//Creates a new FlowNetwork, sets it as the current graph
public FlowNetwork NewFlowNetwork(string name)
{
FlowNetwork g = new FlowNetwork();
g.Name = name;
graphs.Add(g);
currentGraph = g;
return g;
}
//Creates a new FlowNetwork, sets it as the current graph
public FlowNetwork NewFlowNetwork(string name)
{
FlowNetwork g = new FlowNetwork();
g.Name = name;
graphs.Add(g);
currentGraph = g;
return(g);
}
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);
}
private void copyLinkedGraph(FlowNetwork to)
{
to.Clear();
for (int i = 0; i < this.GetVertices().Count; i++)
{
vertices[i].Tag = i;
Vertex v = new Vertex();
v.Tag = i;
to.AddVertex(v);
}
for (int i = 0; i < this.GetEdges().Count; i++)
{
Edge currentEdge = this.GetEdges()[i];
Vertex v1 = new Vertex();
v1.Label = currentEdge.GetFromVertex().Label;
int cd = (int)currentEdge.GetFromVertex().Tag;
if ((int)to.GetVertices()[cd].Tag == cd)
{
v1 = to.GetVertices()[cd];
}
Vertex v2 = new Vertex();
v2.Label = currentEdge.GetToVertex().Label;
int cd2 = (int)currentEdge.GetToVertex().Tag;
if ((int)to.GetVertices()[cd2].Tag == cd2)
{
v2 = to.GetVertices()[cd2];
}
FlowEdge fe = currentEdge as FlowEdge;
Edge e = new FlowEdge(v1, v2, fe.CurrentFlow, fe.Capacity);
to.AddEdge(e);
}
FlowNetwork fn = this as FlowNetwork;
if (fn != null)
{
to.SetSource(fn.GetSource());
to.SetSink(fn.GetSink());
}
}
private void copyLinkedGraph(FlowNetwork to)
{
to.Clear();
for (int i = 0; i < this.GetVertices().Count; i++)
{
vertices[i].Tag = i;
Vertex v = new Vertex();
v.Tag = i;
to.AddVertex(v);
}
for (int i = 0; i < this.GetEdges().Count; i++)
{
Edge currentEdge = this.GetEdges()[i];
Vertex v1 = new Vertex();
v1.Label = currentEdge.GetFromVertex().Label;
int cd = (int)currentEdge.GetFromVertex().Tag;
if ((int)to.GetVertices()[cd].Tag == cd)
{
v1 = to.GetVertices()[cd];
}
Vertex v2 = new Vertex();
v2.Label = currentEdge.GetToVertex().Label;
int cd2 = (int)currentEdge.GetToVertex().Tag;
if ((int)to.GetVertices()[cd2].Tag == cd2)
{
v2 = to.GetVertices()[cd2];
}
FlowEdge fe = currentEdge as FlowEdge;
Edge e = new FlowEdge(v1, v2, fe.CurrentFlow, fe.Capacity);
to.AddEdge(e);
}
FlowNetwork fn = this as FlowNetwork;
if (fn != null)
{
to.SetSource(fn.GetSource());
to.SetSink(fn.GetSink());
}
}
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;
}
private static void TestResidualNetwork()
{
//Create graph from Figure 6.10
FlowNetwork fn = new FlowNetwork();
Vertex v1 = new Vertex();
Vertex v2 = new Vertex();
Vertex v3 = new Vertex();
Vertex v4 = new Vertex();
fn.AddVertex(v1);
fn.AddVertex(v2);
fn.AddVertex(v3);
fn.AddVertex(v4);
fn.SetSource(v1);
fn.SetSink(v4);
fn.AddEdge(new FlowEdge(v1, v3, 3, 4));
fn.AddEdge(new FlowEdge(v1, v2, 2, 2));
fn.AddEdge(new FlowEdge(v2, v3, 2, 3));
fn.AddEdge(new FlowEdge(v3, v4, 5, 5));
fn.AddEdge(new FlowEdge(v2, v4, 0, 1));
Graph g = GraphAlgorithms.CreateResidualNetwork(fn);
}
private static void TestMaxFlow()
{
FlowNetwork fn = new FlowNetwork();
Vertex v1 = new Vertex();
Vertex v2 = new Vertex();
Vertex v3 = new Vertex();
Vertex v4 = new Vertex();
Vertex v5 = new Vertex();
Vertex v6 = new Vertex();
fn.AddVertex(v1);
fn.AddVertex(v2);
fn.AddVertex(v3);
fn.AddVertex(v4);
fn.AddVertex(v5);
fn.AddVertex(v6);
fn.SetSource(v1);
fn.SetSink(v6);
fn.AddEdge(new FlowEdge(v1, v2, 0f, 2f));
fn.AddEdge(new FlowEdge(v1, v3, 0f, 2f));
fn.AddEdge(new FlowEdge(v2, v4, 0f, 2f));
fn.AddEdge(new FlowEdge(v3, v4, 1f, 2f));
fn.AddEdge(new FlowEdge(v3, v5, 0f, 2f));
fn.AddEdge(new FlowEdge(v4, v6, 1f, 2f));
fn.AddEdge(new FlowEdge(v5, v6, 0f, 2f));
//float maxFlow = GraphAlgorithms.MaximumFlow(fn);
//Console.WriteLine("Max flow is " + maxFlow);
}
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);
}
