HamiltonianCycle.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.
 */
/* ----------------
 * HamiltonianCycle.java
 * ----------------
 * (C) Copyright 2003-2008, by Barak Naveh and Contributors.
 *
 * Original Author:  Andrew Newell
 * Contributor(s):   -
 *
 * $Id: HamiltonianCycle.java 681 2009-05-25 06:17:31Z perfecthash $
 *
 * Changes
 * -------
 * 17-Feb-2008 : Initial revision (AN);
 *
 */
package edu.nd.nina.alg;

import java.util.LinkedList;
import java.util.List;

import edu.nd.nina.graph.SimpleWeightedGraph;


/**
 * This class will deal with finding the optimal or approximately optimal
 * minimum tour (hamiltonian cycle) or commonly known as the <a
 * href="http://mathworld.wolfram.com/TravelingSalesmanProblem.html">Traveling
 * Salesman Problem</a>.
 *
 * @author Andrew Newell
 */
public class HamiltonianCycle
{
    //~ Methods ----------------------------------------------------------------

    /**
     * This method will return an approximate minimal traveling salesman tour
     * (hamiltonian cycle). This algorithm requires that the graph be complete
     * and the triangle inequality exists (if x,y,z are vertices then
     * d(x,y)+d(y,z)<d(x,z) for all x,y,z) then this algorithm will guarantee a
     * hamiltonian cycle such that the total weight of the cycle is less than or
     * equal to double the total weight of the optimal hamiltonian cycle. The
     * optimal solution is NP-complete, so this is a decent approximation that
     * runs in polynomial time.
     *
     * @param <V>
     * @param <E>
     * @param g is the graph to find the optimal tour for.
     *
     * @return The optimal tour as a list of vertices.
     */
    public static <V, E> List<V> getApproximateOptimalForCompleteGraph(
        SimpleWeightedGraph<V, E> g)
    {
        List<V> vertices = new LinkedList<V>(g.vertexSet());

        // If the graph is not complete then return null since this algorithm
        // requires the graph be complete
        if ((vertices.size() * (vertices.size() - 1) / 2)
            != g.edgeSet().size())
        {
            return null;
        }

        List<V> tour = new LinkedList<V>();

        // Each iteration a new vertex will be added to the tour until all
        // vertices have been added
        while (tour.size() != g.vertexSet().size()) {
            boolean firstEdge = true;
            double minEdgeValue = 0;
            int minVertexFound = 0;
            int vertexConnectedTo = 0;

            // A check will be made for the shortest edge to a vertex not within
            // the tour and that new vertex will be added to the vertex
            for (int i = 0; i < tour.size(); i++) {
                V v = tour.get(i);
                for (int j = 0; j < vertices.size(); j++) {
                    double weight =
                        g.getEdgeWeight(g.getEdge(v, vertices.get(j)));
                    if (firstEdge || (weight < minEdgeValue)) {
                        firstEdge = false;
                        minEdgeValue = weight;
                        minVertexFound = j;
                        vertexConnectedTo = i;
                    }
                }
            }
            tour.add(vertexConnectedTo, vertices.get(minVertexFound));
            vertices.remove(minVertexFound);
        }
        return tour;
    }
}

// End HamiltonianCycle.java