public void EdmondKarp_Smoke_Test()
{
var graph = new WeightedDiGraph <char, int>();
graph.AddVertex('S');
graph.AddVertex('A');
graph.AddVertex('B');
graph.AddVertex('C');
graph.AddVertex('D');
graph.AddVertex('T');
graph.AddEdge('S', 'A', 10);
graph.AddEdge('S', 'C', 10);
graph.AddEdge('A', 'B', 4);
graph.AddEdge('A', 'C', 2);
graph.AddEdge('A', 'D', 8);
graph.AddEdge('B', 'T', 10);
graph.AddEdge('C', 'D', 9);
graph.AddEdge('D', 'B', 6);
graph.AddEdge('D', 'T', 10);
var algo = new EdmondKarpMaxFlow <char, int>(new EdmondKarpOperators());
var result = algo.ComputeMaxFlow(graph, 'S', 'T');
Assert.AreEqual(result, 19);
}
public List <MinCutEdge <T> > ComputeMinCut(WeightedDiGraph <T, W> graph,
T source, T sink)
{
var edmondsKarpMaxFlow = new EdmondKarpMaxFlow <T, W>(operators);
var maxFlowResidualGraph = edmondsKarpMaxFlow
.ComputeMaxFlowAndReturnResidualGraph(graph, source, sink);
//according to Min Max theory
//the Min Cut can be obtained by Finding edges
//from Reachable Vertices from Source
//to unreachable vertices in residual graph
var reachableVertices = GetReachable(graph, maxFlowResidualGraph, source);
var result = new List <MinCutEdge <T> >();
foreach (var vertex in reachableVertices)
{
foreach (var edge in graph.Vertices[vertex].OutEdges)
{
//if unreachable
if (!reachableVertices.Contains(edge.Key.Value))
{
result.Add(new MinCutEdge <T>(vertex, edge.Key.Value));
}
}
}
return(result);
}
public void EdmondKarp_AdjacencyMatrixGraph_Smoke_Test()
{
var graph = new Advanced.Algorithms.DataStructures.Graph.AdjacencyMatrix.WeightedDiGraph <char, int>();
graph.AddVertex('S');
graph.AddVertex('A');
graph.AddVertex('B');
graph.AddVertex('C');
graph.AddVertex('D');
graph.AddVertex('T');
graph.AddEdge('S', 'A', 10);
graph.AddEdge('S', 'C', 10);
graph.AddEdge('A', 'B', 4);
graph.AddEdge('A', 'C', 2);
graph.AddEdge('A', 'D', 8);
graph.AddEdge('B', 'T', 10);
graph.AddEdge('C', 'D', 9);
graph.AddEdge('D', 'B', 6);
graph.AddEdge('D', 'T', 10);
var algorithm = new EdmondKarpMaxFlow <char, int>(new EdmondKarpOperators());
var result = algorithm.ComputeMaxFlow(graph, 'S', 'T');
Assert.AreEqual(result, 19);
}
/// <summary>
/// Get Max Match from Given BiPartitioned Graph
/// </summary>
/// <param name="graph"></param>
/// <param name="partitions"></param>
/// <returns></returns>
private List <MatchEdge <T> > GetMaxBiPartiteMatching(Graph <T> graph,
Dictionary <int, List <T> > partitions)
{
//add unit edges from dymmy source to group 1 vertices
var dummySource = operators.GetRandomUniqueVertex();
if (graph.Vertices.ContainsKey(dummySource))
{
throw new Exception("Dummy vertex provided is not unique to given graph.");
}
//add unit edges from group 2 vertices to sink
var dummySink = operators.GetRandomUniqueVertex();
if (graph.Vertices.ContainsKey(dummySink))
{
throw new Exception("Dummy vertex provided is not unique to given graph.");
}
var workGraph = createFlowGraph(graph, dummySource, dummySink, partitions);
//run ford fulkerson using edmon karp method
var fordFulkerson = new EdmondKarpMaxFlow <T, int>(operators);
var flowPaths = fordFulkerson
.ComputeMaxFlowAndReturnFlowPath(workGraph, dummySource, dummySink);
//now gather all group1 to group 2 edges in residual graph with positive flow
var result = new List <MatchEdge <T> >();
foreach (var path in flowPaths)
{
result.Add(new MatchEdge <T>(path[1], path[2]));
}
return(result);
}
