ChromaticNumber.java

/* ==========================================
 * 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 2003-2008, 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.
 */
/* -------------------
 * ChromaticNumber.java
 * -------------------
 * (C) Copyright 2008-2008, by Andrew Newell and Contributors.
 *
 * Original Author:  Andrew Newell
 * Contributor(s):   gpaschos@netscape.net, harshalv@telenav.com
 *
 * $Id: ChromaticNumber.java 741 2011-02-26 06:30:49Z perfecthash $
 *
 * Changes
 * -------
 * 24-Dec-2008 : Initial revision (AN);
 *
 */
package edu.nd.nina.alg;

import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Set;

import edu.nd.nina.UndirectedGraph;
import edu.nd.nina.alg.util.VertexDegreeComparator;
import edu.nd.nina.graph.UndirectedSubgraph;


/**
 * Allows the <a href="http://mathworld.wolfram.com/ChromaticNumber.html">
 * chromatic number</a> of a graph to be calculated. This is the minimal number
 * of colors needed to color each vertex such that no two adjacent vertices
 * share the same color. This algorithm will not find the true chromatic number,
 * since this is an NP-complete problem. So, a greedy algorithm will find an
 * approximate chromatic number.
 *
 * @author Andrew Newell
 * @since Dec 21, 2008
 */
public abstract class ChromaticNumber
{
    //~ Methods ----------------------------------------------------------------

    /**
     * Finds the number of colors required for a greedy coloring of the graph.
     *
     * @param g an undirected graph to find the chromatic number of
     *
     * @return integer the approximate chromatic number from the greedy
     * algorithm
     */
    public static <V, E> int findGreedyChromaticNumber(UndirectedGraph<V, E> g)
    {
        Map<Integer, Set<V>> coloredGroups = findGreedyColoredGroups(g);
        return coloredGroups.keySet().size();
    }

    /**
     * Finds a greedy coloring of the graph.
     *
     * @param g an undirected graph for which to find the coloring
     */
    public static <V, E> Map<Integer, Set<V>> findGreedyColoredGroups(
        UndirectedGraph<V, E> g)
    {
        // A copy of the graph is made, so that elements of the graph may be
        // removed to carry out the algorithm
        UndirectedGraph<V, E> sg = new UndirectedSubgraph<V, E>(g, null, null);

        // The Vertices will be sorted in decreasing order by degree, so that
        // higher degree vertices have priority to be colored first
        VertexDegreeComparator<V, E> comp =
            new VertexDegreeComparator<V, E>(sg);
        List<V> sortedVertices = new LinkedList<V>(sg.vertexSet());
        Collections.sort(sortedVertices, comp);
        Collections.reverse(sortedVertices);

        int color;

        // create a map which will hold color as key and Set<V> as value
        Map<Integer, Set<V>> coloredGroups = new HashMap<Integer, Set<V>>();

        // We'll attempt to color each vertex with a single color each
        // iteration, and these vertices will be removed from the graph at the
        // end of each iteration
        for (color = 0; sg.vertexSet().size() > 0; color++) {
            // This set will contain vertices that are colored with the
            // current color of this iteration
            Set<V> currentColor = new HashSet<V>();
            for (
                Iterator<V> iter = sortedVertices.iterator();
                iter.hasNext();)
            {
                V v = iter.next();

                // Add new vertices to be colored as long as they are not
                // adjacent with any other vertex that has already been colored
                // with the current color
                boolean flag = true;
                for (
                    Iterator<V> innerIter = currentColor.iterator();
                    innerIter.hasNext();)
                {
                    V temp = innerIter.next();
                    if (sg.containsEdge(temp, v)) {
                        flag = false;
                        break;
                    }
                }
                if (flag) {
                    currentColor.add(v);
                    iter.remove();
                }
            }

            // Add all these vertices as a group for this color
            coloredGroups.put(color, currentColor);

            // Remove vertices from the graph and then repeat the process for
            // the next iteration
            sg.removeAllVertices(currentColor);
        }
        return coloredGroups;
    }
}

// End ChromaticNumber.java