void _MarkExternalFaceVertices(graphP theGraph, int startVertex)
{
int nextVertex = startVertex;
int e = gp_GetFirstArc(theGraph, nextVertex);
int eTwin;
// Handle the case of an isolated vertex
if (gp_IsNotArc(e))
{
gp_SetVertexVisited(theGraph, startVertex);
return;
}
// Process a non-trivial connected component
do {
gp_SetVertexVisited(theGraph, nextVertex);
// The arc out of the vertex just visited points to the next vertex
nextVertex = gp_GetNeighbor(theGraph, e);
// Arc used to enter the next vertex is needed so we can get the
// next edge in rotation order.
// Note: for bicomps, first and last arcs of all external face vertices
// indicate the edges that hold them to the external face
// But _JoinBicomps() has already occurred, so cut vertices
// will have external face edges other than the first and last arcs
// Hence we need this more sophisticated traversal method
eTwin = gp_GetTwinArc(theGraph, e);
// Now we get the next arc in rotation order as the new arc out to the
// vertex after nextVertex. This sets us up for the next iteration.
// Note: We cannot simply follow the chain of nextVertex first arcs
// as we started out doing at the top of this method. This is
// because we are no longer dealing with bicomps only.
// Since _JoinBicomps() has already been invoked, there may now
// be cut vertices on the external face whose adjacency lists
// contain external face arcs in positions other than the first and
// and last arcs. We will visit those vertices multiple times,
// which is OK (just that we have to explain why we're calculating
// jout in this way).
e = gp_GetNextArcCircular(theGraph, eTwin);
// Now things get really interesting. The DFS root (startVertex) may
// itself be a cut vertex to which multiple bicomps have been joined.
// So we cannot simply stop when the external face walk gets back to
// startVertex. We must actually get back to startVertex using its
// last arc. This ensures that we've looped down into all the DFS
// subtrees rooted at startVertex and walked their external faces.
// Since we started the whole external face walk with the first arc
// of startVertex, we need to proceed until we reenter startVertex
// using its last arc.
} while (eTwin != gp_GetLastArc(theGraph, startVertex));
}
void _MarkPath(graphP theGraph, int e)
{
int eTwin, nextVertex;
nextVertex = gp_GetNeighbor(theGraph, e);
// while nextVertex is strictly degree 2
while (gp_IsArc(gp_GetFirstArc(theGraph, nextVertex)) &&
gp_IsArc(gp_GetLastArc(theGraph, nextVertex)) &&
gp_GetNextArc(theGraph, gp_GetFirstArc(theGraph, nextVertex)) == gp_GetLastArc(theGraph, nextVertex))
{
gp_SetVertexVisited(theGraph, nextVertex);
eTwin = gp_GetTwinArc(theGraph, e);
e = gp_GetFirstArc(theGraph, nextVertex);
if (e == eTwin)
e = gp_GetLastArc(theGraph, nextVertex);
nextVertex = gp_GetNeighbor(theGraph, e);
}
}
int _TryPath(graphP theGraph, int e, int V)
{
int eTwin, nextVertex;
nextVertex = gp_GetNeighbor(theGraph, e);
// while nextVertex is strictly degree 2
while (gp_IsArc(gp_GetFirstArc(theGraph, nextVertex)) &&
gp_IsArc(gp_GetLastArc(theGraph, nextVertex)) &&
gp_GetNextArc(theGraph, gp_GetFirstArc(theGraph, nextVertex)) == gp_GetLastArc(theGraph, nextVertex))
{
eTwin = gp_GetTwinArc(theGraph, e);
e = gp_GetFirstArc(theGraph, nextVertex);
if (e == eTwin)
e = gp_GetLastArc(theGraph, nextVertex);
