public static IWeightedGraph <TV, TW> FindCostMinimalFlow <TV, TW>(IWeightedGraph <TV, TW> graph,
TV superSourceValue,
TV superTargetValue,
Func <TW, TW, TW> combineValues,
Func <TW, TW, TW> substractValues,
Func <TW, TW> negateValue,
TW zeroValue,
TW maxValue)
where TV : IEquatable <TV> where TW : IComparable
{
// Build graph with super nodes
IWeightedGraph <TV, TW> graphWithSuperNodes = BuildGraphWithSuperNodes(graph, superSourceValue, superTargetValue, negateValue);
// Get max flow in graph with super nodes
IWeightedGraph <TV, TW> maxFlow = EdmondsKarp.FindMaxFlow(graphWithSuperNodes,
graphWithSuperNodes.GetFirstMatchingVertex(v => v.Value.Equals(superSourceValue)),
graphWithSuperNodes.GetFirstMatchingVertex(v => v.Value.Equals(superTargetValue)),
combineValues,
substractValues,
zeroValue);
TW maxFlowValue = FlowValue(maxFlow, superSourceValue, combineValues, zeroValue);
// Check for existance of a b-flow
IEnumerable <IVertex <TV> > sources = graph.GetAllMatchingVerteces(v => v.GetAttribute <double>(Constants.BALANCE) > 0);
IEnumerable <IVertex <TV> > targets = graph.GetAllMatchingVerteces(v => v.GetAttribute <double>(Constants.BALANCE) < 0);
TW sourcesBalance = zeroValue;
TW targetsBalance = zeroValue;
foreach (IVertex <TV> source in sources)
{
sourcesBalance = combineValues(sourcesBalance, source.GetAttribute <TW>(Constants.BALANCE));
}
foreach (IVertex <TV> target in targets)
{
targetsBalance = combineValues(targetsBalance, target.GetAttribute <TW>(Constants.BALANCE));
}
if (maxFlowValue.Equals(sourcesBalance) &&
maxFlowValue.Equals(negateValue(targetsBalance)))
{
// Copy flow values from graph with super nodes to original graph
foreach (IWeightedEdge <TV, TW> edge in graphWithSuperNodes.GetAllEdges())
{
if (edge is IWeightedDirectedEdge <TV, TW> directedEdge)
{
if (!directedEdge.OriginVertex.Value.Equals(superSourceValue) &&
!directedEdge.TargetVertex.Value.Equals(superTargetValue))
{
graph.GetEdgeBetweenVerteces(directedEdge.OriginVertex.Value, directedEdge.TargetVertex.Value)
.SetAttribute(Constants.FLOW, edge.GetAttribute <TW>(Constants.FLOW));
}
}
else
{
throw new GraphNotDirectedException();
}
}
bool modifyingCycleLeft;
do
{
// Build residual graph
IWeightedGraph <TV, TW> residualGraph = BuildResidualGraph(graph, substractValues, negateValue, zeroValue);
// Prepare graph for BellmanFordMoore
IWeightedGraph <TV, TW> bfmGraph = BuildGraphForBellmanFordMoore(residualGraph, superSourceValue, zeroValue);
// Attempt to find modifying cycle
IVertex <TV> bfmSuperSource = bfmGraph.GetFirstMatchingVertex(v => v.Value.Equals(superSourceValue));
if (modifyingCycleLeft = BellmanFordMoore.TryFindNegativeCycle(bfmGraph,
bfmSuperSource,
zeroValue,
maxValue,
combineValues,
out IEnumerable <IWeightedDirectedEdge <TV, TW> > cycle))
{
// Get minimum capacity of the cycle in the residual graph
List <IWeightedDirectedEdge <TV, TW> > rgCycle = new List <IWeightedDirectedEdge <TV, TW> >();
foreach (IWeightedDirectedEdge <TV, TW> edge in cycle)
{
rgCycle.Add((IWeightedDirectedEdge <TV, TW>)residualGraph.GetEdgeBetweenVerteces(edge.OriginVertex.Value, edge.TargetVertex.Value));
}
TW minCycleCapacity = rgCycle.Min(e => e.Weight);
// Modify b-flow along cycle
foreach (IWeightedDirectedEdge <TV, TW> edge in rgCycle)
{
