int _K33Search_MergeBicomps(graphP theGraph, int v, int RootVertex, int W, int WPrevLink)
{
K33SearchContext *context = NULL;
gp_FindExtension(theGraph, K33SEARCH_ID, (void *)&context);
if (context != NULL)
{
/* If the merge is blocked, then a K_{3,3} homeomorph is isolated,
and NONEMBEDDABLE is returned so that the Walkdown terminates */
if (theGraph->embedFlags == EMBEDFLAGS_SEARCHFORK33)
{
int mergeBlocker;
// We want to test all merge points on the stack
// as well as W, since the connection will go
// from W. So we push W as a 'degenerate' merge point.
sp_Push2(theGraph->theStack, W, WPrevLink);
sp_Push2(theGraph->theStack, NIL, NIL);
if (_SearchForMergeBlocker(theGraph, context, v, &mergeBlocker) != OK)
return NOTOK;
if (gp_IsVertex(mergeBlocker))
{
if (_FindK33WithMergeBlocker(theGraph, context, v, mergeBlocker) != OK)
return NOTOK;
return NONEMBEDDABLE;
}
// If no merge blocker was found, then remove W from the stack.
sp_Pop2(theGraph->theStack, W, WPrevLink);
sp_Pop2(theGraph->theStack, W, WPrevLink);
}
// If the merge was not blocked, then we perform the merge
// When not doing a K3,3 search, then the merge is not
// blocked as far as the K3,3 search method is concerned
// Another algorithms could overload MergeBicomps and block
// merges under certain conditions, but those would be based
// on data maintained by the extension that implements the
// other algorithm-- if *that* algorithm is the one being run
return context->functions.fpMergeBicomps(theGraph, v, RootVertex, W, WPrevLink);
}
return NOTOK;
}
int _FindNonplanarityBicompRoot(graphP theGraph)
{
int R, tempChild, fwdArc, W=NIL, C=NIL, I=theGraph->IC.v;
/* If the stack is non-empty, then the Walkdown stopped on a descendant
bicomp, not one rooted by I. We need to get that root before the
stack is destroyed by other routines. */
if (sp_NonEmpty(theGraph->theStack))
{
int e;
sp_Pop2(theGraph->theStack, R, e);
return R;
}
/* Obtain the forward arc of an unembedded back edge from I to one of its
descendants (edges are removed from the forward arc list as they are
embedded, so the list will be empty if all edges were embedded). */
if ((fwdArc = theGraph->V[I].fwdArcList) == NIL)
return NIL;
W = theGraph->G[fwdArc].v;
/* Find the greatest DFS child C of I that is less than W. This will
give us the ancestor of W that is a child of I. Since the
ancestors of I have not been processed by the planarity algorithm,
the separatedDFSChildList of I contains all the children of I. */
tempChild = theGraph->V[I].separatedDFSChildList;
while (tempChild != NIL)
{
if (tempChild > C && tempChild < W)
C = tempChild;
tempChild = LCGetNext(theGraph->DFSChildLists,
theGraph->V[I].separatedDFSChildList, tempChild);
}
if (C == NIL) return NIL;
/* The root vertex of a bicomp rooted by edge (I, C) is located at
position C+N in our data structures */
R = C + theGraph->N;
return R;
}
int _K4Search_HandleBlockedBicomp(graphP theGraph, int v, int RootVertex, int R)
{
K4SearchContext *context = NULL;
gp_FindExtension(theGraph, K4SEARCH_ID, (void *)&context);
if (context == NULL)
return NOTOK;
if (theGraph->embedFlags == EMBEDFLAGS_SEARCHFORK4)
{
int RetVal = OK;
// If invoked on a descendant bicomp, then we push its root then search once
// since not finding a K4 homeomorph will also clear the blockage and allow
// the Walkdown to continue walking down
if (R != RootVertex)
{
sp_Push2(theGraph->theStack, R, 0);
if ((RetVal = _SearchForK4InBicomp(theGraph, context, v, R)) == OK)
{
// If the Walkdown will be told it is OK to continue, then we have to take the descendant
// bicomp root back off the stack so the Walkdown can try to descend to it again.
int dummy;
sp_Pop2(theGraph->theStack, R, dummy);
// And we have to clear the indicator of the minor A that was reduced, since it was eliminated.
theGraph->IC.minorType = 0;
}
}
// Otherwise, if invoked on a child bicomp rooted by a virtual copy of v,
// then we search for a K4 homeomorph, and if OK is returned, then that indicates
// the blockage has been cleared and it is OK to Walkdown the bicomp.
// But the Walkdown finished, already, so we launch it again.
