public Instance Match(Instance instance, string path, bool print)
{
Instance oldcopy = instance.Copy();
if (!System.IO.Directory.Exists(path) && print)
System.IO.Directory.CreateDirectory(path);
if (print)
{
Bitmap Bmp1 = instance.Draw();
Bmp1.Save(path + "/0Start.bmp");
Bmp1.Dispose();
}
instance = GetReduced(instance);
if (print)
{
Bitmap Bmp2 = instance.Draw();
Bmp2.Save(path + "/1Reduced.bmp");
Bmp2.Dispose();
}
if (print)
{
Bitmap Bmp3 = instance.Draw();
Bmp3.Save(path + "/2Inflated.bmp");
Bmp3.Dispose();
}
// check for applicant-complete matching
instance = GetApplicantComplete(instance);
if (instance == null)
{
if (print)
{
Bitmap Result = new Bitmap(1000, 1000);
Graphics G = Graphics.FromImage(Result);
Pen P = new Pen(new SolidBrush(Color.Black));
G.DrawString("No Popular Matching", new Font("Arial", 36), new SolidBrush(Color.Black), 100, 100);
Result.Save(path + "/3NoPop.bmp");
G.Dispose();
Result.Dispose();
}
return null;
}
else
{
if (print)
{
Bitmap Bmp4 = instance.Draw();
Bmp4.Save(path + "/3ApplicantComplete.bmp");
Bmp4.Dispose();
}
}
List<int>[] FPosts = new List<int>[instance.Posts.Length];
for (int i = 0; i < instance.Posts.Length; i++)
{
FPosts[i] = new List<int>();
}
for (int i = 0; i < instance.Applicants.Length; i++)
{
FPosts[instance.Applicants[i].Priorities.ElementAt(0).Target].Add(i);
}
for (int i = 0; i < instance.Posts.Length; i++)
{
if (FPosts[i].Count > 0 && instance.Posts[i].NrMatchings == 0)
{
instance.DeleteMatch(FPosts[i][0]);
instance.AddMatch(i, FPosts[i][0]);
}
}
if (print)
{
Bitmap Bmp4 = instance.Draw();
Bmp4.Save(path + "/4AllFPostsMatched.bmp");
Bmp4.Dispose();
}
return instance;
}
/// <summary>
/// Completess the applicant-complete matching, by traversing the disjoint cycle and taking every second edge.
/// </summary>
/// <param name="instance"></param>
/// <param name="start"></param>
/// <returns></returns>
private Instance GoPath(Instance instance, int start)
{
if (instance.Applicants[start].Matched)
return instance;
else
{
int Target = -1;
if (!instance.Posts[instance.Applicants[start].Priorities.ElementAt(0).Target].Full)
{
instance.AddMatch(instance.Applicants[start].Priorities.ElementAt(0).Target, start);
Target = instance.Applicants[start].Priorities.ElementAt(0).Target;
}
else
{
if (!instance.Posts[instance.Applicants[start].Priorities.ElementAt(1).Target].Full)
{
instance.AddMatch(instance.Applicants[start].Priorities.ElementAt(1).Target, start);
Target = instance.Applicants[start].Priorities.ElementAt(1).Target;
}
else
return instance;
}
for (int j = 0; j < instance.Applicants.Length; j++)
{
if (instance.Applicants[j].Priorities.ElementAt(0).Target == Target || instance.Applicants[j].Priorities.ElementAt(1).Target == Target)
{
if (!instance.Applicants[j].Matched)
instance = GoPath(instance, j);
}
}
}
return instance;
}
public Instance Match(Instance instance, string path, bool print)
{
try
{
LP = "";
if (!System.IO.Directory.Exists(path) && print)
System.IO.Directory.CreateDirectory(path);
GRBEnv env = new GRBEnv("mip1.log");
GRBModel model = new GRBModel(env);
List<LPEdge> LPEdges = new List<LPEdge>();
if (print)
{
instance.Draw().Save(path + "/0Start.bmp");
}
int EdgeCounter = 0;
foreach (Instance.Applicant a in instance.Applicants)
{
EdgeCounter += a.Priorities.Count;
foreach (Instance.Priority Prio in a.Priorities)
{
{
LPEdges.Add(new LPEdge(a, instance.Posts[Prio.Target], Prio.Rank));
if (Prio.Rank == 0)
instance.Posts[Prio.Target].IsF = 1;
}
}
}
// Create variables
GRBVar[] Edges = new GRBVar[EdgeCounter];
for (int i = 0; i < Edges.Length; i++)
{
Edges[i] = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, "ve" + i.ToString());
}
// Integrate new variables
model.Update();
if (print)
LP += "Applicant Matching Conditions:" + Environment.NewLine;
foreach (Instance.Applicant a in instance.Applicants)
{
GRBLinExpr Temp = new GRBLinExpr();
for (int i = 0; i < LPEdges.Count; i++)
{
if (LPEdges[i].Applicant == a)
{
Temp += Edges[i];
if (print)
LP += "(a" + LPEdges[i].Applicant.ID + ", p" + LPEdges[i].Post.ID + ") + ";
}
}
model.AddConstr(Temp == 1.0, "a" + a.ID.ToString());
if (print)
LP += " = 1;" + Environment.NewLine;
}
if (print)
LP += Environment.NewLine + "Post Matching Conditions:" + Environment.NewLine;
foreach (Instance.Post p in instance.Posts)
{
