private void ENUM_MAXIMUM_MATCHINGS(BipartiteGraph G, bool getAllMatchings)
{
/*-------------------------------------------------------------------------------------------------------------------
* Step1: Find a maximum matching M of G and output M.
* ------------------------------------------------------------------------------------------------------------------*/
EdgeList M = MaximumMatching.Get(G); //Edges of Matching
MatchingList matching = EdgeListToMatching(M);
matching.Sort();
FindOverconstrainedModelsReversalCost(matching);
if (OverConstrainedModels.Count > 0)
{
OverConstrained = true;
return;
}
AddMatching(matching);
if (MinimumCost > minimumAchievableCost)
{
/*-------------------------------------------------------------------------------------------------------------------
* Step2: Trim unnecessary arcs from D(G,M) by a strongly connected component decomposition algorithm.
* ------------------------------------------------------------------------------------------------------------------*/
//Need further action on this to trim edges after finding SCCs in a D(G,M). Here only SCCs are found. Edges are not trimmed yet.
//Graph D_GM = Get_D_GM(G.Clone(), M); //Directed graph is obtained here with reversing edges of matchingEdges.
//List<List<GraphNode>> sCCs = TarjanCycleDetect.DetectCycle(D_GM);
/*-------------------------------------------------------------------------------------------------------------------
* Step3: Call ENUM_MAXIMUM_MATCHINGS_ITER(G, M, D(G,M))
* ------------------------------------------------------------------------------------------------------------------*/
if (getAllMatchings)
{
ENUM_MAXIMUM_MATCHINGS_ITER(G.Clone(), M, matching, 0);
}
}
FilterDuplicateMatchings();
}
//This method find the corresponding edges of matching M(which contains edges from other Graph) for the given Graph G
private static EdgeList CorrespondingEdgeList(BipartiteGraph G, EdgeList M)
{
var corresponding = new EdgeList();
foreach (Edge edge in M)
{
GraphNode from = G.GetNode(edge.FromNode.Value);
GraphNode to = G.GetNode(edge.ToNode.Value);
if (from == null && to == null)
{
continue;
}
if (G.Edges.FindByNodes(from, to) != null)
{
corresponding.Add(G.Edges.FindByNodes(from, to));
}
else
{
corresponding.Add(G.Edges.FindByNodes(to, from));
}
}
return(corresponding);
}
private EdgeList MatchingToEdgeList(BipartiteGraph G, MatchingList M_String)
{
var edgeList = new EdgeList();
foreach (string edg in M_String)
{
GraphNode node1 = G.GetNode(edg.Split('-')[0]);
GraphNode node2 = G.GetNode(edg.Split('-')[1]);
if (G.Contains(node1, node2))
{
edgeList.Add(G.Edges.FindByNodes(node1, node2));
}
else if (G.Contains(node2, node1))
{
edgeList.Add(G.Edges.FindByNodes(node2, node1));
}
//else
//{
// M_to_EdgeListM.Add(new Edge(nd1,nd2,0));
//}
}
return(edgeList);
}
private static EdgeList CorrespondingListForTheGraph(BipartiteGraph G, EdgeList M) //This method find the corresponding edges of matching M(which contains edges from other Graph) for the given Graph G
{
var M_corresp = new EdgeList();
foreach (Edge edg in M)
{
GraphNode frm = G.GetNode(edg.FromNode.Value);
GraphNode to = G.GetNode(edg.ToNode.Value);
if (frm == null && to == null)
{
goto xyz;
}
if (G.Edges.FindByNodes(frm, to) != null)
{
M_corresp.Add(G.Edges.FindByNodes(frm, to));
}
else
{
M_corresp.Add(G.Edges.FindByNodes(to, frm));
}
xyz :;
}
return(M_corresp);
}
//Here matching edges nodes are checked if it is model or variable
//And then directed graph is created, where matching edges are oriented from model to variable whereas,
//other graph edges(original graph edges) are from variable to model.
