private WeightedMultigraph<Vertex, LabeledWeightedEdge> step1() {
logger.debug("<enter");
WeightedMultigraph<Vertex, LabeledWeightedEdge> g =
new WeightedMultigraph<Vertex, LabeledWeightedEdge>(LabeledWeightedEdge.class);
for (int i = 0; i < steinerNodes.size(); i++) {
g.addVertex(steinerNodes.get(i));
}
BellmanFordShortestPath<Vertex, LabeledWeightedEdge> path;
for (int i = 0; i < steinerNodes.size(); i++) {
path =
new BellmanFordShortestPath<Vertex, LabeledWeightedEdge>(this.graph, steinerNodes.get(i));
for (int j = 0; j < steinerNodes.size(); j++) {
if (i == j) continue;
if (g.containsEdge(steinerNodes.get(i), steinerNodes.get(j))) continue;
String id = "e" + String.valueOf(i) + String.valueOf(j);
LabeledWeightedEdge e = new LabeledWeightedEdge(id, new URI(id, null, null), null);
g.addEdge(steinerNodes.get(i), steinerNodes.get(j), e);
g.setEdgeWeight(e, path.getCost(steinerNodes.get(j)));
}
}
logger.debug("exit>");
return g;
}
private void runAlgorithm() {
logger.debug("<enter");
WeightedMultigraph<Vertex, LabeledWeightedEdge> g1 = step1();
// GraphUtil.printGraph(g1);
// GraphUtil.printGraphSimple(g1);
if (g1.vertexSet().size() < 2) {
this.tree = g1;
return;
}
WeightedMultigraph<Vertex, LabeledWeightedEdge> g2 = step2(g1);
// GraphUtil.printGraph(g2);
// GraphUtil.printGraphSimple(g2);
WeightedMultigraph<Vertex, LabeledWeightedEdge> g3 = step3(g2);
// GraphUtil.printGraph(g3);
// GraphUtil.printGraphSimple(g3);
WeightedMultigraph<Vertex, LabeledWeightedEdge> g4 = step4(g3);
// GraphUtil.printGraph(g4);
// GraphUtil.printGraphSimple(g4);
WeightedMultigraph<Vertex, LabeledWeightedEdge> g5 = step5(g4);
// GraphUtil.printGraph(g5);
// GraphUtil.printGraphSimple(g5);
this.tree = g5;
logger.debug("exit>");
}
private WeightedMultigraph<Vertex, LabeledWeightedEdge> step2(
WeightedMultigraph<Vertex, LabeledWeightedEdge> g1) {
logger.debug("<enter");
KruskalMinimumSpanningTree<Vertex, LabeledWeightedEdge> mst =
new KruskalMinimumSpanningTree<Vertex, LabeledWeightedEdge>(g1);
// System.out.println("Total MST Cost: " + mst.getSpanningTreeCost());
Set<LabeledWeightedEdge> edges = mst.getEdgeSet();
WeightedMultigraph<Vertex, LabeledWeightedEdge> g2 =
new WeightedMultigraph<Vertex, LabeledWeightedEdge>(LabeledWeightedEdge.class);
List<LabeledWeightedEdge> edgesSortedByLabel = new ArrayList<LabeledWeightedEdge>();
for (LabeledWeightedEdge e : edges) edgesSortedByLabel.add(e);
Collections.sort(edgesSortedByLabel, new EdgeComparatorByLabel());
for (LabeledWeightedEdge edge : edgesSortedByLabel) {
// //just for test, forcing to select another equal minimal spanning tree
// if (g1.getEdgeSource(edge).getLabel().equalsIgnoreCase("v1") &&
// g1.getEdgeTarget(edge).getLabel().equalsIgnoreCase("v3") ) {
// Vertex v2 = steinerNodes.get(1);
// g2.addVertex(g1.getEdgeTarget(edge));
// g2.addVertex(v2);
// LabeledWeightedEdge e = new LabeledWeightedEdge("e");
// g2.setEdgeWeight(e, g1.getEdgeWeight(edge));
// g2.addEdge(g1.getEdgeTarget(edge), v2, e);
// } else
{
g2.addVertex(edge.getSource());
g2.addVertex(edge.getTarget());
g2.addEdge(edge.getSource(), edge.getTarget(), edge);
}
}
logger.debug("exit>");
return g2;
}
private WeightedMultigraph<Vertex, LabeledWeightedEdge> step5(
WeightedMultigraph<Vertex, LabeledWeightedEdge> g4) {
logger.debug("<enter");
WeightedMultigraph<Vertex, LabeledWeightedEdge> g5 = g4;
List<Vertex> nonSteinerLeaves = new ArrayList<Vertex>();
Set<Vertex> vertexSet = g4.vertexSet();
for (Vertex vertex : vertexSet) {
if (g5.degreeOf(vertex) == 1 && steinerNodes.indexOf(vertex) == -1) {
nonSteinerLeaves.add(vertex);
}
}
Vertex source, target;
for (int i = 0; i < nonSteinerLeaves.size(); i++) {
source = nonSteinerLeaves.get(i);
do {
LabeledWeightedEdge e = g5.edgesOf(source).toArray(new LabeledWeightedEdge[0])[0];
target = this.graph.getEdgeTarget(e);
// this should not happen, but just in case of ...