if (edge.GetAttribute <EdgeDirection>(Constants.DIRECTION) == EdgeDirection.Forward)
{
IWeightedDirectedEdge <TV, TW> graphEdge = (IWeightedDirectedEdge <TV, TW>)graph.GetEdgeBetweenVerteces(edge.OriginVertex.Value, edge.TargetVertex.Value);
graphEdge.SetAttribute(Constants.FLOW, combineValues(graphEdge.GetAttribute <TW>(Constants.FLOW), minCycleCapacity));
}
else
{
IWeightedDirectedEdge <TV, TW> graphEdge = (IWeightedDirectedEdge <TV, TW>)graph.GetEdgeBetweenVerteces(edge.TargetVertex.Value, edge.OriginVertex.Value);
graphEdge.SetAttribute(Constants.FLOW, substractValues(graphEdge.GetAttribute <TW>(Constants.FLOW), minCycleCapacity));
}
}
}
}while (modifyingCycleLeft);
// Return same graph
return(graph);
}
else
{
throw new NoBFlowException();
}
}
public static IWeightedGraph <TV, TW> FindMaxFlow <TV, TW>(IWeightedGraph <TV, TW> graph,
IVertex <TV> source,
IVertex <TV> target,
Func <TW, TW, TW> combineFlowValues,
Func <TW, TW, TW> substractFlowValues,
TW zeroValue) where TV : IEquatable <TV> where TW : IComparable
{
// Set initial flow to 0
foreach (IWeightedEdge <TV, TW> edge in graph.GetAllEdges())
{
edge.SetAttribute(ATTR_FLOW, zeroValue);
}
// Augment flow until there are not augmenting paths in the residual graph left
IWeightedGraph <TV, TW> residualGraph = null;
bool anyPathLeft = true;
do
{
// Build residual graph
residualGraph = BuildResidualGraph(graph, substractFlowValues, zeroValue);
// Find (s,t)-path in residual graph
IVertex <TV> residualSource = residualGraph.GetFirstMatchingVertex(v => v.Value.Equals(source.Value));
IVertex <TV> residualTarget = residualGraph.GetFirstMatchingVertex(v => v.Value.Equals(target.Value));
if (TryFindPath(residualGraph, residualSource, residualTarget, out List <IWeightedEdge <TV, TW> > path))
{
// Augment f according to the found path
TW augmentingFlowValue = path.Min(e => e.Weight);
foreach (IWeightedDirectedEdge <TV, TW> edge in path)
{
// Add or substract augmenting flow value from current value depending on edge direction
if (edge.GetAttribute <EdgeDirection>(ATTR_DIRECTION) == EdgeDirection.Forward)
{
IWeightedDirectedEdge <TV, TW> graphEdge = (IWeightedDirectedEdge <TV, TW>)
graph.GetEdgeBetweenVerteces(edge.OriginVertex.Value, edge.TargetVertex.Value);
TW currentFlow = graphEdge.GetAttribute <TW>(ATTR_FLOW);
graphEdge.SetAttribute(ATTR_FLOW, combineFlowValues(currentFlow, augmentingFlowValue));
}
else
{
IWeightedDirectedEdge <TV, TW> graphEdge = (IWeightedDirectedEdge <TV, TW>)
graph.GetEdgeBetweenVerteces(edge.TargetVertex.Value, edge.OriginVertex.Value);
TW currentFlow = graphEdge.GetAttribute <TW>(ATTR_FLOW);
graphEdge.SetAttribute(ATTR_FLOW, substractFlowValues(currentFlow, augmentingFlowValue));
}
}
}
else
{
// Terminate if there is no (s,t)-path left in the residual graph
anyPathLeft = false;
}
} while (anyPathLeft);
// Build copy of input graph with max flow as edge weight
GraphBuilder <TV, TW> builder = new GraphBuilder <TV, TW>(true)
.AddVerteces(graph.GetAllVerteces().Select(v => v.Value));
foreach (IWeightedEdge <TV, TW> edge in graph.GetAllEdges())
{
IWeightedDirectedEdge <TV, TW> graphEdge = (IWeightedDirectedEdge <TV, TW>)edge;
builder.AddEdge(graphEdge.OriginVertex.Value,
graphEdge.TargetVertex.Value,
graphEdge.GetAttribute <TW>(ATTR_FLOW));
}
return(builder.Build());
}