//returns the new node containing B, plus a marker vertex representing A(while the old node is transformed into the A part)
private DegenerateNode SplitNode(DegenerateNode node, System.Collections.Generic.HashSet<MarkerVertex> A, System.Collections.Generic.HashSet<MarkerVertex> B)
{
//XXX A set here is not necessary...
//since node must be degenerate(otherwise not splittable due to the definition of prime node), there's an easy way to build frontiers:
//see paper notes.
//assume the original node contains A part, now we remove the B part
node.RemoveMarkerVertices(B);
var v1 = new MarkerVertex();
var v2 = new MarkerVertex();
DegenerateNode newNode = new DegenerateNode()
{
Vu = new List<MarkerVertex>(B),
};
if (node.isStar)//address the center issue
{
if (A.Contains(node.center))
{
//node center doesn't change
newNode.center = v2;
}
else
{
newNode.center = node.center;
node.center = v1;
}
}
node.Vu.Add(v1);
newNode.Vu.Add(v2);
v1.opposite = v2;
v2.opposite = v1;
if (B.Contains(node.rootMarkerVertex))//B is being splitted out, if B has the root marker vertex, newNode should point to the original parent
{
newNode.rootMarkerVertex = node.rootMarkerVertex;
newNode.parent = node.parent;
newNode.rootMarkerVertex.node = newNode;
node.rootMarkerVertex = v1;
v1.node = node;
//before assigning parent, check if a clone is necessary
if (node.parent is PrimeNode)
{
var cloned = node.Clone();
node = cloned as DegenerateNode;//thus the old node deprecated
}
node.parent = newNode;
}
else//A has root marker vertex, thus old parent unchanged.
{
newNode.rootMarkerVertex = v2;
newNode.parent = node;
v2.node = newNode;
}
//update the parent links of the children in the new node
newNode.ForEachChild((v) =>
{
v.parent = newNode;
return IterationFlag.Continue;
}, subtree: false);
return newNode;
}
private void VertexInsertion(SplitTree ST, List<int> sigma, int idx)
{
#region Bootstrapping
if (ST.vertices.Count == 0)//initialization
{
Leaf v = new Leaf
{
id = sigma[idx],
parent = null,
};
ST.AddLeaf(v);
ST.root = v;
}
else if (ST.vertices.Count == 1)//only the root, thus we cache the second vertex
{
Leaf v = new Leaf
{
id = sigma[idx],
parent = null,
};
ST.AddLeaf(v);
}
else if (ST.vertices.Count == 2)//now we're building the first trinity
{
Leaf v = new Leaf
{
id = sigma[idx],
parent = null
};
ST.AddLeaf(v);
int missingConnection = -1; //test the missing connection between the cached 3 leave
if (!storage[(ST.vertices[0] as Leaf).id].Contains((ST.vertices[1] as Leaf).id))
{
missingConnection = 0;
}
else if (!storage[(ST.vertices[0] as Leaf).id].Contains((ST.vertices[2] as Leaf).id))
{
missingConnection = 1;
}
else if (!storage[(ST.vertices[1] as Leaf).id].Contains((ST.vertices[2] as Leaf).id))
{
missingConnection = 2;
}
MarkerVertex v1 = new MarkerVertex()
{
opposite = ST.vertices[0]
};
MarkerVertex v2 = new MarkerVertex()
{
opposite = ST.vertices[1]
};
MarkerVertex v3 = new MarkerVertex()
{
opposite = ST.vertices[2]
};
(ST.vertices[0] as Leaf).opposite = v1;
(ST.vertices[1] as Leaf).opposite = v2;
(ST.vertices[2] as Leaf).opposite = v3;
MarkerVertex center = null;
switch (missingConnection)
{
case 0:
center = v3;
break;
case 1:
center = v2;
break;
case 2:
center = v1;
break;
default: break;
}
var deg = new DegenerateNode()
{
parent = ST.vertices[0],
Vu = new List<MarkerVertex> { v1, v2, v3 },
center = center,
rootMarkerVertex = v1
};
v1.node = deg;
ST.vertices[1].parent = ST.vertices[2].parent = deg;
ST.vertices.Add(deg);
ST.lastVertex = ST.vertices[2] as Leaf;
}
#endregion
else
{
TreeEdge e; Vertex u; SplitTree tPrime;
var returnType = SplitTree_CaseIdentification(ST, sigma, idx, out e, out u, out tPrime);
switch (returnType)
{
case CaseIdentification_ResultType.SingleLeaf:
//This case is not discussed in paper. However, if there's only a single leaf in neighbor set,
//then a unique PE edge can be found.
