org.jgrapht.alg.VertexCovers Maven / Gradle / Ivy

Go to download
Show more of this group Show more artifacts with this name
Show all versions of jgrapht-core Show documentation
There is a newer version: 1.5.2
/*
 * (C) Copyright 2003-2016, by Linda Buisman and Contributors.
 *
 * JGraphT : a free Java graph-theory library
 *
 * This program and the accompanying materials are dual-licensed under
 * either
 *
 * (a) the terms of the GNU Lesser General Public License version 2.1
 * as published by the Free Software Foundation, or (at your option) any
 * later version.
 *
 * or (per the licensee's choosing)
 *
 * (b) the terms of the Eclipse Public License v1.0 as published by
 * the Eclipse Foundation.
 */
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
 */
@Deprecated
public abstract class VertexCovers
{
    /**
     * 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.
     * @param  the graph vertex type
     * @param  the graph edge type
     *
     * @return a set of vertices which is a vertex cover for the specified graph.
     *
     * @deprecated Use {@link org.jgrapht.alg.vertexcover.EdgeBasedTwoApproxVCImpl},
     *             {@link org.jgrapht.alg.vertexcover.ClarksonTwoApproxVCImpl}, or
     *             {@link org.jgrapht.alg.vertexcover.BarYehudaEvenTwoApproxVCImpl} instead.
     */
    @Deprecated
    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.
     * @param  the graph vertex type
     * @param  the graph edge type
     *
     * @return a set of vertices which is a vertex cover for the specified graph.
     *
     * @deprecated use {@link org.jgrapht.alg.vertexcover.GreedyVCImpl} instead.
     */
    @Deprecated
    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