org.jgrapht.alg.HamiltonianCycle Maven / Gradle / Ivy
/*
* (C) Copyright 2003-2017, by Barak Naveh 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.graph.*;
/**
* This class will deal with finding the optimal or approximately optimal minimum tour (hamiltonian
* cycle) or commonly known as the
* Traveling Salesman
* Problem.
*
* @author Andrew Newell
*/
public class HamiltonianCycle
{
/**
* 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 g is the graph to find the optimal tour for.
* @param the graph vertex type
* @param the graph edge type
*
* @return The optimal tour as a list of vertices.
*/
public static List getApproximateOptimalForCompleteGraph(SimpleWeightedGraph g)
{
List vertices = new LinkedList<>(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 tour = new LinkedList<>();
// 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