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(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 List <MinCutEdge <T> > ComputeMinCut(IDiGraph <T> graph,
T source, T sink)
{
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 IFlowOperators<int> operator implementation during initialization.");
}
}
var edmondsKarpMaxFlow = new EdmondKarpMaxFlow <T, W>(@operator);
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(maxFlowResidualGraph, source);
var result = new List <MinCutEdge <T> >();
foreach (var vertex in reachableVertices)
{
foreach (var edge in graph.GetVertex(vertex).OutEdges)
{
//if unreachable
if (!reachableVertices.Contains(edge.TargetVertexKey))
{
result.Add(new MinCutEdge <T>(vertex, edge.TargetVertexKey));
}
}
}
return(result);
}
/// <summary>
/// Get Max Match from Given BiPartitioned Graph.
/// </summary>
private List <MatchEdge <T> > getMaxBiPartiteMatching(IGraph <T> graph,
Dictionary <int, List <T> > partitions)
{
//add unit edges from dymmy source to group 1 vertices
var dummySource = @operator.GetRandomUniqueVertex();
if (graph.ContainsVertex(dummySource))
{
throw new Exception("Dummy vertex provided is not unique to given graph.");
}
//add unit edges from group 2 vertices to sink
var dummySink = @operator.GetRandomUniqueVertex();
if (graph.ContainsVertex(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>(@operator);
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);
}