public BipartiteGraph GetDirectedGraphAsPerMatching(EdgeList M)
{
foreach (Edge edge in M)
{
GraphNode from = edge.FromNode;
GraphNode to = edge.ToNode;
if (from != null && to != null)
{
if (from.NodeType == GraphNode.Type.Type2)
{
if (Contains(from, to))
{
RemoveDirectedEdge(to, from);
}
else if (Contains(to, from))
{
RemoveDirectedEdge(to, from);
AddDirectedEdge(from, to, 0, 0);
}
}
else
{
if (Contains(from, to))
{
RemoveDirectedEdge(from, to);
AddDirectedEdge(to, from, 0, 0);
}
else if (Contains(to, from))
{
RemoveDirectedEdge(from, to);
}
}
}
}
return(this);
}
//This code has been tested and works fine for test-case under consideration
private void ENUM_MAXIMUM_MATCHINGS_ITER(BipartiteGraph G, EdgeList M, MatchingList matching, int recursionLevel)
{
//System.Console.WriteLine(recursionLevel); //System.Console.WriteLine(recursionLevel);
if (recursionLevel >= MaximumRecursionLevel)
{
return;
}
/*-------------------------------------------------------------------------------------------------------------------
* Step1: If G has no edge, stop.
* ------------------------------------------------------------------------------------------------------------------*/
if (G.Edges.Count <= 1)
{
return;
}
/*-------------------------------------------------------------------------------------------------------------------
* Step2: If D(G,M) contains no cylce, Go to Step8.
* ------------------------------------------------------------------------------------------------------------------*/
BipartiteGraph directedGraph = G.Clone().GetDirectedGraphAsPerMatching(M);
var CIDG = new CycleInDirectedGraph(directedGraph); //Class object containing Method to detect and get cycle in a grah
Edge e;
MatchingList Mdash;
BipartiteGraph Gplus, Gminus;
if (CIDG.HasCycle)
{
/*-------------------------------------------------------------------------------------------------------------------
* Step3 & 4: Choose an edge e as the same manner in ENUM_PERFECT_MATCHINGS_ITER.
* Find a cycle containing e by a depth-first-search algorithm.
* ------------------------------------------------------------------------------------------------------------------*/
// Cycle is found using DFS algorithm and edge-e is chosen such that it is in cycle and in matching M
// ( and not in M'(which is found next)) of the directed graph(DG)
List <GraphNode> cycle = CIDG.Cycle; //returns here cycle in a directed graph DG //'Cycle': Vertices can not repeate and Edges can not repeat
EdgeList cycleEdges = directedGraph.ToEdges(cycle); //cycleInDG is list of nodes in a Cycle . Here this list is converted into edges in the Cycle.
EdgeList MEdgeList = CorrespondingEdgeList(directedGraph, M);
e = ChooseEdge(MEdgeList, cycleEdges); //Edge - e is chosen here.
/*-------------------------------------------------------------------------------------------------------------------
* Step5: Exchange edges along the cycle and output the obtained maximum matching M'.
* ------------------------------------------------------------------------------------------------------------------*/
Mdash = ExchangeEdgesAlongCycleOrPath(matching, CycleToMatching(cycle)); //this.matchingToStringList(M)
Mdash.Sort();
AddMatching(Mdash);
if (MinimumCost > minimumAchievableCost)
{
/*-------------------------------------------------------------------------------------------------------------------
* Step6: Enumerate all maximum matchings including e by ENUM_MAXIMUM_MATCHINGS_ITER with G+(e), M and trimmed D(G+(e), M\e).
* ------------------------------------------------------------------------------------------------------------------*/
Gplus = BuildGplus(G, e); //G+(e) is obtained here //!! here G+(e) graph will not have edge which is there in matching
ENUM_MAXIMUM_MATCHINGS_ITER(Gplus, M, matching, recursionLevel + 1); //recursive call with G+(e) and M
/*-------------------------------------------------------------------------------------------------------------------
* Step7: Enumerate all maximum matchings not including e by ENUM_MAXIMUM_MATCHINGS_ITER with G-(e), M' and trimmed D(G-(e), M'). Stop.
