public void Run()
{
Render("flowGraph", true);
// add reversed edges
reversedEdgeAugmentor.AddReversedEdges();
// render with reversed edges
Render("flowGraphWithReversedEdges", true);
// create max flow algorithm
this.maxFlow = new PushRelabelMaximumFlowAlgorithm(
this.graph,
this.capacities,
this.reversedEdgeAugmentor.ReversedEdges
);
// compute max flow
double f = this.maxFlow.Compute(s, t);
Console.WriteLine("Maximum flow: {0}", f);
// clean up
reversedEdgeAugmentor.RemoveReversedEdges();
// render without reversed edges
Render("flowWithOutReversedEdges", true);
}
public void SimpleGraph(MaximumFlowAlgorithm maxFlow)
{
double flow = maxFlow.Compute(source, sink);
Assert.AreEqual(23, flow, double.Epsilon);
Assert.IsTrue(IsFlow(maxFlow));
Assert.IsTrue(IsOptimal(maxFlow));
}
private void Initialize()
{
this.reverser = new ReversedEdgeAugmentorAlgorithm(this.VisitedGraph);
this.reverser.ReversedEdgeAdded += new EdgeEventHandler(reverser_ReversedEdgeAdded);
this.maxFlowF1 = new PushRelabelMaximumFlowAlgorithm(
this.VisitedGraph,
this.capacities,
this.reverser.ReversedEdges);
}
private bool IsFlow(MaximumFlowAlgorithm maxFlow)
{
// check edge flow values
foreach (IVertex u in maxFlow.VisitedGraph.Vertices)
{
foreach (IEdge a in maxFlow.VisitedGraph.OutEdges(u))
{
if (maxFlow.Capacities[a] > 0)
if ((maxFlow.ResidualCapacities[a] + maxFlow.ResidualCapacities[maxFlow.ReversedEdges[a]]
!= maxFlow.Capacities[a])
|| (maxFlow.ResidualCapacities[a] < 0)
|| (maxFlow.ResidualCapacities[maxFlow.ReversedEdges[a]] < 0))
return false;
}
}
// check conservation
VertexDoubleDictionary inFlows = new VertexDoubleDictionary();
VertexDoubleDictionary outFlows = new VertexDoubleDictionary();
foreach (IVertex u in maxFlow.VisitedGraph.Vertices)
{
inFlows[u] = 0;
outFlows[u] = 0;
}
foreach (IVertex u in maxFlow.VisitedGraph.Vertices)
{
foreach (IEdge e in maxFlow.VisitedGraph.OutEdges(u))
{
if (maxFlow.Capacities[e] > 0)
{
double flow = maxFlow.Capacities[e] - maxFlow.ResidualCapacities[e];
inFlows[e.Target] += flow;
outFlows[e.Source] += flow;
}
}
}
foreach (IVertex u in maxFlow.VisitedGraph.Vertices)
{
if (u != source && u != sink)
if (inFlows[u] != outFlows[u])
return false;
}
return true;
}
private bool IsOptimal(MaximumFlowAlgorithm maxFlow)
{
// check if mincut is saturated...
FilteredVertexListGraph residualGraph = new FilteredVertexListGraph(
maxFlow.VisitedGraph,
new ReversedResidualEdgePredicate(maxFlow.ResidualCapacities, maxFlow.ReversedEdges)
);
BreadthFirstSearchAlgorithm bfs = new BreadthFirstSearchAlgorithm(residualGraph);
VertexIntDictionary distances = new VertexIntDictionary();
DistanceRecorderVisitor vis = new DistanceRecorderVisitor(distances);
bfs.RegisterDistanceRecorderHandlers(vis);
bfs.Compute(sink);
return distances[source] >= maxFlow.VisitedGraph.VerticesCount;
}
