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JGraphT is a free Java graph library
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/* ==========================================
* JGraphT : a free Java graph-theory library
* ==========================================
*
* Project Info: http://jgrapht.sourceforge.net/
* Project Creator: Barak Naveh (http://sourceforge.net/users/barak_naveh)
*
* (C) Copyright 2003-2007, by Barak Naveh and Contributors.
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This library is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
*/
/* -----------------
* VertexCovers.java
* -----------------
* (C) Copyright 2003-2007, by Linda Buisman and Contributors.
*
* Original Author: Linda Buisman
* Contributor(s): Barak Naveh
* Christian Hammer
*
* $Id: VertexCovers.java 568 2007-09-30 00:12:18Z perfecthash $
*
* Changes
* -------
* 06-Nov-2003 : Initial revision (LB);
* 07-Jun-2005 : Made generic (CH);
*
*/
package org.jgrapht.alg;
import java.util.*;
import org.jgrapht.*;
import org.jgrapht.alg.util.*;
import org.jgrapht.graph.*;
/**
* Algorithms to find a vertex cover for a graph. A vertex cover is a set of
* vertices that touches all the edges in the graph. The graph's vertex set is a
* trivial cover. However, a minimal vertex set (or at least an
* approximation for it) is usually desired. Finding a true minimal vertex cover
* is an NP-Complete problem. For more on the vertex cover problem, see
* http://mathworld.wolfram.com/VertexCover.html
*
* @author Linda Buisman
* @since Nov 6, 2003
*/
public abstract class VertexCovers
{
//~ Methods ----------------------------------------------------------------
/**
* Finds a 2-approximation for a minimal vertex cover of the specified
* graph. The algorithm promises a cover that is at most double the size of
* a minimal cover. The algorithm takes O(|E|) time.
*
* For more details see Jenny Walter, CMPU-240: Lecture notes for
* Language Theory and Computation, Fall 2002, Vassar College,
* http://www.cs.vassar.edu/~walter/cs241index/lectures/PDF/approx.pdf.
*
*
* @param g the graph for which vertex cover approximation is to be found.
*
* @return a set of vertices which is a vertex cover for the specified
* graph.
*/
public static Set find2ApproximationCover(Graph g)
{
// C <-- {}
Set cover = new HashSet();
// G'=(V',E') <-- G(V,E)
Subgraph> sg =
new Subgraph>(
g,
null,
null);
// while E' is non-empty
while (sg.edgeSet().size() > 0) {
// let (u,v) be an arbitrary edge of E'
E e = sg.edgeSet().iterator().next();
// C <-- C U {u,v}
V u = g.getEdgeSource(e);
V v = g.getEdgeTarget(e);
cover.add(u);
cover.add(v);
// remove from E' every edge incident on either u or v
sg.removeVertex(u);
sg.removeVertex(v);
}
return cover; // return C
}
/**
* Finds a greedy approximation for a minimal vertex cover of a specified
* graph. At each iteration, the algorithm picks the vertex with the highest
* degree and adds it to the cover, until all edges are covered.
*
* The algorithm works on undirected graphs, but can also work on
* directed graphs when their edge-directions are ignored. To ignore edge
* directions you can use {@link org.jgrapht.Graphs#undirectedGraph(Graph)}
* or {@link org.jgrapht.graph.AsUndirectedGraph}.
*
* @param g the graph for which vertex cover approximation is to be found.
*
* @return a set of vertices which is a vertex cover for the specified
* graph.
*/
public static Set findGreedyCover(UndirectedGraph g)
{
// C <-- {}
Set cover = new HashSet();
// G' <-- G
UndirectedGraph sg = new UndirectedSubgraph(g, null, null);
// compare vertices in descending order of degree
VertexDegreeComparator comp =
new VertexDegreeComparator(sg);
// while G' != {}
while (sg.edgeSet().size() > 0) {
// v <-- vertex with maximum degree in G'
V v = Collections.max(sg.vertexSet(), comp);
// C <-- C U {v}
cover.add(v);
// remove from G' every edge incident on v, and v itself
sg.removeVertex(v);
}
return cover;
}
}
// End VertexCovers.java