* ------------------------------------------------------------------------------------------------------------------*/
Gminus = BuildGminus(G, e); //G-(e) is obtained here
ENUM_MAXIMUM_MATCHINGS_ITER(Gminus, MatchingToEdgeList(Gminus, Mdash), Mdash, recursionLevel + 1); //recursive call with G-(e) and M
}
return;
}
/*----------------------------------------------------------------------------------------------------------------------
* Step8: Find a feasible path with length 2 and generate a new maximum matching M'.
* Let e be the edge of the path not included in M.
* ------------------------------------------------------------------------------------------------------------------*/
//'Feasible Path':
NodeList unmatchedVertices = directedGraph.GetUnmatchedVertices(matching);
var path = new MatchingList();
foreach (GraphNode node in directedGraph)
{
if (node.NodeType == GraphNode.Type.Type1 || node.NodeType == GraphNode.Type.Type2 && !unmatchedVertices.Contains(node))
{
var dfs = new DepthFirstSearch(directedGraph, node, unmatchedVertices);
path = dfs.length2Path;
if (path.Count == 3 && IsFeasiblePath(directedGraph, path, unmatchedVertices))
{
break;
}
}
}
if (path.Count != 3)
{
return;
}
e = GetEdgeInPathNotInM(G, matching, PathToMatching(G, path));
Mdash = ExchangeEdgesAlongCycleOrPath(matching, PathToMatching(G, path));
Mdash.Sort();
AddMatching(Mdash);
if (MinimumCost > minimumAchievableCost)
{
/*-------------------------------------------------------------------------------------------------------------------
* Step9: Call ENUM_MAXIMUM+MATCHINGS_ITER(G+(e), M', theta).
* -* ------------------------------------------------------------------------------------------------------------------*/
Gplus = BuildGplus(G, e); //G+(e) is obtained here
ENUM_MAXIMUM_MATCHINGS_ITER(Gplus, MatchingToEdgeList(Gplus, Mdash), Mdash, recursionLevel + 1);
/*-------------------------------------------------------------------------------------------------------------------
* Step10: Call ENUM_MAXIMUM+MATCHINGS_ITER(G-(e), M, theta).
* ------------------------------------------------------------------------------------------------------------------*/
Gminus = BuildGminus(G, e); //G-(e) is obtained here
ENUM_MAXIMUM_MATCHINGS_ITER(Gminus, M, matching, recursionLevel + 1);
}
}
private void ENUM_PERFECT_MATCHINGS_ITER(BipartiteGraph G, EdgeList M, List <string> M_String)
{
/*-------------------------------
* Step1: If G has no edge, stop.
* ---------------------------------*/
if (G.Edges.Count == 0)
{
return;
}
/*-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step2 & Step3: Choosing Edge-e and Finding Cycle. //Cycle is found using DFS algorithm and edge-e is chosen such that it is in cycle and in matching M ( and not in M'(which is found next)) of the directed graph(DG)
* ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
BipartiteGraph d_G = G.Clone().GetDirectedGraphAsPerMatching(M);
var CIDG = new CycleInDirectedGraph(d_G); //Class object containing Method to detect and get cycle in a grah
if (!CIDG.HasCycle)
{
return;
}
List <GraphNode> cycleInDG = CIDG.Cycle; //returns here cycle in a directed graph DG
//Cycle: Vertices can not repeate and Edges can not repeat
EdgeList cycleInDG_Edges = d_G.ToEdges(cycleInDG); //cycleInDG is list of nodes in a Cycle . Here this list is converted into edges in the Cycle.
List <string> cycleInDG_EdgesAsStrings = d_G.ToEdgesAsStrings(cycleInDG);
EdgeList M_corresp = CorrespondingListForTheGraph(d_G, M);
Edge e = chooseEdge(M_corresp, cycleInDG_Edges); //Edge - e is chosen here.
////String e_string = chooseEdgeStringVersion(M_String, cycleInDG_EdgesAsStrings); //Edge - e is chosen here.
