org.jgrapht.alg.tour.TwoApproxMetricTSP Maven / Gradle / Ivy
/*
* (C) Copyright 2017-2021, by Dimitrios Michail and Contributors.
*
* JGraphT : a free Java graph-theory library
*
* See the CONTRIBUTORS.md file distributed with this work for additional
* information regarding copyright ownership.
*
* This program and the accompanying materials are made available under the
* terms of the Eclipse Public License 2.0 which is available at
* http://www.eclipse.org/legal/epl-2.0, or the
* GNU Lesser General Public License v2.1 or later
* which is available at
* http://www.gnu.org/licenses/old-licenses/lgpl-2.1-standalone.html.
*
* SPDX-License-Identifier: EPL-2.0 OR LGPL-2.1-or-later
*/
package org.jgrapht.alg.tour;
import org.jgrapht.*;
import org.jgrapht.alg.spanning.*;
import org.jgrapht.graph.*;
import org.jgrapht.traverse.*;
import org.jgrapht.util.*;
import java.util.*;
/**
* A 2-approximation algorithm for the metric TSP problem.
*
*
* The travelling salesman problem (TSP) asks the following question: "Given a list of cities and
* the distances between each pair of cities, what is the shortest possible route that visits each
* city exactly once and returns to the origin city?". In the metric TSP, the intercity distances
* satisfy the triangle inequality.
*
*
* This is an implementation of the folklore algorithm which returns a depth-first ordering of the
* minimum spanning tree. The algorithm is a 2-approximation assuming that the instance satisfies
* the triangle inequality. The implementation requires the input graph to be undirected and
* complete. The running time is $O(|V|^2 \log |V|)$.
*
*
* See wikipedia for more
* details.
*
* @param the graph vertex type
* @param the graph edge type
*
* @author Dimitrios Michail
*/
public class TwoApproxMetricTSP
extends
HamiltonianCycleAlgorithmBase
{
/**
* Computes a 2-approximate tour.
*
* @param graph the input graph
* @return a tour
* @throws IllegalArgumentException if the graph is not undirected
* @throws IllegalArgumentException if the graph is not complete
* @throws IllegalArgumentException if the graph contains no vertices
*/
@Override
public GraphPath getTour(Graph graph)
{
checkGraph(graph);
Set vertices = graph.vertexSet();
int n = vertices.size();
if (vertices.size() == 1) {
return getSingletonTour(graph);
}
// Create MST
Graph mst = new SimpleGraph<>(null, DefaultEdge::new, false);
vertices.forEach(mst::addVertex);
for (E e : new KruskalMinimumSpanningTree<>(graph).getSpanningTree().getEdges()) {
mst.addEdge(graph.getEdgeSource(e), graph.getEdgeTarget(e));
}
// Perform a depth-first-search traversal
Set found = CollectionUtil.newHashSetWithExpectedSize(n);
List tour = new ArrayList<>(n + 1);
V start = vertices.iterator().next();
Iterator dfsIt = new DepthFirstIterator<>(mst, start);
while (dfsIt.hasNext()) {
V v = dfsIt.next();
if (found.add(v)) {
tour.add(v);
}
}
// Explicitly build the path.
return vertexListToTour(tour, graph);
}
}