tom | 0633d68 | 2014-09-10 12:10:03 -0700 | [diff] [blame] | 1 | package org.onlab.graph; |
| 2 | |
| 3 | import java.util.ArrayList; |
| 4 | import java.util.Collections; |
| 5 | import java.util.HashMap; |
| 6 | import java.util.HashSet; |
| 7 | import java.util.List; |
| 8 | import java.util.Map; |
| 9 | import java.util.Set; |
| 10 | |
| 11 | /** |
| 12 | * Tarjan algorithm for searching a graph and producing results describing |
| 13 | * the graph SCC (strongly-connected components). |
| 14 | */ |
| 15 | public class TarjanGraphSearch<V extends Vertex, E extends Edge<V>> |
| 16 | implements GraphSearch<V, E> { |
| 17 | |
| 18 | /** |
| 19 | * {@inheritDoc} |
| 20 | * <p/> |
| 21 | * This implementation produces results augmented with information on |
| 22 | * SCCs within the graph. |
| 23 | * <p/> |
| 24 | * To prevent traversal of an edge, the {@link EdgeWeight#weight} should |
| 25 | * return a negative value as an edge weight. |
| 26 | */ |
| 27 | @Override |
| 28 | public SCCResult<V, E> search(Graph<V, E> graph, EdgeWeight<V, E> weight) { |
| 29 | SCCResult<V, E> result = new SCCResult<>(graph); |
| 30 | for (V vertex : graph.getVertexes()) { |
| 31 | VertexData data = result.data(vertex); |
| 32 | if (data == null) { |
| 33 | connect(graph, vertex, weight, result); |
| 34 | } |
| 35 | } |
| 36 | return result.build(); |
| 37 | } |
| 38 | |
| 39 | /** |
| 40 | * Scans the specified graph, using recursion, and produces SCC results. |
| 41 | * |
| 42 | * @param graph graph to search |
| 43 | * @param vertex current vertex to scan and connect |
| 44 | * @param weight optional edge weight |
| 45 | * @param result graph search result |
| 46 | * @return augmentation vertexData for the current vertex |
| 47 | */ |
| 48 | private VertexData<V> connect(Graph<V, E> graph, V vertex, |
| 49 | EdgeWeight<V, E> weight, |
| 50 | SCCResult<V, E> result) { |
| 51 | VertexData<V> data = result.addData(vertex); |
| 52 | |
| 53 | // Scan through all egress edges of the current vertex. |
| 54 | for (E edge : graph.getEdgesFrom(vertex)) { |
| 55 | V nextVertex = edge.dst(); |
| 56 | |
| 57 | // If edge weight is negative, skip it. |
| 58 | if (weight != null && weight.weight(edge) < 0) { |
| 59 | continue; |
| 60 | } |
| 61 | |
| 62 | // Attempt to get the augmentation vertexData for the next vertex. |
| 63 | VertexData<V> nextData = result.data(nextVertex); |
| 64 | if (nextData == null) { |
| 65 | // Next vertex has not been visited yet, so do this now. |
| 66 | nextData = connect(graph, nextVertex, weight, result); |
| 67 | data.lowLink = Math.min(data.lowLink, nextData.lowLink); |
| 68 | |
| 69 | } else if (result.visited(nextData)) { |
| 70 | // Next vertex has been visited, which means it is in the |
| 71 | // same cluster as the current vertex. |
| 72 | data.lowLink = Math.min(data.lowLink, nextData.index); |
| 73 | } |
| 74 | } |
| 75 | |
| 76 | if (data.lowLink == data.index) { |
| 77 | result.addCluster(data); |
| 78 | } |
| 79 | return data; |
| 80 | } |
| 81 | |
| 82 | /** |
| 83 | * Graph search result augmented with SCC vertexData. |
| 84 | */ |
| 85 | public static final class SCCResult<V extends Vertex, E extends Edge<V>> |
| 86 | implements Result { |
| 87 | |
| 88 | private final Graph<V, E> graph; |
| 89 | private List<Set<V>> clusterVertexes = new ArrayList<>(); |
| 90 | private List<Set<E>> clusterEdges = new ArrayList<>(); |
| 91 | |
| 92 | private int index = 0; |
