public static INCRCliqueTree GenerateKTree(long n, int k, Random random)
{
var node = new INCRNode(Enumerable.Range(0, k + 1).Select(i => (uint)i));
var cliqueTree = new INCRCliqueTree()
{
MaximalCliques = 1,
Edges = k * (k + 1) / 2,
Cardinalities = new List <int>()
{
k + 1
},
Cliques = new List <INCRNode>()
{
node
}
};
for (int u = 1; u < n - k; u++)
{
var i = random.Next(cliqueTree.MaximalCliques);
var y = random.Next(cliqueTree.Cardinalities[i]);
var sep = cliqueTree.Cliques[i].Where((x, ii) => ii != y);
// var newSep = new List<ushort>(sep);
var newNode = new INCRNode(sep);
newNode.Add((uint)(u + k));
cliqueTree.Cliques.Add(newNode);
cliqueTree.Cardinalities.Add(k + 1);
cliqueTree.MaximalCliques++;
cliqueTree.Edges += k;
cliqueTree.EdgesList.Add(new INCREdge(i, cliqueTree.Cliques.Count - 1, null, k));
}
return(cliqueTree);
}
public long SplitEdgesK(long upperBound, long n, Random random, int k = 1)
{
var loops = 0;
var disSet = new MVA.UnionFind <int>();
for (int i = 0; i < this.MaximalCliques; i++)
{
var tmp = disSet[i];
}
while (this.EdgesList.Count > 0 && this.Edges < upperBound)
{
loops++;
var rndEdgeI = random.Next(this.EdgesList.Count);
var rndEdge = this.EdgesList[rndEdgeI];
int i = disSet[rndEdge.Node1], j = disSet[rndEdge.Node2];
var sep = new HashSet <uint>(this.Cliques[i]);
sep.IntersectWith(this.Cliques[j]);
var xSep = new HashSet <uint>(this.Cliques[i]); // O(n)
xSep.ExceptWith(sep);
var ySep = new HashSet <uint>(this.Cliques[j]); // O(n)
ySep.ExceptWith(sep);
if (xSep.Count == 0 && ySep.Count == 0)
{
throw new Exception("Not a valid clique tree");
}
else if (xSep.Count <= k || ySep.Count <= k)
{
// merge x,y
var edgesAdded = xSep.Count * ySep.Count;
var mergedIndex = disSet.Union(rndEdge.Node1, rndEdge.Node2);
if (mergedIndex == i)
{
// Union find merged in i
this.Cliques[i].AddRange(ySep);
this.Cardinalities[i] += ySep.Count;
this.Cliques[j] = null;
this.Cardinalities[j] = 0;
}
else
{
this.Cliques[j].AddRange(xSep);
this.Cardinalities[j] += xSep.Count;
this.Cliques[i] = null;
this.Cardinalities[i] = 0;
}
this.Edges += edgesAdded;
this.MaximalCliques--;
this.EdgesList.RemoveAt(rndEdgeI);
}
else if (xSep.Count <= k)
{
// merge x,z
var yLen = random.Next(1, ySep.Count);
var yRandom = ySep.Take(yLen);
this.Cliques[i].AddRange(yRandom);
this.Cardinalities[i] += yLen;
// this.EdgesList[rndEdgeI].Seperator.Union(yRandom);
this.EdgesList[rndEdgeI].SeperatorWeight += yLen;
}
else if (ySep.Count <= k)
{
//merge y,z
var xLen = random.Next(1, xSep.Count);
var xRandom = xSep.Take(xLen);
this.Cliques[i].AddRange(xRandom);
this.Cardinalities[i] += xLen;
// this.EdgesList[rndEdgeI].Seperator.Union(xRandom);
this.EdgesList[rndEdgeI].SeperatorWeight += xLen;
}
else
{
// make new z node
var xLen = random.Next(1, xSep.Count);
var yLen = random.Next(1, ySep.Count);
var xRandom = xSep.Take(xLen);
var yRandom = ySep.Take(yLen);
var z = new INCRNode(xRandom);
z.AddRange(yRandom);
z.AddRange(sep);
var edgesAdded = xLen * yLen;
this.Cliques.Add(z);
this.Cardinalities.Add(xLen + yLen + rndEdge.SeperatorWeight);
// var sep1 = new List<ushort>(xRandom); // Ο(n)
// sep1.AddRange(rndEdge.Seperator);
// this.EdgesList.Add(new INCREdge(rndEdge.Node1, this.Cliques.Count - 1, sep1, edgesAdded + rndEdge.SeperatorWeight));
this.EdgesList.Add(new INCREdge(rndEdge.Node1, this.Cliques.Count - 1, null, edgesAdded + rndEdge.SeperatorWeight));
// var sep2 = new List<ushort>(yRandom);
// sep2.AddRange(rndEdge.Seperator);
// this.EdgesList.Add(new INCREdge(rndEdge.Node2, this.Cliques.Count - 1, sep2, edgesAdded + rndEdge.SeperatorWeight));
this.EdgesList.Add(new INCREdge(rndEdge.Node2, this.Cliques.Count - 1, null, edgesAdded + rndEdge.SeperatorWeight));
this.MaximalCliques++;
this.Edges += edgesAdded;
this.EdgesList.RemoveAt(rndEdgeI);
}
}
foreach (var edge in this.EdgesList)
{
edge.Node1 = disSet[edge.Node1];
edge.Node2 = disSet[edge.Node2];
}
return(loops);
}
