public EdgeList matchingStringsToEdgeList(BipartiteGraph G, List <string> M_String)
{
var M_to_EdgeListM = new EdgeList();
GraphNode nd1, nd2;
foreach (string edg in M_String)
{
nd1 = G.GetNode(edg.Split('-')[0]);
nd2 = G.GetNode(edg.Split('-')[1]);
if (G.Contains(nd1, nd2))
{
M_to_EdgeListM.Add(G.Edges.FindByNodes(nd1, nd2));
}
else if (G.Contains(nd2, nd1))
{
M_to_EdgeListM.Add(G.Edges.FindByNodes(nd2, nd1));
}
//else
//{
// M_to_EdgeListM.Add(new Edge(nd1,nd2,0));
//}
}
return(M_to_EdgeListM);
}
private void ENUM_PERFECT_MATCHINGS(BipartiteGraph G)
{
/*-------------------------------------------------------------------------------
* Step1: Find a perfect matching M of G and output M. If M is not found, stop.
* ---------------------------------------------------------------------------------*/
//////G.GetAdjListInTheFormOfIntegers(); //Graph is converted to AdjList containing integers which are assigned to each model type node in a graph
//////IList<int> match = HopcroftKarp.GetMatching(G.AdjList, G.ModSet.Count); //Max. matching algorithm is called here with above AdjList of graph and number of model type nodes in a graph as input
//This returns matching as IList of integers associated with models
throw new NotImplementedException();
EdgeList M = null; //G.MatchingToEdgeList(); //Edges of Matching
//// List<List<T>> M_String = G.MatchingToEdgeListAsValues();//Matching Edges as Strings( "Node - Node")
list_AllPerfectMatchings.Add(matchingToStringList(M));
/*-----------------------------------------------------------------------------------------------------------
* Step2: Trim unnecessary edges from G by a strongly connected component decomposition algorithm with D(G,M)
* -------------------------------------------------------------------------------------------------------------*/
////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); //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.
/*----------------------------------------
* Step3: Call ENUM_PERFECT_MATCHINGS_ITER
* ------------------------------------------*/
ENUM_PERFECT_MATCHINGS_ITER(G.Clone(), M, matchingToStringList(M));
//list_AllPerfectMatchings.Add(M_String);
}
//YHB: this method find the graph G_plus by deleting given edge-e, its end vertices and edges associated with the end vertices
private static BipartiteGraph BuildGplus(BipartiteGraph G, Edge e)
{
BipartiteGraph Gplus = G.Clone();
Gplus.Remove(e.FromNode.Value);
Gplus.Remove(e.ToNode.Value);
return(Gplus);
}
public MaximumMatchings(BipartiteGraph G, bool getAllMatchings = false)
{
list_AllMaximumMatchings.Clear();
this.G = G;
this.G.UpdateAddingDuplicateNodes();
edgePrims = this.G.edgeNodesCost;
ENUM_MAXIMUM_MATCHINGS(this.G.Clone(), getAllMatchings);
}
private bool IsFeasiblePath(BipartiteGraph G, MatchingList path, NodeList unmatchedNodes)
{
if (unmatchedNodes.Contains(G.GetNode(path[0])) || unmatchedNodes.Contains(G.GetNode(path[2])))
{
return(true);
}
return(false);
}
public MaximumMatchings2(BipartiteGraph G, bool getAllMatchings = false)
{
this.G = G;
this.G.UpdateAddingDuplicateNodes();
edgePrims = this.G.edgeNodesCost;
minimumAchievableCost = 0;
ENUM_MAXIMUM_MATCHINGS(this.G.Clone(), getAllMatchings);
}
private bool isFeasiblePath(BipartiteGraph G, List <String> path, NodeList unmatchedNodes)
{
bool isFeasiblePath = false;
if (unmatchedNodes.Contains(G.GetNode(path[0])) || unmatchedNodes.Contains(G.GetNode(path[2])))
{
isFeasiblePath = true;
}
return(isFeasiblePath);
}
private readonly GraphNode _s; //source vertex
public DepthFirstDirectedPaths(BipartiteGraph G, GraphNode s)
{
_marked = new Dictionary <string, bool>();//create dictionary containing vertex, statur(true/false) wehter marked or not for all vertices
foreach (GraphNode item in G)
{
_marked.Add(item.Value.ToString(), false);
}
_edgeTo = new Dictionary <String, GraphNode>(); //create a boolean array for all vertices
_s = s; //mark the source vertex
DFS(G, s);
}
public static EdgeList Get(BipartiteGraph bipartiteGraph)
{
NodeList models = bipartiteGraph.ModelsSet;
if (models is null)
{
throw new ArgumentException("Graph has no models", nameof(bipartiteGraph));
}
NodeList variables = bipartiteGraph.VariablesSet;
if (variables is null)
{
throw new ArgumentException("Graph has no variables", nameof(bipartiteGraph));
}
//Assigning int values to each node in the graph starting from 0.