// If the Walkdown returns OK then all forward arcs were embedded. If NONEMBEDDABLE
// is returned, then the bicomp got blocked again, so we have to reiterate the K4 search
else
{
// If Walkdown has recursively called this handler on the bicomp rooted by RootVertex,
// then it is still blocked, so we just return NONEMBEDDABLE, which causes Walkdown to
// return to the loop below and signal that the loop should invoke the Walkdown again.
if (context->handlingBlockedBicomp)
return NONEMBEDDABLE;
context->handlingBlockedBicomp = TRUE;
do {
// Detect whether bicomp can be used to find a K4 homeomorph. It it does, then
// it returns NONEMBEDDABLE so we break the search because we found the desired K4
// If OK is returned, then the blockage was cleared and it is OK to Walkdown again.
if ((RetVal = _SearchForK4InBicomp(theGraph, context, v, RootVertex)) != OK)
break;
// Walkdown again to embed more edges. If Walkdown returns OK, then all remaining
// edges to its descendants are embedded, so we'll get out of this loop. If Walkdown
// detects that it still has not embedded all the edges to descendants of the bicomp's
// root edge child, then Walkdown calls this routine again, and the above non-reentrancy
// code returns NONEMBEDDABLE, causing this loop to search again for a K4.
theGraph->IC.minorType = 0;
RetVal = theGraph->functions.fpWalkDown(theGraph, v, RootVertex);
// Except if the Walkdown returns NONEMBEDDABLE due to finding a K4 homeomorph entangled
// with a descendant bicomp (the R != RootVertex case above), then it was found
// entangled with Minor A, so we can stop the search if minor A is detected
if (theGraph->IC.minorType & MINORTYPE_A)
break;
} while (RetVal == NONEMBEDDABLE);
context->handlingBlockedBicomp = FALSE;
}
return RetVal;
}
else
{
return context->functions.fpHandleBlockedBicomp(theGraph, v, RootVertex, R);
}
return NOTOK;
}
int gp_CreateDFSTree(graphP theGraph)
{
stackP theStack;
int N, DFI = 0, I, uparent, u, e, J;
#ifdef PROFILE
platform_time start, end;
platform_GetTime(start);
#endif
if (theGraph==NULL) return NOTOK;
if (theGraph->internalFlags & FLAGS_DFSNUMBERED) return OK;
gp_LogLine("\ngraphPreprocess.c/gp_CreateDFSTree() start");
N = theGraph->N;
theStack = theGraph->theStack;
/* There are 2M edge records (arcs) and for each we can push 2 integers,
so a stack of 2 * arcCapacity integers suffices.
This is already in theGraph structure, so we make sure it's empty,
then clear all visited flags in prep for the Depth first search. */
if (sp_GetCapacity(theStack) < 2*gp_GetArcCapacity(theGraph))
return NOTOK;
sp_ClearStack(theStack);
for (I=0; I < N; I++)
theGraph->G[I].visited = 0;
/* This outer loop causes the connected subgraphs of a disconnected
graph to be numbered */
for (I=0; I < N && DFI < N; I++)
{
if (theGraph->V[I].DFSParent != NIL)
continue;
sp_Push2(theStack, NIL, NIL);
while (sp_NonEmpty(theStack))
{
sp_Pop2(theStack, uparent, e);
u = uparent == NIL ? I : theGraph->G[e].v;
if (!theGraph->G[u].visited)
{
gp_LogLine(gp_MakeLogStr3("V=%d, DFI=%d, Parent=%d", u, DFI, uparent));
theGraph->G[u].visited = 1;
theGraph->G[u].v = DFI++;
theGraph->V[u].DFSParent = uparent;
if (e != NIL)
{
theGraph->G[e].type = EDGE_DFSCHILD;
theGraph->G[gp_GetTwinArc(theGraph, e)].type = EDGE_DFSPARENT;
// We want the child arcs to be at the beginning
// of the adjacency list.
gp_MoveArcToFirst(theGraph, uparent, e);
}
/* Push edges to all unvisited neighbors. These will be either
tree edges to children or forward arcs of back edges */
J = gp_GetFirstArc(theGraph, u);
while (gp_IsArc(theGraph, J))
{
if (!theGraph->G[theGraph->G[J].v].visited)
sp_Push2(theStack, u, J);
J = gp_GetNextArc(theGraph, J);
}
}
else
{
// If the edge leads to a visited vertex, then it is
// the forward arc of a back edge.
theGraph->G[e].type = EDGE_FORWARD;
theGraph->G[gp_GetTwinArc(theGraph, e)].type = EDGE_BACK;
// We want all of the forward edges to descendants to
// be at the end of the adjacency list.
// The tree edge to the parent and the back edges to ancestors
// are in the middle, between the child edges and forward edges.
gp_MoveArcToLast(theGraph, uparent, e);
}
}
}
gp_LogLine("graphPreprocess.c/gp_CreateDFSTree() end\n");
theGraph->internalFlags |= FLAGS_DFSNUMBERED;
#ifdef PROFILE
platform_GetTime(end);
printf("DFS in %.3lf seconds.\n", platform_GetDuration(start,end));
#endif
return OK;
}