280 lines
8.3 KiB
Java
280 lines
8.3 KiB
Java
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package de.normalisiert.utils.graphs;
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import java.util.Vector;
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/**
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* This is a helpclass for the search of all elementary cycles in a graph
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* with the algorithm of Johnson. For this it searches for strong connected
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* components, using the algorithm of Tarjan. The constructor gets an
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* adjacency-list of a graph. Based on this graph, it gets a nodenumber s,
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* for which it calculates the subgraph, containing all nodes
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* {s, s + 1, ..., n}, where n is the highest nodenumber in the original
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* graph (e.g. it builds a subgraph with all nodes with higher or same
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* nodenumbers like the given node s). It returns the strong connected
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* component of this subgraph which contains the lowest nodenumber of all
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* nodes in the subgraph.<br><br>
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*
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* For a description of the algorithm for calculating the strong connected
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* components see:<br>
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* Robert Tarjan: Depth-first search and linear graph algorithms. In: SIAM
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* Journal on Computing. Volume 1, Nr. 2 (1972), pp. 146-160.<br>
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* For a description of the algorithm for searching all elementary cycles in
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* a directed graph see:<br>
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* Donald B. Johnson: Finding All the Elementary Circuits of a Directed Graph.
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* SIAM Journal on Computing. Volumne 4, Nr. 1 (1975), pp. 77-84.<br><br>
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*
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* @author Frank Meyer, web_at_normalisiert_dot_de
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* @version 1.1, 22.03.2009
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*
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*/
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public class StrongConnectedComponents {
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/** Adjacency-list of original graph */
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private int[][] adjListOriginal = null;
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/** Adjacency-list of currently viewed subgraph */
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private int[][] adjList = null;
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/** Helpattribute for finding scc's */
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private boolean[] visited = null;
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/** Helpattribute for finding scc's */
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private Vector stack = null;
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/** Helpattribute for finding scc's */
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private int[] lowlink = null;
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/** Helpattribute for finding scc's */
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private int[] number = null;
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/** Helpattribute for finding scc's */
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private int sccCounter = 0;
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/** Helpattribute for finding scc's */
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private Vector currentSCCs = null;
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/**
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* Constructor.
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*
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* @param adjList adjacency-list of the graph
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*/
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public StrongConnectedComponents(int[][] adjList) {
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this.adjListOriginal = adjList;
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}
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/**
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* This method returns the adjacency-structure of the strong connected
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* component with the least vertex in a subgraph of the original graph
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* induced by the nodes {s, s + 1, ..., n}, where s is a given node. Note
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* that trivial strong connected components with just one node will not
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* be returned.
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*
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* @param node node s
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* @return SCCResult with adjacency-structure of the strong
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* connected component; null, if no such component exists
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*/
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public SCCResult getAdjacencyList(int node) {
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this.visited = new boolean[this.adjListOriginal.length];
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this.lowlink = new int[this.adjListOriginal.length];
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this.number = new int[this.adjListOriginal.length];
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this.visited = new boolean[this.adjListOriginal.length];
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this.stack = new Vector();
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this.currentSCCs = new Vector();
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this.makeAdjListSubgraph(node);
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for (int i = node; i < this.adjListOriginal.length; i++) {
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if (!this.visited[i]) {
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this.getStrongConnectedComponents(i);
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Vector nodes = this.getLowestIdComponent();
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if (nodes != null && !nodes.contains(new Integer(node)) && !nodes.contains(new Integer(node + 1))) {
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return this.getAdjacencyList(node + 1);
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} else {
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Vector[] adjacencyList = this.getAdjList(nodes);
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if (adjacencyList != null) {
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for (int j = 0; j < this.adjListOriginal.length; j++) {
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if (adjacencyList[j].size() > 0) {
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return new SCCResult(adjacencyList, j);
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}
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}
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}
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}
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}
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}
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return null;
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}
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/**
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* Builds the adjacency-list for a subgraph containing just nodes
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* >= a given index.
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*
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* @param node Node with lowest index in the subgraph
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*/
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private void makeAdjListSubgraph(int node) {
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this.adjList = new int[this.adjListOriginal.length][0];
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for (int i = node; i < this.adjList.length; i++) {
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Vector successors = new Vector();
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for (int j = 0; j < this.adjListOriginal[i].length; j++) {
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if (this.adjListOriginal[i][j] >= node) {
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successors.add(new Integer(this.adjListOriginal[i][j]));
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}
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}
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if (successors.size() > 0) {
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this.adjList[i] = new int[successors.size()];
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for (int j = 0; j < successors.size(); j++) {
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Integer succ = (Integer) successors.get(j);
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this.adjList[i][j] = succ.intValue();
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}
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}
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}
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}
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/**
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* Calculates the strong connected component out of a set of scc's, that
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* contains the node with the lowest index.