nextVertex = gp_GetNeighbor(theGraph, e);
}
return nextVertex == V ? TRUE : FALSE;
}
int _WriteAdjList(graphP theGraph, FILE *Outfile)
{
int I, J;
if (theGraph==NULL || Outfile==NULL) return NOTOK;
fprintf(Outfile, "N=%d\n", theGraph->N);
for (I=0; I < theGraph->N; I++)
{
fprintf(Outfile, "%d:", I);
J = gp_GetLastArc(theGraph, I);
while (gp_IsArc(theGraph, J))
{
if (!gp_GetDirection(theGraph, J, EDGEFLAG_DIRECTION_INONLY))
fprintf(Outfile, " %d", theGraph->G[J].v);
J = gp_GetPrevArc(theGraph, J);
}
fprintf(Outfile, " %d\n", NIL);
}
return OK;
}
int _WriteDebugInfo(graphP theGraph, FILE *Outfile)
{
int I, J, Gsize;
if (theGraph==NULL || Outfile==NULL) return NOTOK;
/* Print parent copy vertices and their adjacency lists */
fprintf(Outfile, "DEBUG N=%d M=%d\n", theGraph->N, theGraph->M);
for (I=0; I < theGraph->N; I++)
{
fprintf(Outfile, "%d(P=%d,lA=%d,LowPt=%d,v=%d):",
I, theGraph->V[I].DFSParent,
theGraph->V[I].leastAncestor,
theGraph->V[I].Lowpoint,
theGraph->G[I].v);
J = gp_GetFirstArc(theGraph, I);
while (gp_IsArc(theGraph, J))
{
fprintf(Outfile, " %d(J=%d)", theGraph->G[J].v, J);
J = gp_GetNextArc(theGraph, J);
}
fprintf(Outfile, " %d\n", NIL);
}
/* Print any root copy vertices and their adjacency lists */
for (I = theGraph->N; I < 2*theGraph->N; I++)
{
if (theGraph->G[I].v == NIL)
continue;
fprintf(Outfile, "%d(copy of=%d, DFS child=%d):",
I, theGraph->G[I].v, I-theGraph->N);
J = gp_GetFirstArc(theGraph, I);
while (gp_IsArc(theGraph, J))
{
fprintf(Outfile, " %d(J=%d)", theGraph->G[J].v, J);
J = gp_GetNextArc(theGraph, J);
}
fprintf(Outfile, " %d\n", NIL);
}
/* Print information about vertices and root copy (virtual) vertices */
fprintf(Outfile, "\nVERTEX INFORMATION\n");
for (I=0; I < 2*theGraph->N; I++)
{
if (theGraph->G[I].v == NIL)
continue;
fprintf(Outfile, "V[%3d] v=%3d, type=%c, first arc=%3d, last arc=%3d\n",
I,
theGraph->G[I].v,
theGraph->G[I].type,
gp_GetFirstArc(theGraph, I),
gp_GetLastArc(theGraph, I));
}
/* Print information about edges */
fprintf(Outfile, "\nEDGE INFORMATION\n");
Gsize = theGraph->edgeOffset + theGraph->arcCapacity;
for (J=theGraph->edgeOffset; J < Gsize; J++)
{
if (theGraph->G[J].v == NIL)
continue;
fprintf(Outfile, "E[%3d] v=%3d, type=%c, next arc=%3d, prev arc=%3d\n",
J,
theGraph->G[J].v,
theGraph->G[J].type,
gp_GetNextArc(theGraph, J),
gp_GetPrevArc(theGraph, J));
}
return OK;
}
int _ReadAdjList(graphP theGraph, FILE *Infile)
{
int N, I, W, ErrorCode, adjList, J;
if (Infile == NULL) return NOTOK;
fgetc(Infile); /* Skip the N= */
fgetc(Infile);
fscanf(Infile, " %d ", &N); /* Read N */
if (gp_InitGraph(theGraph, N) != OK)
{
printf("Failed to init graph");
return NOTOK;
}
// Clear the visited members of the vertices so they can be used
// during the adjacency list read operation
for (I=0; I < N; I++)
theGraph->G[I].visited = 0;
// Do the adjacency list read operation for each vertex in order
for (I = 0, ErrorCode = OK; I < N && ErrorCode==OK; I++)
{
// Read the vertex number
fscanf(Infile, "%d", &theGraph->G[I].v);
// The vertices are expected to be in numeric ascending order
if (theGraph->G[I].v != I)
return NOTOK;
// Skip the colon after the vertex number
fgetc(Infile);
// If the vertex already has a non-empty adjacency list, then it is
// the result of adding edges during processing of preceding vertices.