if (target.equals(source)) target = e.getSource();
g5.removeVertex(source);
source = target;
} while (g5.degreeOf(source) == 1 && steinerNodes.indexOf(source) == -1);
}
logger.debug("exit>");
return g5;
}
private WeightedMultigraph<Vertex, LabeledWeightedEdge> step3(
WeightedMultigraph<Vertex, LabeledWeightedEdge> g2) {
logger.debug("<enter");
WeightedMultigraph<Vertex, LabeledWeightedEdge> g3 =
new WeightedMultigraph<Vertex, LabeledWeightedEdge>(LabeledWeightedEdge.class);
Set<LabeledWeightedEdge> edges = g2.edgeSet();
DijkstraShortestPath<Vertex, LabeledWeightedEdge> path;
Vertex source, target;
for (LabeledWeightedEdge edge : edges) {
source = edge.getSource();
target = edge.getTarget();
path = new DijkstraShortestPath<Vertex, LabeledWeightedEdge>(this.graph, source, target);
List<LabeledWeightedEdge> pathEdges = path.getPathEdgeList();
if (pathEdges == null) continue;
for (int i = 0; i < pathEdges.size(); i++) {
if (g3.edgeSet().contains(pathEdges.get(i))) continue;
source = pathEdges.get(i).getSource();
target = pathEdges.get(i).getTarget();
if (!g3.vertexSet().contains(source)) g3.addVertex(source);
if (!g3.vertexSet().contains(target)) g3.addVertex(target);
g3.addEdge(source, target, pathEdges.get(i));
}
}
logger.debug("exit>");
return g3;
}
public EdgeBetweennessGraph(WeightedMultigraph<String, DefaultWeightedEdge> originalGraph) {
super(DefaultWeightedEdge.class); // Constructor inherented from parent class
// 1. Initialize the edge betweenness digraph
// 1.1. Add vertices
for (String thisVertex : originalGraph.vertexSet()) this.addVertex(thisVertex);
// 1.2. Add edges
for (DefaultWeightedEdge thisEdge : originalGraph.edgeSet()) {
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
String sendingName = originalGraph.getEdgeSource(thisEdge);
String receivingName = originalGraph.getEdgeTarget(thisEdge);
this.addEdge(sendingName, receivingName, newEdge);
this.setEdgeWeight(newEdge, 0.0);
}
// 1.3. Create corresponding unweighted graph
// 1.3.1. Add vertices
WeightedMultigraph<String, DefaultWeightedEdge> originalUnweightedGraph =
new WeightedMultigraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
for (String thisVertex : originalGraph.vertexSet())
originalUnweightedGraph.addVertex(thisVertex);
// 1.3.2. Add edges
for (DefaultWeightedEdge thisEdge : originalGraph.edgeSet()) {
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
String sendingName = originalGraph.getEdgeSource(thisEdge);
String receivingName = originalGraph.getEdgeTarget(thisEdge);
originalUnweightedGraph.addEdge(sendingName, receivingName, newEdge);
originalUnweightedGraph.setEdgeWeight(newEdge, 1.0);
}
for (String thisVertex : this.vertexSet()) {
// 2. Create shortest-path graph for every vertex by Dijkstra algorithm
Multigraph<String, DefaultEdge> shortestPathDigraph =
DijkstraAlgorithm(originalUnweightedGraph, thisVertex);
// 3. Calculate the contribution of current vertex's shortest-path graph to final edge
