org.jgrapht.alg.vertexcover.EdgeBasedTwoApproxVCImpl Maven / Gradle / Ivy
/*
* (C) Copyright 2003-2021, by Linda Buisman 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.vertexcover;
import org.jgrapht.*;
import org.jgrapht.alg.interfaces.*;
import org.jgrapht.graph.*;
import java.util.*;
/**
* Finds a 2-approximation for a minimum vertex cover 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
*
* Note: this class supports pseudo-graphs
*
* @param the graph vertex type
* @param the graph edge type
*
* @author Linda Buisman
*/
public class EdgeBasedTwoApproxVCImpl
implements
VertexCoverAlgorithm
{
private final Graph graph;
/**
* Constructs a new EdgeBasedTwoApproxVCImpl instance
*
* @param graph input graph
*/
public EdgeBasedTwoApproxVCImpl(Graph graph)
{
this.graph = GraphTests.requireUndirected(graph);
}
/**
* 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.
*
* Note: this class supports pseudo-graphs Runtime: O(|E|)
*
* Albeit the fact that this is a 2-approximation algorithm for vertex cover, its results are
* often of lower quality than the results produced by {@link BarYehudaEvenTwoApproxVCImpl} or
* {@link ClarksonTwoApproxVCImpl}.
*
*
* 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.
*
*
*
* @return a set of vertices which is a vertex cover for the specified graph.
*/
@Override
public VertexCoverAlgorithm.VertexCover getVertexCover()
{
// C <-- {}
Set cover = new LinkedHashSet<>();
// G'=(V',E') <-- G(V,E)
Graph sg = new AsSubgraph<>(graph, 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 = graph.getEdgeSource(e);
V v = graph.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 new VertexCoverAlgorithm.VertexCoverImpl<>(cover);
}
}