public static Graph CreateResidualNetwork(FlowNetwork fn) { FlowNetwork copy = new FlowNetwork(); fn.CopyTo(copy); Graph g = new Graph(); g.Directed = true; for (int i = 0; i < copy.GetVertices().Count; i++) { Vertex v = copy.GetVertices()[i]; v.Tag = i; v.RemoveAllEdges(); g.AddVertex(v); } foreach (FlowEdge e in copy.GetEdges()) { float backflow = e.CurrentFlow; float capacity = e.Capacity; float forwardFlow = capacity - backflow; Vertex fromVertex = e.GetFromVertex(); Vertex toVertex = e.GetToVertex(); int fromIndex = (int)fromVertex.Tag; int toindex = (int)toVertex.Tag; Vertex newTo = g.GetVertices()[toindex]; Vertex newFrom = g.GetVertices()[fromIndex]; if (backflow > 0) { Edge backEdge = new Edge(newTo, newFrom, backflow); g.AddEdge(backEdge); } if (forwardFlow > 0) { Edge forwardEdge = new Edge(newFrom, newTo, forwardFlow); g.AddEdge(forwardEdge); } } return(g); }
public static float MaximumFlow(FlowNetwork fn, int source, int sink) { float maxFlow = 0f; int sourceIndex = source; int sinkIndex = sink; foreach (FlowEdge e in fn.GetEdges()) { e.CurrentFlow = 0f; } Graph g = CreateResidualNetwork(fn); List<Edge> augmentingPath = BreadthFirstSearch(g, sourceIndex, sinkIndex); while (augmentingPath != null) { float minFlow = float.MaxValue; //find min flow foreach (Edge e in augmentingPath) { if (e.Weight < minFlow) { minFlow = e.Weight; } } maxFlow += minFlow; foreach (Edge e in augmentingPath) { //Update residual graph Edge currentForwardResid = g.FindEdge(e); Edge currentBackwardResid = g.FindEdge(new Edge(e.GetToVertex(), e.GetFromVertex())); float newForwardWeight = currentForwardResid.Weight - minFlow; if (newForwardWeight <= 0f) { g.RemoveEdge(currentForwardResid); } else { currentForwardResid.Weight = newForwardWeight; } if (currentBackwardResid != null) { float newBackwardWeight = currentBackwardResid.Weight + minFlow; currentBackwardResid.Weight = newBackwardWeight; } else { currentBackwardResid = new Edge(e.GetToVertex(), e.GetFromVertex(), minFlow); g.AddEdge(currentBackwardResid); } //Update flow network FlowEdge fe = fn.FindEdge(new FlowEdge(e.GetFromVertex(), e.GetToVertex(), 0, 0)); fe.CurrentFlow = fe.CurrentFlow + minFlow; } augmentingPath = BreadthFirstSearch(g, sourceIndex, sinkIndex); //augmentingPath = null; } return maxFlow; }
public static Graph CreateResidualNetwork(FlowNetwork fn) { FlowNetwork copy = new FlowNetwork(); fn.CopyTo(copy); Graph g = new Graph(); g.Directed = true; for (int i = 0; i < copy.GetVertices().Count; i++) { Vertex v = copy.GetVertices()[i]; v.Tag = i; v.RemoveAllEdges(); g.AddVertex(v); } foreach (FlowEdge e in copy.GetEdges()) { float backflow = e.CurrentFlow; float capacity = e.Capacity; float forwardFlow = capacity - backflow; Vertex fromVertex = e.GetFromVertex(); Vertex toVertex = e.GetToVertex(); int fromIndex = (int)fromVertex.Tag; int toindex = (int)toVertex.Tag; Vertex newTo = g.GetVertices()[toindex]; Vertex newFrom = g.GetVertices()[fromIndex]; if (backflow > 0) { Edge backEdge = new Edge(newTo, newFrom, backflow); g.AddEdge(backEdge); } if (forwardFlow > 0) { Edge forwardEdge = new Edge(newFrom, newTo, forwardFlow); g.AddEdge(forwardEdge); } } return g; }
public static float MaximumFlow(FlowNetwork fn, int source, int sink) { float maxFlow = 0f; int sourceIndex = source; int sinkIndex = sink; foreach (FlowEdge e in fn.GetEdges()) { e.CurrentFlow = 0f; } Graph g = CreateResidualNetwork(fn); List <Edge> augmentingPath = BreadthFirstSearch(g, sourceIndex, sinkIndex); while (augmentingPath != null) { float minFlow = float.MaxValue; //find min flow foreach (Edge e in augmentingPath) { if (e.Weight < minFlow) { minFlow = e.Weight; } } maxFlow += minFlow; foreach (Edge e in augmentingPath) { //Update residual graph Edge currentForwardResid = g.FindEdge(e); Edge currentBackwardResid = g.FindEdge(new Edge(e.GetToVertex(), e.GetFromVertex())); float newForwardWeight = currentForwardResid.Weight - minFlow; if (newForwardWeight <= 0f) { g.RemoveEdge(currentForwardResid); } else { currentForwardResid.Weight = newForwardWeight; } if (currentBackwardResid != null) { float newBackwardWeight = currentBackwardResid.Weight + minFlow; currentBackwardResid.Weight = newBackwardWeight; } else { currentBackwardResid = new Edge(e.GetToVertex(), e.GetFromVertex(), minFlow); g.AddEdge(currentBackwardResid); } //Update flow network FlowEdge fe = fn.FindEdge(new FlowEdge(e.GetFromVertex(), e.GetToVertex(), 0, 0)); fe.CurrentFlow = fe.CurrentFlow + minFlow; } augmentingPath = BreadthFirstSearch(g, sourceIndex, sinkIndex); //augmentingPath = null; } return(maxFlow); }