// betweenness (Newman algorithm)
SimpleWeightedGraph<String, DefaultWeightedEdge> edgeBetweennessDigraph =
NewmanAlgorithm(shortestPathDigraph, thisVertex);
// 4. Update final edge betweenness digraph with current vertex's shortest-path graph
if (edgeBetweennessDigraph != null)
for (DefaultWeightedEdge thisEdge : edgeBetweennessDigraph.edgeSet()) {
String sourceVertex = edgeBetweennessDigraph.getEdgeSource(thisEdge);
String targetVertex = edgeBetweennessDigraph.getEdgeTarget(thisEdge);
double betweennessWeight = edgeBetweennessDigraph.getEdgeWeight(thisEdge);
DefaultWeightedEdge edgeInWholeGraph = this.getEdge(sourceVertex, targetVertex);
double newWeight = this.getEdgeWeight(edgeInWholeGraph) + betweennessWeight;
this.setEdgeWeight(edgeInWholeGraph, newWeight);
}
}
// 5. Revise the edge betweenness digraph with the original active power digraph
for (DefaultWeightedEdge thisEdge : this.edgeSet()) {
String sourceVertex = this.getEdgeSource(thisEdge);
String targetVertex = this.getEdgeTarget(thisEdge);
double betweennessWeight = this.getEdgeWeight(thisEdge);
DefaultWeightedEdge edgeInWholeGraph = originalGraph.getEdge(sourceVertex, targetVertex);
double newWeight = betweennessWeight / originalGraph.getEdgeWeight(edgeInWholeGraph);
this.setEdgeWeight(thisEdge, newWeight);
// System.out.println("Final edge betweenness between " + sourceVertex + " and " +
// targetVertex + ": " + newWeight);
}
}
// Create shortest-path graph for every vertex by depth-first traversal algorithm
private Multigraph<String, DefaultEdge> DijkstraAlgorithm(
WeightedMultigraph<String, DefaultWeightedEdge> originalGraph, String thisVertex) {
// 1. Simplify the multi-graph of the active power flow into a simple graph
SimpleWeightedGraph<String, DefaultWeightedEdge> originalSimpleGraph =
new SimpleWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
for (String curVertex : originalGraph.vertexSet()) originalSimpleGraph.addVertex(curVertex);
for (DefaultWeightedEdge curEdge : originalGraph.edgeSet()) {
String sourceVertex = originalGraph.getEdgeSource(curEdge);
String targetVertex = originalGraph.getEdgeTarget(curEdge);
if (originalSimpleGraph.containsEdge(sourceVertex, targetVertex)) {
DefaultWeightedEdge modifiedEdge = originalSimpleGraph.getEdge(sourceVertex, targetVertex);
double newEdgeWeight =
originalSimpleGraph.getEdgeWeight(modifiedEdge) + originalGraph.getEdgeWeight(curEdge);
originalSimpleGraph.setEdgeWeight(modifiedEdge, newEdgeWeight);
} else {
DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
originalSimpleGraph.addEdge(sourceVertex, targetVertex, newEdge);
originalSimpleGraph.setEdgeWeight(newEdge, originalGraph.getEdgeWeight(curEdge));
}
}
// Issue (2010/10/25): Maybe larger amount of active power transfer still means weaker
// relationship between the two terminal buses of a certain branch,
// thus originalSimpleGraph other than inverseGraph should be used here.