//Applying proposition 4.17, case 6
e.u = (u as Leaf).opposite;
e.v = u;
ST.SplitEdgeToStar(e, sigma[idx]);
break;
case CaseIdentification_ResultType.TreeEdge://PP or PE
{
bool unique = true;
bool pp;
//testing uniqueness, page 24
//check whether pp or pe
if (!e.u.Perfect())
{
var tmp = e.u;
e.u = e.v;
e.v = tmp;
}
pp = e.v.Perfect();
var u_GLT = e.u_GLT;
var v_GLT = e.v_GLT;
DegenerateNode degNode = null;
if (u_GLT is DegenerateNode)
degNode = u_GLT as DegenerateNode;
if (v_GLT is DegenerateNode)
degNode = v_GLT as DegenerateNode;
if (degNode != null)//attached to a clique or a star
{
if ((pp && degNode.isClique) || (!pp/*pe*/ && degNode.isStar && (e.u == degNode.center || degNode.Degree(e.v as MarkerVertex) == 1)))
{
unique = false;
}
}
if (unique)
{
//Proposition 4.17 case 5 or 6
if (pp)//PP
{
ST.SplitEdgeToClique(e, sigma[idx]);
}
else//PE
{
ST.SplitEdgeToStar(e, sigma[idx]);
}
}
else
{
//Proposition 4.15, case 1 or 2
var deg = u_GLT;
if (v_GLT is DegenerateNode)
deg = v_GLT;
ST.AttachToDegenerateNode(deg as DegenerateNode, sigma[idx]);
}
}
break;
case CaseIdentification_ResultType.HybridNode:
if (u is DegenerateNode)
{
//Proposition 4.16
var uDeg = u as DegenerateNode;
System.Collections.Generic.HashSet<MarkerVertex> PStar = new System.Collections.Generic.HashSet<MarkerVertex>();
System.Collections.Generic.HashSet<MarkerVertex> EStar = new System.Collections.Generic.HashSet<MarkerVertex>();
uDeg.ForEachMarkerVertex((v) =>
{
if (v.perfect && v != uDeg.center)
PStar.Add(v);
else
EStar.Add(v);
return IterationFlag.Continue;
});
//before we split, determine the new perfect states for the two new markers to be generated
bool pp = false;
if (uDeg.isStar && uDeg.center.perfect)
{
pp = true;//see figure 7. pp==true iff star and center is perfect.
}
var newNode = SplitNode(uDeg, PStar, EStar);
ST.vertices.Add(newNode);
//e.u \in PStar ; e.v \in EStar (thus containing the original center, if star)
//PStar in uDeg; EStar in newNode
if (newNode.parent == uDeg)
{
e.u = newNode.rootMarkerVertex.opposite;
e.v = newNode.rootMarkerVertex;
}
else
{
e.u = uDeg.rootMarkerVertex;
e.v = uDeg.rootMarkerVertex.opposite;
}
//assign perfect state values
if (pp)
{
e.u.MarkAsPerfect();
e.v.MarkAsPerfect();
}
else//PE, and PStar part always has an empty state and EStar part has perfect.
