edu.uci.ics.jung.algorithms.cluster
Class BicomponentClusterer<V,E>

java.lang.Object
  edu.uci.ics.jung.algorithms.cluster.BicomponentClusterer<V,E>

All Implemented Interfaces:

org.apache.commons.collections15.Transformer<UndirectedGraph<V,E>,Set<Set<V>>>

public class BicomponentClusterer<V,E>
extends Object
implements org.apache.commons.collections15.Transformer<UndirectedGraph<V,E>,Set<Set<V>>>

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

Author:

Joshua O'Madadhain

See Also:

"Depth first search and linear graph algorithms by R. E. Tarjan (1972), SIAM J. Comp."

Field Summary

protected int	converse_depth
protected Map<V,Number>	dfs_num
protected Map<V,Number>	high
protected Map<V,V>	parents
protected Stack<E>	stack

Constructor Summary

BicomponentClusterer()
Constructs a new bicomponent finder

Method Summary

protected void	findBiconnectedComponents(UndirectedGraph<V,E> g, V v, Set<Set<V>> bicomponents) Stores, in bicomponents, all the biconnected components that are reachable from v.
Set<Set<V>>	transform(UndirectedGraph<V,E> theGraph) Extracts the bicomponents from the graph.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

dfs_num

protected Map<V,Number> dfs_num

high

protected Map<V,Number> high

parents

protected Map<V,V> parents

stack

protected Stack<E> stack

converse_depth

protected int converse_depth

Constructor Detail

BicomponentClusterer

public BicomponentClusterer()

Constructs a new bicomponent finder

Method Detail

transform

public Set<Set<V>> transform(UndirectedGraph<V,E> theGraph)

Extracts the bicomponents from the graph.

Specified by:

transform in interface org.apache.commons.collections15.Transformer<UndirectedGraph<V,E>,Set<Set<V>>>

Parameters:

theGraph - the graph whose bicomponents are to be extracted

Returns:

the ClusterSet of bicomponents

findBiconnectedComponents

protected void findBiconnectedComponents(UndirectedGraph<V,E> g,
                                         V v,
                                         Set<Set<V>> 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)