edu.uci.ics.jung.algorithms.cluster.BicomponentClusterer Maven / Gradle / Ivy
/*
* 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.
*
* 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 implements Transformer, Set>>
{
protected Map dfs_num;
protected Map high;
protected Map parents;
protected Stack 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 ClusterSet of bicomponents
*/
public Set> transform(UndirectedGraph theGraph)
{
Set> bicomponents = new LinkedHashSet>();
if (theGraph.getVertices().isEmpty())
return bicomponents;
// initialize DFS number for each vertex to 0
dfs_num = new HashMap();
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();
stack = new Stack();
parents = new HashMap();
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 s = new HashSet();
s.add(v);
bicomponents.add(s);
}
}
}
return bicomponents;
}
/**
* Stores, in bicomponents, all the biconnected
* components that are reachable from v.
*
* The algorithm basically proceeds as follows: do a depth-first
* traversal starting from v, 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.
*
*
(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)
*
*/
protected void findBiconnectedComponents(UndirectedGraph g, V v, Set> 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 bicomponent = new HashSet();
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()));
}
}
}