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*
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* @return Vector::Integer of the scc containing the lowest nodenumber
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*/
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private Vector getLowestIdComponent() {
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int min = this.adjList.length;
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Vector currScc = null;
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for (int i = 0; i < this.currentSCCs.size(); i++) {
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Vector scc = (Vector) this.currentSCCs.get(i);
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for (int j = 0; j < scc.size(); j++) {
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Integer node = (Integer) scc.get(j);
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if (node.intValue() < min) {
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currScc = scc;
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min = node.intValue();
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}
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}
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}
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return currScc;
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}
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/**
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* @return Vector[]::Integer representing the adjacency-structure of the
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* strong connected component with least vertex in the currently viewed
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* subgraph
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*/
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private Vector[] getAdjList(Vector nodes) {
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Vector[] lowestIdAdjacencyList = null;
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if (nodes != null) {
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lowestIdAdjacencyList = new Vector[this.adjList.length];
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for (int i = 0; i < lowestIdAdjacencyList.length; i++) {
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lowestIdAdjacencyList[i] = new Vector();
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}
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for (int i = 0; i < nodes.size(); i++) {
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int node = ((Integer) nodes.get(i)).intValue();
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for (int j = 0; j < this.adjList[node].length; j++) {
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int succ = this.adjList[node][j];
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if (nodes.contains(new Integer(succ))) {
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lowestIdAdjacencyList[node].add(new Integer(succ));
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}
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}
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}
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}
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return lowestIdAdjacencyList;
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}
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/**
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* Searchs for strong connected components reachable from a given node.
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*
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* @param root node to start from.
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*/
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private void getStrongConnectedComponents(int root) {
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this.sccCounter++;
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this.lowlink[root] = this.sccCounter;
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this.number[root] = this.sccCounter;
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this.visited[root] = true;
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this.stack.add(new Integer(root));
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for (int i = 0; i < this.adjList[root].length; i++) {
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int w = this.adjList[root][i];
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if (!this.visited[w]) {
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this.getStrongConnectedComponents(w);
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this.lowlink[root] = Math.min(lowlink[root], lowlink[w]);
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} else if (this.number[w] < this.number[root]) {
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if (this.stack.contains(new Integer(w))) {
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lowlink[root] = Math.min(this.lowlink[root], this.number[w]);
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}
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}
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}
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// found scc
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if ((lowlink[root] == number[root]) && (stack.size() > 0)) {
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int next = -1;
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Vector scc = new Vector();
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do {
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next = ((Integer) this.stack.get(stack.size() - 1)).intValue();
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this.stack.remove(stack.size() - 1);
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scc.add(new Integer(next));
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} while (this.number[next] > this.number[root]);
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// simple scc's with just one node will not be added
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if (scc.size() > 1) {
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this.currentSCCs.add(scc);
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}
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}
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}
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public static void main(String[] args) {
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boolean[][] adjMatrix = new boolean[10][];
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for (int i = 0; i < 10; i++) {
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adjMatrix[i] = new boolean[10];
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}
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/*adjMatrix[0][1] = true;
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adjMatrix[1][2] = true;
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adjMatrix[2][0] = true;
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adjMatrix[2][4] = true;
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adjMatrix[1][3] = true;
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adjMatrix[3][6] = true;
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adjMatrix[6][5] = true;
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adjMatrix[5][3] = true;
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adjMatrix[6][7] = true;
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adjMatrix[7][8] = true;
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adjMatrix[7][9] = true;
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adjMatrix[9][6] = true;*/
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adjMatrix[0][1] = true;
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adjMatrix[1][2] = true;
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adjMatrix[2][0] = true; adjMatrix[2][6] = true;
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adjMatrix[3][4] = true;
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adjMatrix[4][5] = true; adjMatrix[4][6] = true;
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adjMatrix[5][3] = true;
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adjMatrix[6][7] = true;
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adjMatrix[7][8] = true;
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adjMatrix[8][6] = true;
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adjMatrix[6][1] = true;
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int[][] adjList = AdjacencyList.getAdjacencyList(adjMatrix);
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StrongConnectedComponents scc = new StrongConnectedComponents(adjList);
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for (int i = 0; i < adjList.length; i++) {
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System.out.print("i: " + i + "\n");
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SCCResult r = scc.getAdjacencyList(i);
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if (r != null) {
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Vector[] al = scc.getAdjacencyList(i).getAdjList();
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for (int j = i; j < al.length; j++) {
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if (al[j].size() > 0) {
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System.out.print("j: " + j);
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for (int k = 0; k < al[j].size(); k++) {
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System.out.print(" _" + al[j].get(k).toString());
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}
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System.out.print("\n");
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}
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}
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System.out.print("\n");
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}
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}
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}
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}
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