Beispiel #1
0
        FindAllPairShortestPaths(WeightedDiGraph <T, W> graph)
        {
            var workGraph = graph.Clone();

            //add an extra vertex with zero weight edge to all nodes
            var randomVetex = operators.RandomVertex();

            if (workGraph.Vertices.ContainsKey(randomVetex))
            {
                throw new Exception("Random Vertex is not unique for given graph.");
            }
            workGraph.AddVertex(randomVetex);

            foreach (var vertex in workGraph.Vertices)
            {
                workGraph.AddEdge(randomVetex, vertex.Key, operators.DefaultValue);
            }

            //now compute shortest path from random vertex to all other vertices
            var bellmanFordSp  = new BellmanFordShortestPath <T, W>(operators);
            var bellFordResult = new Dictionary <T, W>();

            foreach (var vertex in workGraph.Vertices)
            {
                var result = bellmanFordSp.FindShortestPath(workGraph, randomVetex, vertex.Key);
                bellFordResult.Add(vertex.Key, result.Length);
            }

            //adjust edges so that all edge values are now +ive
            foreach (var vertex in workGraph.Vertices)
            {
                foreach (var edge in vertex.Value.OutEdges.ToList())
                {
                    vertex.Value.OutEdges[edge.Key] = operators.Substract(
                        operators.Sum(bellFordResult[vertex.Key], edge.Value),
                        bellFordResult[edge.Key.Value]);
                }
            }

            workGraph.RemoveVertex(randomVetex);
            //now run dijikstra for all pairs of vertices
            //trace path
            var dijikstras  = new DijikstraShortestPath <T, W>(operators);
            var finalResult = new List <AllPairShortestPathResult <T, W> >();

            foreach (var vertexA in workGraph.Vertices)
            {
                foreach (var vertexB in workGraph.Vertices)
                {
                    var source = vertexA.Key;
                    var dest   = vertexB.Key;
                    var sp     = dijikstras.FindShortestPath(workGraph, source, dest);

                    //no path exists
                    if (sp.Length.Equals(operators.MaxValue))
                    {
                        continue;
                    }

                    var distance = sp.Length;
                    var path     = sp.Path;

                    finalResult.Add(new AllPairShortestPathResult <T, W>(source, dest, distance, path));
                }
            }

            return(finalResult);
        }
Beispiel #2
0
        FindAllPairShortestPaths(IDiGraph <T> graph)
        {
            if (this.@operator == null)
            {
                throw new ArgumentException("Provide an operator implementation for generic type W during initialization.");
            }

            if (!graph.IsWeightedGraph)
            {
                if ([email protected]() != typeof(int))
                {
                    throw new ArgumentException("Edges of unweighted graphs are assigned an imaginary weight of one (1)." +
                                                "Provide an appropriate IJohnsonsShortestPathOperators<T, int> operator implementation during initialization.");
                }
            }

            var workGraph = clone(graph);

            //add an extra vertex with zero weight edge to all nodes
            var randomVetex = @operator.RandomVertex();

            if (workGraph.Vertices.ContainsKey(randomVetex))
            {
                throw new Exception("Random Vertex is not unique for given graph.");
            }
            workGraph.AddVertex(randomVetex);

            foreach (var vertex in workGraph.Vertices)
            {
                workGraph.AddEdge(randomVetex, vertex.Key, @operator.DefaultValue);
            }

            //now compute shortest path from random vertex to all other vertices
            var bellmanFordSp  = new BellmanFordShortestPath <T, W>(@operator);
            var bellFordResult = new Dictionary <T, W>();

            foreach (var vertex in workGraph.Vertices)
            {
                var result = bellmanFordSp.FindShortestPath(workGraph, randomVetex, vertex.Key);
                bellFordResult.Add(vertex.Key, result.Length);
            }

            //adjust edges so that all edge values are now +ive
            foreach (var vertex in workGraph.Vertices)
            {
                foreach (var edge in vertex.Value.OutEdges.ToList())
                {
                    vertex.Value.OutEdges[edge.Key] = @operator.Substract(
                        @operator.Sum(bellFordResult[vertex.Key], edge.Value),
                        bellFordResult[edge.Key.Key]);
                }
            }

            workGraph.RemoveVertex(randomVetex);
            //now run dijikstra for all pairs of vertices
            //trace path
            var dijikstras  = new DijikstraShortestPath <T, W>(@operator);
            var finalResult = new List <AllPairShortestPathResult <T, W> >();

            foreach (var vertexA in workGraph.Vertices)
            {
                foreach (var vertexB in workGraph.Vertices)
                {
                    var source = vertexA.Key;
                    var dest   = vertexB.Key;
                    var sp     = dijikstras.FindShortestPath(workGraph, source, dest);

                    //no path exists
                    if (sp.Length.Equals(@operator.MaxValue))
                    {
                        continue;
                    }

                    var distance = sp.Length;
                    var path     = sp.Path;

                    finalResult.Add(new AllPairShortestPathResult <T, W>(source, dest, distance, path));
                }
            }

            return(finalResult);
        }