/*---------------------------------------------------------------------------------
* Step4: Find a perfect matching M' by exchanging edges along the cycle. Output M'.
* ------------------------------------------------------------------------------------*/
EdgeList M_dash = ExchangingEdgesAlongCycle(M_corresp, cycleInDG_Edges); /* Write code here to find M' here */
List <string> M_dash_String = ExchangingEdgesAlongCycleStringVersion(M_String, cycleToStringList(cycleInDG)); //this.matchingToStringList(M)
//list_PerfectMatchings.Add(M_dash);
list_AllPerfectMatchings.Add(M_dash_String);
/*-----------------------------------------------------------------------------------------
* Step5: Find G+(e), trim unnecessary edges of G+(e) using SCC decomposition algorithm.
* ------------------------------------------------------------------------------------------*/
//Graph<T> G_plus = G_plus_e(DG.Clone(), e); //G+(e) is obtained here
BipartiteGraph G_plus = G_plus_e(G.Clone(), e);
List <List <GraphNode> > sCCs_G_plus = TarjanCycleDetect.DetectCycle(G_plus); // /SCCs in G+(e) to trim unnecessary edges
/* Write code for trimming edges here*/
/*-----------------------------------------------------------------------------------------------------------
* Step6: Enumerate all perfect matchings including e by ENUM_PERFECT_MATCHING_ITER with obtained graph and M
* ------------------------------------------------------------------------------------------------------------*/
ENUM_PERFECT_MATCHINGS_ITER(G_plus, M, M_String); //recursive call with G+(e) and M // !! here G+(e) graph will not have edge which is there in matching
/*-----------------------------------------------------------------------------------------
* Step7: Find G-(e), trim unnecessary edges of G-(e) using SCC decomposition algorithm.
* -----------------------------------------------------------------------------------------*/
BipartiteGraph G_minus = G_minus_e(G.Clone(), e); //G+(e) is obtained here
////G_minus.plotMethod(this.goView1);
List <List <GraphNode> > sCCs_G_minus = TarjanCycleDetect.DetectCycle(G_minus); // SCCs in G-(e) to trim unnecessary edges
/* Write code for trimming edges here*/
/*---------------------------------------------------------------------------------------------------------------
* Step8: Enumerate all perfect matchings not including e by ENUM_PERFECT_MATCHING_ITER with obtained graph and M'
* ---------------------------------------------------------------------------------------------------------------*/
ENUM_PERFECT_MATCHINGS_ITER(G_minus, matchingStringsToEdgeList(G_minus, M_dash_String), M_dash_String); //recursive call with G+(e) and M
}
private void ENUM_MAXIMUM_MATCHINGS_ITER(BipartiteGraph G, EdgeList M, List <String> M_String, int recursionLevel)
{
if (recursionLevel > MaximumRecursionLevel)
{
return;
}
//This code has been tested and works fine for test-case under consideration
/*-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step1: If G has no edge, stop.
* --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
if (G.Edges.Count <= 1)
{
return;
}
/*-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step2: If D(G,M) contains no cylce, Go to Step8.
* --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
BipartiteGraph d_G = G.Clone().GetDirectedGraphAsPerMatching(M);
var CIDG = new CycleInDirectedGraph(d_G); //Class object containing Method to detect and get cycle in a grah
if (!CIDG.HasCycle)
{
goto Step8;
}
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step3 & 4: Choose an edge e as the same manner in ENUM_PERFECT_MATCHINGS_ITER. Find a cycle containing e by a depth-first-search algorithm.
* ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
//Cycle is found using DFS algorithm and edge-e is chosen such that it is in cycle and in matching M ( and not in M'(which is found next)) of the directed graph(DG)
List <GraphNode> cycleInDG = CIDG.Cycle; //returns here cycle in a directed graph DG //'Cycle': Vertices can not repeate and Edges can not repeat
EdgeList cycleInDG_Edges = d_G.ToEdges(cycleInDG); //cycleInDG is list of nodes in a Cycle . Here this list is converted into edges in the Cycle.
