static bool DFS(UndirectedGraph.Graph graph, int v, bool[] discovered, bool[] color)
{
// do for every edge (v -> u)
foreach (int u in graph.AllNodes(v))
{
// if vertex u is explored for first time
if (discovered[u] == false)
{
// mark current node as discovered
discovered[u] = true;
// set color as opposite color of parent node
color[u] = !color[v];
// if DFS on any subtree rooted at v
// we return false
if (DFS(graph, u, discovered, color) == false)
{
return(false);
}
}
// if the vertex is already been discovered and
// color of vertex u and v are same, then the
// graph is not Bipartite
else if (color[v] == color[u])
{
return(false);
}
}
return(true);
}
// Identifies a Bipartition in a bipartite Graph via depth first search
// and returns a boolean array where the vth entry is true if and only if
// the respective node is element of the left set in the bipartition and
// false if and only if it is part of the right set in the bipartition.
// If the graph is not bipartite, this method return null.
public static bool[] Bipartition(UndirectedGraph.Graph graph)
{
bool[] partition = new bool[graph.Nodes()];
// stores vertex is discovered or not
bool[] discovered = new bool[graph.Nodes()];
// stores color 0 or 1 of each vertex in BFS
//bool[] color = new bool[N];
// mark source vertex as discovered and
// set its color to 0
discovered[0] = true;
partition[0] = false;
//List<int> nodes = graph.DFS_recursive();
// start DFS traversal from any node as graph
// is connected and undirected
if (DFS(graph, 1, discovered, partition))
{
return(partition);
}
return(null);
}
public static void Main(string[] args)
{
string path = (args.Length > 0) ? args [0] : "blatt8_aufg2.txt";
// Construct the graph
List <int[]> edges = TupleReader.ReadPairs(path);
UndirectedGraph.Graph graph = new UndirectedGraph.Graph(edges);
// display the graph
graph.Display();
// identify the bipartition
bool[] partition = Bipartition(graph);
if (partition == null)
{
System.Console.WriteLine("The graph is not bipartite!");
return;
}
// show the bipartition
DisplayPartition(partition);
// Find the Bipartite Matching
List <DirectedWeightedGraph.Edge> matching = Matching(graph, partition);
DisplayMatching(matching);
}
// Computes a bipartite matching in the given graph with the given partition of nodes.
// The partition is given in form of a boolean array as returned by the Partition
// function.
public static List <Edge> Matching(UndirectedGraph.Graph graph, bool[] partition)
{
List <Edge> matching = new List <Edge>();
//TODO: Implement
DirectedWeightedGraph.Graph g = new DirectedWeightedGraph.Graph(graph.Nodes() + 2);
int s = 0;
int t = g.Nodes() - 1;
for (int i = 0; i < graph.Nodes(); i++)
{
List <int> nodes = graph.AllNodes(i);
for (int j = 0; j < nodes.Count; j++)
{
g.AddEdge(i + 1, nodes[j], 1);
if (partition[i])
{
g.AddEdge(i + 1, t, 1);
}
else
{
g.AddEdge(s, i + 1, 1);
}
}
}
FlowGraph network = new FlowGraph(g, s, t);
FlowOptimizer optimizer = new EdmondsKarp.EdmondsKarp();
//optimizer.InteractiveOptimumFlow(network);
optimizer.OptimumFlow(network);
network.ComputeFlow();
for (int v = 1; v < network.Nodes() - 1; v++)
{
foreach (Edge edge in network.Edges(v))
{
if (edge.To() != s && edge.From() != t && edge.Weight() > 0)
{
matching.Add(edge);
break;
}
}
}
// Display the optimum flow
//System.Console.WriteLine("Flow is " + network.ComputeFlow());
return(matching);
}