{
e.u.MarkAsEmpty();
e.v.MarkAsPerfect();
}
//check whether pp or pe
if (!e.u.Perfect())
{
var tmp = e.u;
e.u = e.v;
e.v = tmp;
}
if (e.v.Perfect())//PP
{
ST.SplitEdgeToClique(e, sigma[idx]);
}
else//PE
{
ST.SplitEdgeToStar(e, sigma[idx]);
}
}
else
{
//Proposition 4.15, case 3
ST.AttachToPrimeNode(u as PrimeNode, sigma[idx]);
}
break;
case CaseIdentification_ResultType.FullyMixedSubTree:
//Proposition 4.20
Cleaning(ST, tPrime);
//ST.Debug(false);
var contractionNode = Contraction(ST, tPrime, sigma[idx]);
break;
}
}
}
internal override GLTVertex Clone()
{
DegenerateNode newDegNode = new DegenerateNode()
{
activeTimestamp = activeTimestamp,
center = center,
parentLink = parentLink,
rootMarkerVertex = rootMarkerVertex,
unionFind_parent = unionFind_parent,
visitedTimestamp = visitedTimestamp,
Vu = Vu,
};
rootMarkerVertex.node = newDegNode;
ForEachChild((v) =>
{
v.parentLink = newDegNode;
v.unionFind_parent = null;
return IterationFlag.Continue;
}, false);
return newDegNode;
}
//Proposition 4.15
internal void AttachToDegenerateNode(DegenerateNode deg, int xId)
{
MarkerVertex v = new MarkerVertex();
Leaf x = new Leaf()
{
id = xId,
opposite = v,
parent = deg,
};
v.opposite = x;
deg.Vu.Add(v);//and done! if clique, all vertices are P, thus fully connecting v.
//and if star, v is connected to center, the only perfect marker.
AddLeaf(x);
}
//Proposition 4.17
internal void SplitEdgeToStar(TreeEdge e, int xId)
{
//Assume e is P-E
GLTVertex oParent = e.u.GetGLTVertex();
GLTVertex oChild = e.v.GetGLTVertex();
bool uIsParent = true;
//test and swap
if (oChild.parent != oParent)
{
var tmp = oParent;
oParent = oChild;
oChild = tmp;
uIsParent = false;
}
////Fixing multiple-star forking problem
//var oChildDeg = oChild as DegenerateNode;
//if (oChildDeg != null && oChildDeg.isStar && oChildDeg.center == oChildDeg.rootMarkerVertex)
//{
// //note that if child's center is not root, we cannot merge.
// AttachToDegenerateNode(oChildDeg, xId);
// return;
//}
MarkerVertex v1 = new MarkerVertex();
MarkerVertex v2 = new MarkerVertex();
MarkerVertex v3 = new MarkerVertex();
//center is E (e.v) => v2
var deg = new DegenerateNode()
{
active = false,
center = v2,
parent = oParent,
rootMarkerVertex = uIsParent ? v1 : v2,
visited = false,
Vu = new List<MarkerVertex> { v1, v2, v3 }
};
if (uIsParent)
v1.node = deg;
else v2.node = deg;
deg.parent = oParent;
if (oParent is PrimeNode == false)
{
oChild.parent = deg;
}
else
{
//(oParent as PrimeNode).ForEachChild(c =>
// {
// if (c.unionFind_parent == oChild)
// Console.WriteLine("!!!");
// return IterationFlag.Continue;
// }, false);
//oChild.parent = deg;
var newChild = oChild.Clone();//since oChild is potentially pointed by others' unionFind_parent, we have to clone.
if (newChild is Leaf)
{
LeafMapper[(newChild as Leaf).id] = newChild as Leaf;
//a new leaf is cloned. thus e.u / e.v is cloned. check and update.
if (e.u is Leaf)
e.u = newChild;
else
e.v = newChild;
}
newChild.parent = deg;
}
//linking e.u & e.v to v1 & v2
if (e.u is MarkerVertex)
(e.u as MarkerVertex).opposite = v1;
else
(e.u as Leaf).opposite = v1;
if (e.v is MarkerVertex)
(e.v as MarkerVertex).opposite = v2;
else
(e.v as Leaf).opposite = v2;
v1.opposite = e.u;
v2.opposite = e.v;
Leaf x = new Leaf
{
id = xId,
opposite = v3,
};
v3.opposite = x;
x.parent = deg;
//vertices.Add(deg);
AddLeaf(x);
}