graph);
// run algorithm
Set<E> m1 = new HashSet<>();
Set<E> m2 = new HashSet<>();
double m1Weight = 0d, m2Weight = 0d;
int i = 1;
while (!visibleVertex.isEmpty()) {
// find vertex arbitrarily
V x = visibleVertex.stream().findAny().get();
// grow path from x
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 it to either m1 or m2, alternating between them
if (maxWeightedEdge != null) {
switch (i) {
case 1:
m1.add(maxWeightedEdge);
m1Weight += maxWeight;
break;
case 2:
m2.add(maxWeightedEdge);
m2Weight += maxWeight;
break;
default:
throw new RuntimeException("Failed to figure out matching, seems to be a bug");
}
i = 3 - i;
}
// remove x and incident edges
visibleVertex.remove(x);
// go to next vertex
x = maxWeightedNeighbor;
}
}
// return best matching
if (comparator.compare(m1Weight, m2Weight) > 0) {
return Pair.of(m1Weight, m1);
} else {
return Pair.of(m2Weight, m2);
}
}
@Override
public int compare(V2 v1, V2 v2) {
return graph.edgesOf(v1).size() - graph.edgesOf(v2).size();
}
/** @see CrossComponentIterator.Specifics#edgesOf(Object) */
public Set<EE> edgesOf(VV vertex) {
return graph.edgesOf(vertex);
}
/* Each
time a node in G1 is tentatively paired with a node in G2, MARCS is refined on the
basis of this node correspondence. Say node i in G1 is tentatively paired with node j in
G2. Then any arc r connected to node i in G1 can correspond only to arcs which are
connected to node j in G2. This is represented in MARCS by setting to zero any bit
(r, s) such that arc r is connected to node i in G, and arc s is not connected to node j in
G2. */
public void refine(V v1, V v2) {
// marcs is modified, make sure subgraph is set to null (to prevent errors)
subgraph = null;
mappedVerticesFromG1.add(v1);
mappedVerticesFromG2.add(v2);
List<Integer> edgesV1Ints = null;
List<Integer> edgesV2Ints = null;
List<Integer> edgesV1OutInts = null;
List<Integer> edgesV1InInts = null;
List<Integer> edgesV2OutInts = null;
List<Integer> edgesV2InInts = null;
if (!directed) {
edgesV1Ints = new ArrayList<Integer>();
edgesV2Ints = new ArrayList<Integer>();
for (E e1 : g1.edgesOf(v1)) {
edgesV1Ints.add(edgeList1.indexOf(e1));
}
for (E e2 : g2.edgesOf(v2)) {
edgesV2Ints.add(edgeList2.indexOf(e2));
}
} else { // directed
edgesV1OutInts = new ArrayList<Integer>();
edgesV1InInts = new ArrayList<Integer>();
edgesV2OutInts = new ArrayList<Integer>();
edgesV2InInts = new ArrayList<Integer>();
for (E e1 : ((DirectedGraph<V, E>) g1).outgoingEdgesOf(v1)) {
edgesV1OutInts.add(edgeList1.indexOf(e1));
}
for (E e1 : ((DirectedGraph<V, E>) g1).incomingEdgesOf(v1)) {
edgesV1InInts.add(edgeList1.indexOf(e1));
}
for (E e2 : ((DirectedGraph<V, E>) g2).outgoingEdgesOf(v2)) {
edgesV2OutInts.add(edgeList2.indexOf(e2));
}
for (E e2 : ((DirectedGraph<V, E>) g2).incomingEdgesOf(v2)) {
edgesV2InInts.add(edgeList2.indexOf(e2));
}
}
for (int x = 0; x < dimx; x++) {
if (!rowOrs[x]) continue;
for (int y = 0; y < dimy; y++) {
// if the only one of the two edges x and y are connected to v1 or v2 then x and y are not
// compatible and the matrix should be set to false
if (matrix[x][y]) {
if (directed) {
if ((edgesV1OutInts.contains(x) && !edgesV2OutInts.contains(y))
|| (!edgesV1OutInts.contains(x) && edgesV2OutInts.contains(y))
|| (edgesV1InInts.contains(x) && !edgesV2InInts.contains(y))
|| (!edgesV1InInts.contains(x) && edgesV2InInts.contains(y))) {
matrix[x][y] = false;
}
} else { // undirected
if ((edgesV1Ints.contains(x) && !edgesV2Ints.contains(y))
|| (!edgesV1Ints.contains(x) && edgesV2Ints.contains(y))) {
matrix[x][y] = false;
}
}
}
}
}
}