var modNodeIntMap = models.Select((m, i) => new KeyValuePair <string, int>(m.Value, i)).ToDictionary(kvp => kvp.Key, kvp => kvp.Value);
//Creating Adjacency List
var adjacencyList = new List <int[]>(variables.Count);
foreach (GraphNode variable in variables)
{
adjacencyList.Add(variable.Neighbors.Select(n => modNodeIntMap[n.Value]).ToArray());
}
// Get Match
IList <int> match = new HopcroftKarpClass(adjacencyList, models.Count).GetMatching();
// Format the match
var MatchingEdgeList = new EdgeList();
int idx = 0;
foreach (Node variable in variables)
{
int matchedModelIndex = match[idx];
if (matchedModelIndex != -1)
{
string modelValue = modNodeIntMap.FirstOrDefault(x => x.Value == matchedModelIndex).Key;
//matching edge list contains edges having direction from
MatchingEdgeList.Add(bipartiteGraph.Edges.FindByNodes(variable, bipartiteGraph.GetNode(modelValue)));
// 'variables set' to 'model set'
idx++;
}
else
{
idx++; /*variable associated at that location is unmatched*/ //Implement to store unmatched variable information if required
}
}
return(MatchingEdgeList);
}
/*
* A recursive function to do depth first search.
* We start with the source vertex s, find all vertices connected to it and recursively call
* DFS as move out from s to connected vertices. We avoid "going backwards" or needlessly looking
* at all paths by keeping track of which vertices we've already visited using the _marked[] array.
* We keep track of how we're moving through the graph (from s to v) using _edgeTo[].
*/
private void DFS(BipartiteGraph G, GraphNode v)
{
_marked[v.Value.ToString()] = true;
foreach (GraphNode w in v.Neighbors)
{
if (!_marked[w.Value.ToString()])
{
_edgeTo[w.Value.ToString()] = v;
DFS(G, w);
}
}
}
private static BipartiteGraph G_plus_e(BipartiteGraph G, Edge e)
{//YHB: this method find the graph G_plus by deleting given edge-e, its end vertices and edges associated with the end vertices
BipartiteGraph G_plus = G;
foreach (GraphNode item in G.Nodes)
{
}
G_plus.Remove(e.FromNode.Value);
G_plus.Remove(e.ToNode.Value);
return(G_plus);
}
public DFSDirectedCycle(BipartiteGraph g, GraphNode s)
{
this.g = g;
this.s = s;
marked = new Dictionary <string, bool>();
onStack = new Dictionary <string, bool>();
foreach (GraphNode item in g.Nodes)
{
marked.Add(item.Value.ToString(), false);
onStack.Add(item.Value.ToString(), false);
}
findCycle(g, s);
}
private static BipartiteGraph dg; //graph directed graph(dg)
public static List <List <GraphNode> > DetectCycle(BipartiteGraph g)
{
StronglyConnectedComponents = new List <List <GraphNode> >();
index = 0;
S = new Stack <GraphNode>();
dg = g;
foreach (GraphNode v in g.Nodes)
{
if (v.index < 0)
{
strongconnect(v);
}
}
return(StronglyConnectedComponents);
}
private static BipartiteGraph G_minus_e(BipartiteGraph G, Edge e)
{//YHB: this method find the graph G_minus by deleting given edge-e from the G i.e. given graph
BipartiteGraph G_minus = G;
if (G.Contains(G.GetNode(e.FromNode.Value), G.GetNode(e.ToNode.Value)))
{
G_minus.RemoveDirectedEdge(G.GetNode(e.FromNode.Value), G.GetNode(e.ToNode.Value));
}
else
{
G_minus.RemoveDirectedEdge(G.GetNode(e.ToNode.Value), G.GetNode(e.FromNode.Value));
}
return(G_minus);
}
// A recursive function to find which vertices are connected.
