--- /dev/null
+/*
+* Copyright (c) 2003, the JUNG Project and the Regents of the University
+* of California
+* All rights reserved.
+*
+* This software is open-source under the BSD license; see either
+* "license.txt" or
+* http://jung.sourceforge.net/license.txt for a description.
+*/
+package edu.uci.ics.jung.algorithms.cluster;
+
+import java.util.HashMap;
+import java.util.HashSet;
+import java.util.LinkedHashSet;
+import java.util.Map;
+import java.util.Set;
+import java.util.Stack;
+
+import org.apache.commons.collections15.Transformer;
+
+import edu.uci.ics.jung.graph.UndirectedGraph;
+
+/**
+ * Finds all biconnected components (bicomponents) of an undirected graph.
+ * A graph is a biconnected component if
+ * at least 2 vertices must be removed in order to disconnect the graph. (Graphs
+ * consisting of one vertex, or of two connected vertices, are also biconnected.) Biconnected
+ * components of three or more vertices have the property that every pair of vertices in the component
+ * are connected by two or more vertex-disjoint paths.
+ * <p>
+ * Running time: O(|V| + |E|) where |V| is the number of vertices and |E| is the number of edges
+ * @see "Depth first search and linear graph algorithms by R. E. Tarjan (1972), SIAM J. Comp."
+ *
+ * @author Joshua O'Madadhain
+ */
+public class BicomponentClusterer<V,E> implements Transformer<UndirectedGraph<V,E>, Set<Set<V>>>
+{
+ protected Map<V,Number> dfs_num;
+ protected Map<V,Number> high;
+ protected Map<V,V> parents;
+ protected Stack<E> stack;
+ protected int converse_depth;
+
+ /**
+ * Constructs a new bicomponent finder
+ */
+ public BicomponentClusterer() {
+ }
+
+ /**
+ * Extracts the bicomponents from the graph.
+ * @param theGraph the graph whose bicomponents are to be extracted
+ * @return the <code>ClusterSet</code> of bicomponents
+ */
+ public Set<Set<V>> transform(UndirectedGraph<V,E> theGraph)
+ {
+ Set<Set<V>> bicomponents = new LinkedHashSet<Set<V>>();
+
+ if (theGraph.getVertices().isEmpty())
+ return bicomponents;
+
+ // initialize DFS number for each vertex to 0
+ dfs_num = new HashMap<V,Number>();
+ for (V v : theGraph.getVertices())
+ {
+ dfs_num.put(v, 0);
+ }
+
+ for (V v : theGraph.getVertices())
+ {
+ if (dfs_num.get(v).intValue() == 0) // if we haven't hit this vertex yet...
+ {
+ high = new HashMap<V,Number>();
+ stack = new Stack<E>();
+ parents = new HashMap<V,V>();
+ converse_depth = theGraph.getVertexCount();
+ // find the biconnected components for this subgraph, starting from v
+ findBiconnectedComponents(theGraph, v, bicomponents);
+
+ // if we only visited one vertex, this method won't have
+ // ID'd it as a biconnected component, so mark it as one
+ if (theGraph.getVertexCount() - converse_depth == 1)
+ {
+ Set<V> s = new HashSet<V>();
+ s.add(v);
+ bicomponents.add(s);
+ }
+ }
+ }
+
+ return bicomponents;
+ }
+
+ /**
+ * <p>Stores, in <code>bicomponents</code>, all the biconnected
+ * components that are reachable from <code>v</code>.</p>
+ *
+ * <p>The algorithm basically proceeds as follows: do a depth-first
+ * traversal starting from <code>v</code>, marking each vertex with
+ * a value that indicates the order in which it was encountered (dfs_num),
+ * and with
+ * a value that indicates the highest point in the DFS tree that is known
+ * to be reachable from this vertex using non-DFS edges (high). (Since it
+ * is measured on non-DFS edges, "high" tells you how far back in the DFS
+ * tree you can reach by two distinct paths, hence biconnectivity.)
+ * Each time a new vertex w is encountered, push the edge just traversed
+ * on a stack, and call this method recursively. If w.high is no greater than
+ * v.dfs_num, then the contents of the stack down to (v,w) is a
+ * biconnected component (and v is an articulation point, that is, a
+ * component boundary). In either case, set v.high to max(v.high, w.high),
+ * and continue. If w has already been encountered but is
+ * not v's parent, set v.high max(v.high, w.dfs_num) and continue.
+ *
+ * <p>(In case anyone cares, the version of this algorithm on p. 224 of
+ * Udi Manber's "Introduction to Algorithms: A Creative Approach" seems to be
+ * wrong: the stack should be initialized outside this method,
+ * (v,w) should only be put on the stack if w hasn't been seen already,
+ * and there's no real benefit to putting v on the stack separately: just
+ * check for (v,w) on the stack rather than v. Had I known this, I could
+ * have saved myself a few days. JRTOM)</p>
+ *
+ */
+ protected void findBiconnectedComponents(UndirectedGraph<V,E> g, V v, Set<Set<V>> bicomponents)
+ {
+ int v_dfs_num = converse_depth;
+ dfs_num.put(v, v_dfs_num);
+ converse_depth--;
+ high.put(v, v_dfs_num);
+
+ for (V w : g.getNeighbors(v))
+ {
+ int w_dfs_num = dfs_num.get(w).intValue();//get(w, dfs_num);
+ E vw = g.findEdge(v,w);
+ if (w_dfs_num == 0) // w hasn't yet been visited
+ {
+ parents.put(w, v); // v is w's parent in the DFS tree
+ stack.push(vw);
+ findBiconnectedComponents(g, w, bicomponents);
+ int w_high = high.get(w).intValue();//get(w, high);
+ if (w_high <= v_dfs_num)
+ {
+ // v disconnects w from the rest of the graph,
+ // i.e., v is an articulation point
+ // thus, everything between the top of the stack and
+ // v is part of a single biconnected component
+ Set<V> bicomponent = new HashSet<V>();
+ E e;
+ do
+ {
+ e = stack.pop();
+ bicomponent.addAll(g.getIncidentVertices(e));
+ }
+ while (e != vw);
+ bicomponents.add(bicomponent);
+ }
+ high.put(v, Math.max(w_high, high.get(v).intValue()));
+ }
+ else if (w != parents.get(v)) // (v,w) is a back or a forward edge
+ high.put(v, Math.max(w_dfs_num, high.get(v).intValue()));
+ }
+ }
+}
Code Review / controller.git / blobdiff