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;
}
}
}
private PrimeNode Contraction(SplitTree ST, SplitTree tPrime, int xId)
{
//during the contraction, the active flags won't be used any more. thus available as temporary delete flags
//when a deleted node has non-empty parentLink and empty unionFind_parent, it is a degenerate to prime conversion and the parentLink points to the converted prime node.
//when a deleted node has non-empty unionFind_parent, it is a fake node (only playing a role of child representative)
ST.ResetActiveFlags();
List<DegenerateNode> Phase1List = new List<DegenerateNode>();
List<Node> Phase2List = new List<Node>();
List<Node> nonLeafChildren = new List<Node>();
Node phase3 = null;//since phase 3 is recursive, we need only a start point.
#region Phase 0 Initial sweep
foreach (var v in tPrime.vertices)
{
var d = v as DegenerateNode;
var n = v as Node;
if (d != null && d.isStar && d.rootMarkerVertex == d.center)
Phase1List.Add(d);
if (n != null && n.Degree(n.rootMarkerVertex) == 1)
Phase2List.Add(n);
if (n != null)
phase3 = n;//in case Phase1List and Phase2List are both empty, at least we have a start point for phase 3
}
#endregion
#region Phase 1 node-joins
foreach (var star in Phase1List)
{
if (star.active)//deleted
continue;
phase3 = star;
nonLeafChildren.Clear();
phase3.ForEachChild((v) =>
{
if (v is Node)
{
nonLeafChildren.Add(v as Node);
}
return IterationFlag.Continue;
}, subtree: true);
foreach (var c in nonLeafChildren)
{
phase3 = NodeJoin(ST, phase3, c);
//c.parentLink = dummy;
}
phase3.visited = true;//add the joint node back into T'
}
#endregion
#region Phase 2 node-joins
foreach (var node in Phase2List)
{
if (node.active)//actually I mean "deleted"
continue;
phase3 = node;
var p = phase3.parent;
if (p.visited && p is Node)
{
phase3 = NodeJoin(ST, p as Node, phase3);//make sure phase3 now points to the new parent(which is prime)
}
}
#endregion
#region Phase 3 node-joins
Debug.Assert(phase3 != null, "Phase 3 node is null, which means that there's nothing left in the fully-mixed subtree T'");
while (true)
{
while (true)
{
nonLeafChildren.Clear();
phase3.ForEachChild((v) =>
{
if (v is Node)
{
nonLeafChildren.Add(v as Node);
}
return IterationFlag.Continue;
}, subtree: true);
if (nonLeafChildren.Count == 0)
break;
foreach (var c in nonLeafChildren)
{
phase3 = NodeJoin(ST, phase3, c);
}
}
var p = phase3.parent;
if (p == null || p is Leaf || p.visited == false)
{
break;
}
else
phase3 = p as Node;
}
#endregion
//rebuild ST from dummy flags. Note that this step is very important before using Find() and parent accessor again, because there might be a node with unionFind_parent == dummyFake, and dummyFake has unionFind_parent == null
//List<GLTVertex> newSTList = new List<GLTVertex>();
//foreach (var vertex in ST.vertices)
//{
// if (!vertex.active)
// newSTList.Add(vertex);//a normal vertex
// else if (vertex.parentLink != null && vertex.unionFind_parent == null)
// newSTList.Add(vertex.parentLink);//a converted vertex
// //otherwise, either a fake node, or a truely-removed one, we don't add them back to ST any more.
// //if (vertex.parentLink != deleteDummy && vertex.unionFind_parent != fakeDummy)//neither deleted nor fake
// // newSTList.Add(vertex);
// //else if (vertex.parentLink == deleteDummy && vertex.unionFind_parent != null)//replaced
// // newSTList.Add(vertex.unionFind_parent);
// //else if (vertex.unionFind_parent == fakeDummy)
// // vertex.unionFind_parent = vertex;//point the unionFind_parent back
//}
//ST.vertices = newSTList;
HashSet<MarkerVertex> Pset = new HashSet<MarkerVertex>();
phase3.ForEachMarkerVertex((v) =>
{
if (v.perfect)
Pset.Add(v);
return IterationFlag.Continue;
});
Leaf newLeaf = new Leaf()
{
id = xId,
parent = phase3,
};
MarkerVertex newMarker = new MarkerVertex()
{
opposite = newLeaf,
};
newLeaf.opposite = newMarker;
(phase3 as PrimeNode).AddMarkerVertex(newMarker, Pset);
(phase3 as PrimeNode).lastMarkerVertex = newMarker;
ST.AddLeaf(newLeaf);
return phase3 as PrimeNode;
}