private void DFS(BipartiteGraph G, GraphNode v)
{
length2Path.Add(v.Value);
if (_path2Count++ == 2)
{
return;
}
_count++;
//mark this vertex as being visited
_marked.Add(v.Value.ToString(), true);
/*
* for each vertex w in the linked list for vertex v
* there exists an edge between v and w
* if it is not in _marked it hasn't been visited
* yet so mark it then check all the vertices
* in it's linked list (it has edges to).
* */
foreach (GraphNode w in v.Neighbors)
{
if (!_marked.ContainsKey(w.Value.ToString()))
{
if (_path2Count < 2)
{
DFS(G, w);
}
else if (_path2Count == 2)
{
if (unmatchedVertices.Contains(w) || unmatchedVertices.Contains(G.GetNode(length2Path[0])))
{
DFS(G, w);
}
else
{
goto nextNeighbour;
}
}
}
else
{
goto nextNeighbour;
}
nextNeighbour :;
}
return;
}
private bool AllSetMappedCheck(Combination combination)
{
if (Type == ReversalType.Inputs)
{
BipartiteGraph <Data, Data> G = GraphBuilder.BipartiteFromTwoSets(RequestedInputsToReverse, combination,
i => GetDependenciesFromInput(i), i => GetDependenciesFromInput(i));
List <(Data, Data)> Matching = MaximumMatching.Get(G);
return(Matching.Count == NinRequest);
}
else
{
BipartiteGraph <Data, Data> G = GraphBuilder.BipartiteFromTwoSets(RequestedOutputsToReverse, combination,
o => GetDependenciesFromOutput(o), o => GetDependenciesFromOutput(o));
List <(Data, Data)> Matching = MaximumMatching.Get(G);
return(Matching.Count == NoutRequest);
}
}
//YHB: this method find the graph G_minus by deleting given edge-e from the G i.e. given graph
private static BipartiteGraph BuildGminus(BipartiteGraph G, Edge e)
{
BipartiteGraph Gminus = G.Clone();
GraphNode from = G.GetNode(e.FromNode.Value);
GraphNode to = G.GetNode(e.ToNode.Value);
if (G.Contains(from, to))
{
Gminus.RemoveDirectedEdge(from, to);
}
else
{
Gminus.RemoveDirectedEdge(to, from);
}
return(Gminus);
}
private Edge getEdgeInPathNotInM(BipartiteGraph G, List <String> M, List <String> path)
{
Edge e = null;
String eString = path.Except(M).ToList()[0];
String[] eNodes = eString.Split('-');
GraphNode nd1 = G.GetNode(eNodes[0]);
GraphNode nd2 = G.GetNode(eNodes[1]);
if (G.Contains(nd1, nd2))
{
e = G.Edges.FindByNodes(nd1, nd2);
}
else if (G.Contains(nd2, nd1))
{
e = G.Edges.FindByNodes(nd2, nd1);
}
return(e);
}
private Edge GetEdgeInPathNotInM(BipartiteGraph G, MatchingList M, MatchingList path)
{
Edge e = null;
string edge = path.Except(M).ToList()[0];
string[] nodes = edge.Split('-');
GraphNode node1 = G.GetNode(nodes[0]);
GraphNode node2 = G.GetNode(nodes[1]);
if (G.Contains(node1, node2))
{
e = G.Edges.FindByNodes(node1, node2);
}
else if (G.Contains(node2, node1))
{
e = G.Edges.FindByNodes(node2, node1);
}
return(e);
}
private static BipartiteGraph Get_D_GM(BipartiteGraph G, EdgeList M)
{//Get directed graph from given Graph G and matchings(list of matched edges) M
BipartiteGraph D_GM = G;
//D_GM.GetAdjListInTheFormOfIntegers(); //Graph is converted to AdjList containing integers which are assigned to each model type node in a graph