// Use the inverse of active power to build a new weighted directed graph (the larger the active
// power is, the close the two buses will be)
// SimpleDirectedWeightedGraph<String, DefaultWeightedEdge> inverseGraph =
// new SimpleDirectedWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
// for (String curVertex : originalSimpleGraph.vertexSet())
// inverseGraph.addVertex(curVertex);
// for (DefaultWeightedEdge curEdge : originalSimpleGraph.edgeSet()) {
// String sourceVertex = originalSimpleGraph.getEdgeSource(curEdge);
// String targetVertex = originalSimpleGraph.getEdgeTarget(curEdge);
// DefaultWeightedEdge newEdge = new DefaultWeightedEdge();
// inverseGraph.addEdge(sourceVertex, targetVertex, newEdge);
// inverseGraph.setEdgeWeight(newEdge, 1 / originalSimpleGraph.getEdgeWeight(curEdge));
// }
// 2. Initialize the map of vertices and the corresponding weights (distance from current vertex
// to the first vertex)
HashMap<String, Double> mapVertexShortestDistance = new HashMap<String, Double>();
// for (String thisOriginalVertex : inverseGraph.vertexSet())
for (String thisOriginalVertex : originalSimpleGraph.vertexSet())
mapVertexShortestDistance.put(thisOriginalVertex, 10E10);
// The weight of the first vertex is zero
mapVertexShortestDistance.put(thisVertex, 0.0);
// 3. Depth-first traversing, update the shortest-path values
Stack<String> bfiVertices =
new Stack<String>(); // Stack to store passed vertices in a breadth-first traversing
// The map of a weighted edge and the flag of having been visited
// HashMap<DefaultWeightedEdge, Boolean> mapEdgeVisited = new HashMap<DefaultWeightedEdge,
// Boolean>();
// for (DefaultWeightedEdge thisEdge : inverseGraph.edgeSet())
// mapEdgeVisited.put(thisEdge, false);
String currentVertex = thisVertex;
bfiVertices.push(currentVertex);
// System.out.println(bfiVertices.toString());
while (!bfiVertices.isEmpty()) {
// Operate the following codes for those edges started with current vertex
boolean hasNewEdge = false;
// for (DefaultWeightedEdge curEdge : inverseGraph.outgoingEdgesOf(currentVertex)) {
for (DefaultWeightedEdge curEdge : originalSimpleGraph.edgesOf(currentVertex)) {
// if (!mapEdgeVisited.get(curEdge)) { // Used for those edges that have not been treated
// yet
// 3.1. Mark current edge as already been visited
// mapEdgeVisited.put(curEdge, true);
// String nextVertex = inverseGraph.getEdgeTarget(curEdge);
String nextVertex = originalSimpleGraph.getEdgeTarget(curEdge);
// 3.2. Update shortest-path values
double curSD = mapVertexShortestDistance.get(currentVertex);
// double edgeWeight = inverseGraph.getEdgeWeight(curEdge);
double edgeWeight = originalSimpleGraph.getEdgeWeight(curEdge);
double newSD = curSD + edgeWeight;
if (mapVertexShortestDistance.get(nextVertex) > newSD) {
hasNewEdge = true;
mapVertexShortestDistance.put(nextVertex, newSD);
// 3.3. Push the target vertex of current edge into the stack
bfiVertices.push(nextVertex);
// System.out.println(bfiVertices.toString());
break;
// System.out.println("New shortest path [" + nextVertex + "]: " + newSD);
}
// }
}
if (!hasNewEdge) {
bfiVertices.pop();
}
if (!bfiVertices.isEmpty()) currentVertex = bfiVertices.peek();
}
// 4. Create shortest-path digraph of current vertex
// 4.1. Initialize the shortest-path digraph
Multigraph<String, DefaultEdge> shortestPathGraph =
new Multigraph<String, DefaultEdge>(DefaultEdge.class);
// 4.2. Add all qualified edges
// for (DefaultWeightedEdge curEdge : inverseGraph.edgeSet()) {
for (DefaultWeightedEdge curEdge : originalSimpleGraph.edgeSet()) {
// 4.2.1. Evaluate if current edge is suitable
// String sourceVertex = inverseGraph.getEdgeSource(curEdge);
// String targetVertex = inverseGraph.getEdgeTarget(curEdge);
String sourceVertex = originalSimpleGraph.getEdgeSource(curEdge);
String targetVertex = originalSimpleGraph.getEdgeTarget(curEdge);
// if (Math.abs(inverseGraph.getEdgeWeight(curEdge) -
if (originalSimpleGraph.getEdgeWeight(curEdge) > 1.0E-5) {
if (Math.abs(
originalSimpleGraph.getEdgeWeight(curEdge)
- (mapVertexShortestDistance.get(targetVertex)
- mapVertexShortestDistance.get(sourceVertex)))
< 1.0E-5) {
// 4.2.2. Add suitable edge that found just now
DefaultEdge newEdge = new DefaultEdge();
if (!shortestPathGraph.containsVertex(sourceVertex))
shortestPathGraph.addVertex(sourceVertex);
if (!shortestPathGraph.containsVertex(targetVertex))
shortestPathGraph.addVertex(targetVertex);
shortestPathGraph.addEdge(sourceVertex, targetVertex, newEdge);
}
}
}
return shortestPathGraph;
}
