001/**
002 * Copyright (c) 2011, The University of Southampton and the individual contributors.
003 * All rights reserved.
004 *
005 * Redistribution and use in source and binary forms, with or without modification,
006 * are permitted provided that the following conditions are met:
007 *
008 *   *  Redistributions of source code must retain the above copyright notice,
009 *      this list of conditions and the following disclaimer.
010 *
011 *   *  Redistributions in binary form must reproduce the above copyright notice,
012 *      this list of conditions and the following disclaimer in the documentation
013 *      and/or other materials provided with the distribution.
014 *
015 *   *  Neither the name of the University of Southampton nor the names of its
016 *      contributors may be used to endorse or promote products derived from this
017 *      software without specific prior written permission.
018 *
019 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
020 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
021 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
022 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
023 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
024 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
025 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
026 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
027 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
028 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
029 */
030package org.openimaj.math.graph.algorithm;
031
032import org.jgrapht.Graph;
033import org.jgrapht.UndirectedGraph;
034import org.jgrapht.graph.UndirectedSubgraph;
035import org.jgrapht.util.FibonacciHeap;
036import org.jgrapht.util.FibonacciHeapNode;
037
038/**
039 * Implementation of Charikar's greedy Densest-subgraph algorithm for
040 * unweighted, undirected graphs.
041 *  
042 * @author Jonathon Hare (jsh2@ecs.soton.ac.uk)
043 *
044 * @param <V> type of vertex
045 * @param <E> type of edge
046 */
047public class CharikarDensestSubgraph<V, E> {
048        protected UndirectedGraph<V, E> graph;
049        protected UndirectedSubgraph<V,E> bestSubGraph;
050        protected FibonacciHeap<V> heap = new FibonacciHeap<V>();
051        
052        /**
053         * Compute the densest subgraph of a graph.
054         * @param graph the graph.
055         */
056        public CharikarDensestSubgraph(UndirectedGraph<V, E> graph) {
057                this.graph = graph;
058                
059                for (V vertex : graph.vertexSet())
060                        heap.insert(new FibonacciHeapNode<V>(vertex), graph.degreeOf(vertex));
061                
062                calculateDensestSubgraph();
063        }
064        
065        protected V getMinDegreeVertexBruteForce(UndirectedGraph<V, E> graph) {
066                int minDegree = Integer.MAX_VALUE;
067                V minDegreeVertex = null;
068                
069                for (V vertex : graph.vertexSet()) {
070                        int degree = graph.degreeOf(vertex);
071                        if (degree < minDegree) {
072                                minDegreeVertex = vertex;
073                                break;
074                        }
075                }
076                
077                return minDegreeVertex;
078        }
079        
080        protected V getMinDegreeVertex(UndirectedGraph<V, E> graph) {           
081                return heap.removeMin().getData();
082        }
083        
084        protected void calculateDensestSubgraph() {
085                UndirectedSubgraph<V,E> currentSubGraph = new UndirectedSubgraph<V,E>(graph, graph.vertexSet(), null);
086                double bestDensity = calculateDensity(graph);
087                
088                while (currentSubGraph.vertexSet().size() > 0) {
089                        currentSubGraph = new UndirectedSubgraph<V,E>(graph, currentSubGraph.vertexSet(), null);
090                        currentSubGraph.removeVertex(getMinDegreeVertex(currentSubGraph));
091                        double density = calculateDensity(currentSubGraph);
092                        
093                        if (density > bestDensity) {
094                                bestDensity = density;
095                                bestSubGraph = currentSubGraph;
096                        }
097                }
098        }
099        
100        /**
101         * Calculate the density of the graph as the
102         * number of edges divided by the number of vertices
103         * @param g the graph
104         * @return the density
105         */
106        public static double calculateDensity(Graph<?,?> g) {
107                return (double)g.edgeSet().size() / (double)g.vertexSet().size();
108        }
109        
110        /**
111         * @return The densest subgraph
112         */
113        public UndirectedSubgraph<V, E> getDensestSubgraph() {
114                return bestSubGraph;
115        }
116}