GRBLinExpr Temp = new GRBLinExpr();
for (int i = 0; i < LPEdges.Count; i++)
{
if (LPEdges[i].Post == p)
{
Temp += Edges[i];
if (print)
LP += "(a" + LPEdges[i].Applicant.ID + ", p" + LPEdges[i].Post.ID + ") + ";
}
}
model.AddConstr(Temp <= 1.0, "p" + p.ID.ToString());
if (print)
LP += " <= 1;" + Environment.NewLine;
}
if (print)
LP += Environment.NewLine + "First Choice Conditions:" + Environment.NewLine;
for (int i = 0; i < LPEdges.Count; i++)
{
LPEdge le1 = LPEdges[i];
if (le1.Post.IsF == 1 && le1.Rank != 0)
{
model.AddConstr(Edges[i] <= 0, "s" + i.ToString());
if (print)
LP += "(a" + LPEdges[i].Applicant.ID + ", p" + LPEdges[i].Post.ID + ") <= 0;" + Environment.NewLine;
for (int j = 0; j < LPEdges[i].Applicant.Priorities.Count; j++)
{
if (LPEdges[i].Applicant.Priorities[j].Target == LPEdges[i].Post.ID && LPEdges[i].Rank == LPEdges[i].Applicant.Priorities[j].Rank)
{
LPEdges[i].Applicant.Priorities.RemoveAt(j);
}
}
}
}
if (print)
LP += Environment.NewLine + "Second Choice Conditions:" + Environment.NewLine;
for (int i = 0; i < LPEdges.Count; i++)
{
LPEdge le1 = LPEdges[i];
foreach (LPEdge le2 in LPEdges)
{
if (le2 != le1 && le2.Post.IsF == 0 && le1.Applicant == le2.Applicant && le2.Rank != 0 && le2.Rank < le1.Rank)
{
model.AddConstr(Edges[i] <= 0, "s" + i.ToString());
if (print)
LP += "(a" + LPEdges[i].Applicant.ID + ", p" + LPEdges[i].Post.ID + ") <= 0;" + Environment.NewLine;
for (int j = 0; j < LPEdges[i].Applicant.Priorities.Count; j++)
{
if (LPEdges[i].Applicant.Priorities[j].Target == LPEdges[i].Post.ID && LPEdges[i].Rank == LPEdges[i].Applicant.Priorities[j].Rank)
{
LPEdges[i].Applicant.Priorities.RemoveAt(j);
}
}
break;
}
}
}
if (print)
LP += Environment.NewLine + "First Post Conditions:" + Environment.NewLine;
foreach (Instance.Post p in instance.Posts)
{
if (p.IsF == 1)
{
GRBLinExpr Temp = new GRBLinExpr();
for (int i = 0; i < LPEdges.Count; i++)
{
if (LPEdges[i].Post == p)
{
Temp += Edges[i];
if (print)
LP += "(a" + LPEdges[i].Applicant.ID + ", p" + LPEdges[i].Post.ID + ") + ";
}
}
model.AddConstr(Temp >= 1.0, "f" + p.ID.ToString());
if (print)
LP += ">= 1;" + Environment.NewLine;
}
}
// Optimize model
model.Optimize();
if (print)
{
instance.Draw().Save(path + "/1Reduced.bmp");
}
for (int i = 0; i < Edges.Length; i++)
{
if (Edges[i].Get(GRB.DoubleAttr.X) == 1)
{
instance.AddMatch(LPEdges[i].Post.ID, LPEdges[i].Applicant.ID);
}
}
if (print)
{
instance.Draw().Save(path + "/2Matched.bmp");
}
// Dispose of model and env
model.Dispose();
env.Dispose();
return instance;
}
catch (GRBException e)
{
Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message);
return null;
}
}
/// <summary>
/// Check for applicant complete matching
/// </summary>
/// <param name="instance"></param>
/// <returns></returns>
private Instance GetApplicantComplete(Instance instance)
{
List<int>[] Suitors = new List<int>[instance.Posts.Length];
for (int i = 0; i < instance.Posts.Length; i++)
{
Suitors[i] = new List<int>();
}
// create suitors list
for (int i = 0; i < instance.Applicants.Length; i++)
{
for (int j = 0; j < instance.Applicants[i].Priorities.Count; j++)
{
Suitors[instance.Applicants[i].Priorities.ElementAt(j).Target].Add(i);
}
}
int Unmatched = instance.Posts.Length; // # of not full posts
int UnmatchedApplicants = instance.Applicants.Length; // # unmatched applicants
for (int i = 0; i < instance.Posts.Length; i++)
{
// if a post is connected to only one not matched applicant, match this
if (Suitors[i].Count == 1 && !instance.Posts[i].Matched && !instance.Applicants[Suitors[i].ElementAt(0)].Matched)
{
instance.Posts[i].Matched = true;
instance.AddMatch(i, Suitors[i].ElementAt(0));
UnmatchedApplicants--;
int Applicant = Suitors[i].ElementAt(0);
for (int j = 0; j < instance.Posts.Length; j++)
{
Suitors[j].Remove(Applicant);
}
}
}
for (int i = 0; i < instance.Posts.Length; i++)
{
// delete not connected posts
if (Suitors[i].Count == 0)
{
instance.Posts[i].Matched = true;
Unmatched--;
}
}
// check if there is enough space for the remaining applicants
if (Unmatched < UnmatchedApplicants)
return null;
else
{
// if yes, walk over the disjoint cycle and take every second edge
for (int i = 0; i < instance.Applicants.Length; i++)
{
instance = GoPath(instance, i);
if (instance == null)
instance = null;
}
}
return instance;
}