//IList<int> match = HopcroftKarp.GetMatching(D_GM.AdjList, D_GM.ModSet.Count); //Max. matching algorithm is called here with above AdjList of graph and number of model type nodes in a graph as input
//EdgeList<T> M = D_GM.MatchingToEdgeList(match); //Edges of Matching
foreach (var edge in M)
{
D_GM.ReverseEdgeDirection(edge); //getting directed graph with matched edges with direction from v1 -> v2 and other edges from v2 -> v1
}
return(D_GM);
}
private MatchingList PathToMatching(BipartiteGraph G, MatchingList path)
{
var matching = new MatchingList();
string edge;
for (int i = 0; i < path.Count() - 1; i++)
{
if (G.GetNode(path[i]).NodeType == GraphNode.Type.Type2)
{
edge = EdgeString(path[i], path[i + 1]);
}
else
{
edge = EdgeString(path[i + 1], path[i]);
}
matching.Add(edge);
}
return(matching);
}
private List <String> pathToEdgesAsStrings(BipartiteGraph G, List <String> path) //04-01-2017 Added for MaximumMatchings
{
var pathAsStrings = new List <String>();
String str;
for (int i = 0; i < path.Count() - 1; i++)
{
if (G.GetNode(path[i]).NodeType == GraphNode.Type.Type2)
{
str = path[i] + '-' + path[i + 1];
}
else
{
str = path[i + 1] + '-' + path[i];
}
pathAsStrings.Add(str);
}
return(pathAsStrings);
}
//public bool hasCycle()
//{
// return hasCycle;
//}
public void findCycle(BipartiteGraph g, GraphNode v)
{
marked[v.Value.ToString()] = true;
onStack[v.Value.ToString()] = true;
foreach (GraphNode w in v.Neighbors)
{
if (!marked[w.Value.ToString()])
{
findCycle(g, w);
}
else if (onStack[w.Value.ToString()])
{
hasCycle = true;
return;
}
}
onStack[v.Value.ToString()] = false;
}
private void ENUM_MAXIMUM_MATCHINGS(BipartiteGraph G, bool getAllMatchings)
{
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* Step1: Find a maximum matching M of G and output M.
* --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*/
// The maximum mathing
EdgeList M = MaximumMatching.Get(G);
List <string> M_String = matchingToStringList(M);
M_String.Sort();
findOverconstrainedModelsReversalCost(M_String, out OverConstrainedModels, out unmappedVariables, out revCost);
if (OverConstrainedModels.Count > 0)
{
returnTrue = true;
return;
}
list_AllMaximumMatchings.Add(M_String);
/*--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
* 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, matchingToStringList(M), 0);
}
//list_AllPerfectMatchings.Add(M_String);
filterDuplicateMatchings();
}
} = new List <GraphNode>(); //YHB stores cycle in sequence
public CycleInDirectedGraph(BipartiteGraph graph)
{
var whiteSet = new HashSet <GraphNode>(graph.Nodes.Select(n => n as GraphNode)); //unvisited
var graySet = new HashSet <GraphNode>(); //visiting
var blackSet = new HashSet <GraphNode>(); //visite4
HasCycle = false;
while (whiteSet.Count > 0)
{
stack.Clear();
GraphNode current = whiteSet.First(); //ElementAt(random.Next(whiteSet.Count));
if (DepthFirstSearch(current, whiteSet, graySet, blackSet))
{
Cycle.Add(stack.Pop());
Cycle.AddRange(stack.TakeWhile(n => n != Cycle[0]));
Cycle.Add(Cycle[0]);
HasCycle = true;
break;
}
}
}
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);
}
//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);
}
}