List <String> cycleInDG_EdgesAsStrings = d_G.ToEdgesAsStrings(cycleInDG);
EdgeList M_corresp = CorrespondingListForTheGraph(d_G, M);
Edge e = chooseEdge(M_corresp, cycleInDG_Edges); //Edge - e is chosen here.
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step5: Exchange edges along the cycle and output the obtained maximum matching M'.
* ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
List <String> M_dash_String = ExchangingEdgesAlongCycleOrPathStringVersion(M_String, cycleToStringList(cycleInDG));//this.matchingToStringList(M)
M_dash_String.Sort();
list_AllMaximumMatchings.Add(M_dash_String);
/*-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step6: Enumerate all maximum matchings including e by ENUM_MAXIMUM_MATCHINGS_ITER with G+(e), M and trimmed D(G+(e), M\e).
* --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
BipartiteGraph G_plus = G_plus_e(G.Clone(), e);
ENUM_MAXIMUM_MATCHINGS_ITER(G_plus, M, M_String, ++recursionLevel); //recursive call with G+(e) and M // !! here G+(e) graph will not have edge which is there in matching
/*-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step7: Enumerate all maximum matchings not including e by ENUM_MAXIMUM_MATCHINGS_ITER with G-(e), M' and trimmed D(G-(e), M'). Stop.
* --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
BipartiteGraph G_minus = G_minus_e(G.Clone(), e); //G-(e) is obtained here
ENUM_MAXIMUM_MATCHINGS_ITER(G_minus, matchingStringsToEdgeList(G_minus, M_dash_String), M_dash_String, ++recursionLevel); //recursive call with G-(e) and M
return;
/*-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step8: Find a feasible path with length 2 and generate a new maximum matching M'. Let e be the edge of the path not included in M.
* ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
//'Feasible Path':
Step8 :;
NodeList unmatchedVertices = d_G.GetUnmatchedVertices(M_String);
var path = new List <String>();
foreach (GraphNode Gn in d_G)
{
if (Gn.NodeType == GraphNode.Type.Type1)
{
var dfs = new DepthFirstSearch(d_G, Gn, unmatchedVertices);
path = dfs.length2Path;
if (path.Count == 3 && isFeasiblePath(d_G, path, unmatchedVertices))
{
break;
}
}
if ((Gn.NodeType == GraphNode.Type.Type2) && !(unmatchedVertices.Contains(Gn)))
{
var dfs = new DepthFirstSearch(d_G, Gn, unmatchedVertices);
path = dfs.length2Path;
if (path.Count == 3 && isFeasiblePath(d_G, path, unmatchedVertices))
{
break;
}
}
}
if (path.Count != 3)
{
return;
}
e = getEdgeInPathNotInM(G, M_String, pathToEdgesAsStrings(G, path));
M_dash_String = ExchangingEdgesAlongCycleOrPathStringVersion(M_String, pathToEdgesAsStrings(G, path));
M_dash_String.Sort();
list_AllMaximumMatchings.Add(M_dash_String);
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step9: Call ENUM_MAXIMUM+MATCHINGS_ITER(G+(e), M', theta).
* ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
G_plus = G_plus_e(G.Clone(), e);
ENUM_MAXIMUM_MATCHINGS_ITER(G_plus, matchingStringsToEdgeList(G_plus, M_dash_String), M_dash_String, ++recursionLevel);
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step10: Call ENUM_MAXIMUM+MATCHINGS_ITER(G-(e), M, theta).
* --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
G_minus = G_minus_e(G.Clone(), e); //G-(e) is obtained here
ENUM_MAXIMUM_MATCHINGS_ITER(G_minus, M, M_String, ++recursionLevel);
}
} //here this class constructor is called with inputs as null nodeSet and edgeSet. Here NodeList and EdgeList are created if they are null
public BipartiteGraph(NodeList nodeSet, EdgeList edgeSet)
{
Nodes = nodeSet ?? new NodeList();
Edges = edgeSet ?? new EdgeList();
}
