JGraphT - apply BFS to WeightedGraph

问题

I have written the code finding the optimal path for a Weighted Graph:

SimpleDirectedWeightedGraph<String, DefaultWeightedEdge> graph =
                new SimpleDirectedWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
graph.addVertex("1");
graph.addVertex("2");
graph.addVertex("3");
graph.addVertex("4");
graph.addVertex("5");

DefaultWeightedEdge e1 = graph.addEdge("1", "2");
graph.setEdgeWeight(e1, 5);
DefaultWeightedEdge e2 = graph.addEdge("2", "3");
graph.setEdgeWeight(e2, 10);
DefaultWeightedEdge e3 = graph.addEdge("2", "4");
graph.setEdgeWeight(e3, 2);
DefaultWeightedEdge e4 = graph.addEdge("4", "5");
graph.setEdgeWeight(e4, 2);
DefaultWeightedEdge e5 = graph.addEdge("5", "3");
graph.setEdgeWeight(e5, 2);

System.out.println("Shortest path from vertex 1 to vertex 3:");
List shortest_path = DijkstraShortestPath.findPathBetween(graph, "1", "3");
System.out.println(shortest_path);

It returns the correct, shortest path: 1->2->4->5->3. My problem now is - for the same graph, I want to obtain the path containing the fewest number of transfers between vertices (in this case it would be 1->2->3). For this use-case the BFS would be the perfect solution. Is there a way to somehow use the BreadthFirstIterator from JGraphT API or do I have to write an algorithm by myself?

回答1:

The simplest solution would be to ignore each of the edge weights and calculate the shortest path as per Dijkstra's algorithm.

It is possible to create an unweighted directed graph from a weighted directed graph with the AsUnweightedDirectedGraph class. This simply overrides the getEdgeWeight method for each edge and returns 1.0, i.e. the default weight.

Graph<String, DefaultWeightedEdge> unweightedGraph = new AsUnweightedDirectedGraph<>(graph);
List<DefaultWeightedEdge> path = DijkstraShortestPath.findPathBetween(unweightedGraph, "1", "3");
System.out.println(path); // prints [(1 : 2), (2 : 3)]

This might not provide the best performance. To improve it, you can build your own BreadthFirstIterator to just iterate through the graph. This code is based on this class, but updated to match the more recent versions of JGraphT. It provides a BFSShortestPath class that finds the shortest path between two vertices with a BFS, whatever the weight on each edge.

public class Test {

    public static void main(String[] args) {
        SimpleDirectedWeightedGraph<String, DefaultWeightedEdge> graph =
                new SimpleDirectedWeightedGraph<String, DefaultWeightedEdge>(DefaultWeightedEdge.class);
        graph.addVertex("1");
        graph.addVertex("2");
        graph.addVertex("3");
        graph.addVertex("4");
        graph.addVertex("5");

        DefaultWeightedEdge e1 = graph.addEdge("1", "2");
        graph.setEdgeWeight(e1, 5);
        DefaultWeightedEdge e2 = graph.addEdge("2", "3");
        graph.setEdgeWeight(e2, 10);
        DefaultWeightedEdge e3 = graph.addEdge("2", "4");
        graph.setEdgeWeight(e3, 2);
        DefaultWeightedEdge e4 = graph.addEdge("4", "5");
        graph.setEdgeWeight(e4, 2);
        DefaultWeightedEdge e5 = graph.addEdge("5", "3");
        graph.setEdgeWeight(e5, 2);

        System.out.println(BFSShortestPath.findPathBetween(graph, "1", "3"));
    }

}

final class BFSShortestPath {

    private BFSShortestPath() {} // ensure non-instantiability.

    public static <V, E> List<E> findPathBetween(Graph<V, E> graph, V startVertex, V endVertex) {
        MyBreadthFirstIterator<V, E> iter = new MyBreadthFirstIterator<>(graph, startVertex);
        while (iter.hasNext()) {
            Object vertex = iter.next();
            if (vertex.equals(endVertex)) {
                return createPath(iter, endVertex);
            }
        }
        return null;
    }

    private static <V, E> List<E> createPath(MyBreadthFirstIterator<V, E> iter, V endVertex) {
        List<E> path = new ArrayList<E>();
        while (true) {
            E edge = iter.getSpanningTreeEdge(endVertex);
            if (edge == null) {
                break;
            }
            path.add(edge);
            endVertex = Graphs.getOppositeVertex(iter.getGraph(), edge, endVertex);
        }
        Collections.reverse(path);
        return path;
    }

    private static class MyBreadthFirstIterator<V, E> extends BreadthFirstIterator<V, E> {

        public MyBreadthFirstIterator(Graph<V, E> g, V startVertex) {
            super(g, startVertex);
        }

        @Override
        protected void encounterVertex(V vertex, E edge) {
            super.encounterVertex(vertex, edge);
            putSeenData(vertex, edge);
        }

        @SuppressWarnings("unchecked")
        public E getSpanningTreeEdge(V vertex) {
            return (E) getSeenData(vertex);
        }

    }
}

来源：https://stackoverflow.com/questions/32935692/jgrapht-apply-bfs-to-weightedgraph