| 93 | private final Map<V, VertexData<V>> vertexData = new HashMap<>(); |
| 94 | private final List<VertexData<V>> visited = new ArrayList<>(); |
| 95 | |
| 96 | private SCCResult(Graph<V, E> graph) { |
| 97 | this.graph = graph; |
| 98 | } |
| 99 | |
| 100 | /** |
| 101 | * Returns the number of SCC clusters in the graph. |
| 102 | * |
| 103 | * @return number of clusters |
| 104 | */ |
| 105 | public int clusterCount() { |
| 106 | return clusterEdges.size(); |
| 107 | } |
| 108 | |
| 109 | /** |
| 110 | * Returns the list of strongly connected vertex clusters. |
| 111 | * |
| 112 | * @return list of strongly connected vertex sets |
| 113 | */ |
| 114 | public List<Set<V>> clusterVertexes() { |
| 115 | return clusterVertexes; |
| 116 | } |
| 117 | |
| 118 | /** |
| 119 | * Returns the list of edges linking strongly connected vertex clusters. |
| 120 | * |
| 121 | * @return list of strongly connected edge sets |
| 122 | */ |
| 123 | public List<Set<E>> clusterEdges() { |
| 124 | return clusterEdges; |
| 125 | } |
| 126 | |
| 127 | // Gets the augmentation vertexData for the specified vertex |
| 128 | private VertexData<V> data(V vertex) { |
| 129 | return vertexData.get(vertex); |
| 130 | } |
| 131 | |
| 132 | // Adds augmentation vertexData for the specified vertex |
| 133 | private VertexData<V> addData(V vertex) { |
| 134 | VertexData<V> d = new VertexData<>(vertex, index); |
| 135 | vertexData.put(vertex, d); |
| 136 | visited.add(0, d); |
| 137 | index++; |
| 138 | return d; |
| 139 | } |
| 140 | |
| 141 | // Indicates whether the given vertex has been visited |
| 142 | private boolean visited(VertexData data) { |
| 143 | return visited.contains(data); |
| 144 | } |
| 145 | |
| 146 | // Adds a new cluster for the specified vertex |
| 147 | private void addCluster(VertexData data) { |
| 148 | Set<V> vertexes = findClusterVertices(data); |
| 149 | clusterVertexes.add(vertexes); |
| 150 | clusterEdges.add(findClusterEdges(vertexes)); |
| 151 | } |
| 152 | |
| 153 | private Set<V> findClusterVertices(VertexData data) { |
| 154 | VertexData<V> nextVertexData; |
| 155 | Set<V> vertexes = new HashSet<>(); |
| 156 | do { |
| 157 | nextVertexData = visited.remove(0); |
| 158 | vertexes.add(nextVertexData.vertex); |
| 159 | } while (data != nextVertexData); |
| 160 | return Collections.unmodifiableSet(vertexes); |
| 161 | } |
| 162 | |
| 163 | private Set<E> findClusterEdges(Set<V> vertexes) { |
| 164 | Set<E> edges = new HashSet<>(); |
| 165 | for (V vertex : vertexes) { |
| 166 | for (E edge : graph.getEdgesFrom(vertex)) { |
| 167 | if (vertexes.contains((edge.dst()))) { |
| 168 | edges.add(edge); |
| 169 | } |
| 170 | } |
| 171 | } |
| 172 | return Collections.unmodifiableSet(edges); |
| 173 | } |
| 174 | |
| 175 | public SCCResult<V, E> build() { |
| 176 | clusterVertexes = Collections.unmodifiableList(clusterVertexes); |
| 177 | clusterEdges = Collections.unmodifiableList(clusterEdges); |
| 178 | return this; |
| 179 | } |
| 180 | } |
| 181 | |
| 182 | // Augments the vertex to assist in determining SCC clusters. |
| 183 | private static final class VertexData<V extends Vertex> { |
| 184 | final V vertex; |
| 185 | int index; |
| 186 | int lowLink; |
| 187 | |
| 188 | private VertexData(V vertex, int index) { |
| 189 | this.vertex = vertex; |
| 190 | this.index = index; |
| 191 | this.lowLink = index; |
| 192 | } |
| 193 | } |
| 194 | |
| 195 | } |