/**
* Check if the graph is chordal.
*
* @return true if the graph is chordal, false otherwise.
*/
public boolean isChordal() {
if (chordalGraph == null) {
computeMinimalTriangulation();
}
return (chordalGraph.edgeSet().size() == graph.edgeSet().size());
}
/**
* Compute the unique decomposition of the input graph G (atoms of G). Implementation of algorithm
* Atoms 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 computeAtoms() {
if (chordalGraph == null) {
computeMinimalTriangulation();
}
separators = new HashSet<>();
// initialize g' as subgraph of graph (same vertices and edges)
UndirectedGraph<V, E> gprime = copyAsSimpleGraph(graph);
// initialize h' as subgraph of chordalGraph (same vertices and edges)
UndirectedGraph<V, E> hprime = copyAsSimpleGraph(chordalGraph);
atoms = new HashSet<>();
Iterator<V> iterator = meo.descendingIterator();
while (iterator.hasNext()) {
V v = iterator.next();
if (generators.contains(v)) {
Set<V> separator = new HashSet<>(Graphs.neighborListOf(hprime, v));
if (isClique(graph, separator)) {
if (separator.size() > 0) {
if (separators.contains(separator)) {
fullComponentCount.put(separator, fullComponentCount.get(separator) + 1);
} else {
fullComponentCount.put(separator, 2);
separators.add(separator);
}
}
UndirectedGraph<V, E> tmpGraph = copyAsSimpleGraph(gprime);
tmpGraph.removeAllVertices(separator);
ConnectivityInspector<V, E> con = new ConnectivityInspector<>(tmpGraph);
if (con.isGraphConnected()) {
throw new RuntimeException("separator did not separate the graph");
}
for (Set<V> component : con.connectedSets()) {
if (component.contains(v)) {
gprime.removeAllVertices(component);
component.addAll(separator);
atoms.add(new HashSet<>(component));
assert (component.size() > 0);
break;
}
}
}
}
hprime.removeVertex(v);
}
if (gprime.vertexSet().size() > 0) {
atoms.add(new HashSet<>(gprime.vertexSet()));
}
}
/**
* Check whether the subgraph of <code>graph</code> induced by the given <code>vertices</code> is
* complete, i.e. a clique.
*
* @param graph the graph.
* @param vertices the vertices to induce the subgraph from.
* @return true if the induced subgraph is a clique.
*/
private static <V, E> boolean isClique(UndirectedGraph<V, E> graph, Set<V> vertices) {
for (V v1 : vertices) {
for (V v2 : vertices) {
if ((v1 != v2) && (graph.getEdge(v1, v2) == null)) {
return false;
}
}
}
return true;
}
/**
* Create a copy of a graph for internal use.
*
* @param graph the graph to copy.
* @return A copy of the graph projected to a SimpleGraph.
*/
private static <V, E> UndirectedGraph<V, E> copyAsSimpleGraph(UndirectedGraph<V, E> graph) {
UndirectedGraph<V, E> copy = new SimpleGraph<>(graph.getEdgeFactory());
if (graph instanceof SimpleGraph) {
Graphs.addGraph(copy, graph);
} else {
// project graph to SimpleGraph
Graphs.addAllVertices(copy, graph.vertexSet());
for (E e : graph.edgeSet()) {
V v1 = graph.getEdgeSource(e);
V v2 = graph.getEdgeTarget(e);
if ((v1 != v2) && !copy.containsEdge(e)) {
copy.addEdge(v1, v2);
}
}
}
return copy;
}
/**
* 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);
}
}