private static void SolveWithHeuristic(WeightedGraph graph)
{
int currentAnswerWeight = 0;
int candidateWeight = 0;
List <int> answer = new List <int> ();
_stopwatch.Start();
foreach (int v in graph.Vertices.Keys)
{
candidateWeight = 0;
// Select all neighbors
List <int> neighbors = Neighbors(v, graph);
List <int> cliqueCandidate = new List <int> ();
// Start the candidate clique with the current vertex
cliqueCandidate.Add(v);
// Sort neighbors by combined Weight and degree
List <KeyValuePair <int, int> > neighborsByWeightPlus = SortNeighbors(v, neighbors, graph, "weight+");
// For each neighbor check if it makes a clique with the candidate
foreach (var neighbor in neighborsByWeightPlus)
{
bool makeClique = true;
foreach (int vCand in cliqueCandidate)
{
// Check for maxTime
if (_stopwatch.Elapsed >= _maxRunTime)
{
Log("Abort! Max Run Time exceeded!");
break;
}
if (!graph.Edges[vCand].Contains(neighbor.Key))
{
makeClique = false;
break;
}
}
if (makeClique)
{
cliqueCandidate.Add(neighbor.Key);
}
// Check for maxTime
if (_stopwatch.Elapsed >= _maxRunTime)
{
Log("Abort! Max Run Time exceeded!");
break;
}
}
// Check if the new candidate is better than the current best answer
candidateWeight = 0;
cliqueCandidate.ForEach(c => candidateWeight += graph.Vertices[c]);
Log(String.Format("current weight: {0}", currentAnswerWeight));
Log(String.Format("candidate weight: {0}", candidateWeight));
Log("================================================");
if (candidateWeight < currentAnswerWeight)
{
continue;
}
else
{
currentAnswerWeight = candidateWeight;
answer.Clear();
answer.AddRange(cliqueCandidate);
}
// Check for maxTime
if (_stopwatch.Elapsed >= _maxRunTime)
{
Log("Abort! Max Run Time exceeded!");
break;
}
}
TimeSpan timeElapsed = _stopwatch.Elapsed;
List <string> answerLabels = new List <string> ();
answer.ForEach(v => answerLabels.Add(graph.VertexIndexMap[v]));
Log(String.Format("Max Clique: [{0}]", String.Join(", ", answerLabels)));
Log(String.Format("Max Clique Weight: {0}", currentAnswerWeight));
using (StreamWriter sw = new StreamWriter(_graphInstancePath.Replace(".txt", "out.csv"), append: true))
{
sw.WriteLine(String.Format("{0}\t{1}\t{2}", timeElapsed.ToString(), _graphInstancePath, currentAnswerWeight));
}
}
private static bool BronKerbosch(List <int> R, List <int> P, List <int> X, WeightedGraph graph, ref List <int> answer)
{
_backtrackCallCount++;
//Log ("======================================================");
//Log (String.Format ("R: [{0}]", String.Join(", ", R)));
//Log (String.Format ("P: [{0}]", String.Join(", ", P)));
//Log (String.Format ("X: [{0}]", String.Join(", ", X)));
int currentCliqueWeight = 0;
int possibleMaxCliqueWeight = 0;
int candidateCliqueWeight = 0;
if (_optimizeBacktrack)
{
// Check if we can increase the max clique with the current set
possibleMaxCliqueWeight = 0;
foreach (int vPos in R.Union(P))
{
possibleMaxCliqueWeight += graph.Vertices[vPos];
}
// calculate weight of maximal clique
currentCliqueWeight = 0;
foreach (int vAns in answer)
{
currentCliqueWeight += graph.Vertices[vAns];
}
//Log (String.Format ("Possible Max Weight: {0}", possibleMaxCliqueWeight));
//Log (String.Format ("Current Weight: {0}", currentCliqueWeight));
if (possibleMaxCliqueWeight < currentCliqueWeight)
{
return(false);
}
}
//if P and X are both empty:
if (P.Count == 0 && X.Count == 0)
{
//report R as a maximal clique
return(true);
}
int[] auxP = new int[P.Count];
P.CopyTo(auxP);
List <int> auxPList = auxP.ToList();
//for each vertex v in P:
foreach (int v in P)
{
// Check for maxTime
if (_stopwatch.Elapsed >= _maxRunTime)
{
Log("Abort! Max Run Time exceeded!");
return(false);
}
List <int> Nv = Neighbors(v, graph);
//BronKerbosch1(R ⋃ {v}, P ⋂ N(v), X ⋂ N(v))
if (BronKerbosch(R.Union(new List <int> {
v
}).ToList(), auxPList.Intersect(Nv).ToList(), X.Intersect(Nv).ToList(), graph, ref answer))
{
// calculate weight of maximal clique
currentCliqueWeight = 0;
foreach (int vAns in answer)
{
currentCliqueWeight += graph.Vertices[vAns];
}
Log(String.Format("current weight: {0}", currentCliqueWeight));
candidateCliqueWeight = 0;
foreach (int vCand in R.Union(new List <int> {
v
}).ToList())
{
candidateCliqueWeight += graph.Vertices[vCand];
}
Log(String.Format("candidate weight: {0}", candidateCliqueWeight));
// Save heaviest clique as answer
if (candidateCliqueWeight > currentCliqueWeight)
{
answer = R.Union(new List <int> {
v
}).ToList();
Log(String.Format("Candidate is the new max clique! Weight: {0}. Clique: [{1}]", candidateCliqueWeight, String.Join(", ", answer)));
}
Log("================================================");
}
//P := P \ {v}
auxPList.Remove(v);
//X := X ⋃ {v}
X = X.Union(new List <int> {
v
}).ToList();
}
return(false);
}
private static List <int> Neighbors(int v, WeightedGraph graph)
{
return(graph.Edges[v].ToList());
}
private static List <KeyValuePair <int, int> > SortNeighbors(int v, List <int> neighbors, WeightedGraph graph, string mode)
{
List <KeyValuePair <int, int> > sortedList = new List <KeyValuePair <int, int> >();
switch (mode)
{
case "weight":
foreach (int neighbor in neighbors)
{
sortedList.Add(new KeyValuePair <int, int> (neighbor, graph.Vertices[neighbor]));
}
break;
case "degree":
foreach (int neighbor in neighbors)
{
sortedList.Add(new KeyValuePair <int, int> (neighbor, graph.Edges[neighbor].Count));
}
break;
case "weight+":
foreach (int neighbor in neighbors)
{
sortedList.Add(new KeyValuePair <int, int> (neighbor, CalculateVertexCumulateWeight(neighbor, graph) - graph.Vertices[v] + graph.Vertices[neighbor]));
}
break;
}
sortedList.Sort((pair1, pair2) => pair2.Value.CompareTo(pair1.Value));
return(sortedList);
}