// The list is removed from the current vertex I and saved for use
// during the read operation for I. Adjacencies to preceding vertices
// are pulled from this list, if present, or added as directed edges
// if not. Adjacencies to succeeding vertices are added as undirected
// edges, and will be corrected later if the succeeding vertex does not
// have the matching adjacency using the following mechanism. After the
// read operation for a vertex I, any adjacency nodes left in the saved
// list are converted to directed edges from the preceding vertex to I.
adjList = gp_GetFirstArc(theGraph, I);
if (gp_IsArc(theGraph, adjList))
{
// Store the adjacency node location in the visited member of each
// of the preceding vertices to which I is adjacent so that we can
// efficiently detect the adjacency during the read operation and
// efficiently find the adjacency node.
J = gp_GetFirstArc(theGraph, I);
while (gp_IsArc(theGraph, J))
{
theGraph->G[theGraph->G[J].v].visited = J;
J = gp_GetNextArc(theGraph, J);
}
// Make the adjacency list circular, for later ease of processing
gp_SetPrevArc(theGraph, adjList, gp_GetLastArc(theGraph, I));
gp_SetNextArc(theGraph, gp_GetLastArc(theGraph, I), adjList);
// Remove the list from the vertex
gp_SetFirstArc(theGraph, I, gp_AdjacencyListEndMark(I));
gp_SetLastArc(theGraph, I, gp_AdjacencyListEndMark(I));
}
// Read the adjacency list.
while (1)
{
// Read the next adjacent vertex, with NIL indicating the list end
fscanf(Infile, " %d ", &W);
if (W < 0) break;
// Vertex numbers must be less than N
if (W >= N)
ErrorCode = NOTOK;
// Loop edges are not supported, but no reason to throw an error if they occur
// If a loop occurs, we just do like the ostrich and ignore it
else if (W == I)
ErrorCode = OK;
// If the adjacency is to a succeeding, higher numbered vertex,
// then we'll add an undirected edge for now
else if (I < W)
{
ErrorCode = gp_AddEdge(theGraph, I, 0, W, 0);
}
// If the adjacency is to a preceding, lower numbered vertex, then
// we have to pull the adjacency node from the preexisting adjList,
// if it is there, and if not then we have to add a directed edge.
else
{
// If the adjacency node (arc) already exists, then we add it
// as the new first arc of the vertex and delete it from adjList
if (theGraph->G[W].visited)
{
J = theGraph->G[W].visited;
// Remove the arc J from the adjList construct
theGraph->G[W].visited = 0;
if (adjList == J)
{
if ((adjList = gp_GetNextArc(theGraph, J)) == J)
adjList = NIL;
}
gp_SetPrevArc(theGraph, gp_GetNextArc(theGraph, J), gp_GetPrevArc(theGraph, J));
gp_SetNextArc(theGraph, gp_GetPrevArc(theGraph, J), gp_GetNextArc(theGraph, J));
gp_AttachFirstArc(theGraph, I, J);
}
// If an adjacency node to the lower numbered vertex W does not
// already exist, then we make a new directed arc from the current
// vertex I to W.
else
{
// It is added as the new first arc in both vertices
ErrorCode = gp_AddEdge(theGraph, I, 0, W, 0);
if (ErrorCode == OK)
// Note that this call also sets OUTONLY on the twin arc
gp_SetDirection(theGraph, gp_GetFirstArc(theGraph, W), EDGEFLAG_DIRECTION_INONLY);
}
}
if (ErrorCode != OK) break;
}
// If there are still adjList entries after the read operation
// then those entries are not representative of full undirected edges.
// Rather, they represent incoming directed arcs from other vertices
// into vertex I. They need to be added back into I's adjacency list but
// marked as "INONLY", while the twin is marked "OUTONLY" (by the same function).
while (gp_IsArc(theGraph, adjList))
{
J = adjList;
theGraph->G[theGraph->G[J].v].visited = 0;
if ((adjList = gp_GetNextArc(theGraph, J)) == J)
adjList = NIL;
gp_SetPrevArc(theGraph, gp_GetNextArc(theGraph, J), gp_GetPrevArc(theGraph, J));
gp_SetNextArc(theGraph, gp_GetPrevArc(theGraph, J), gp_GetNextArc(theGraph, J));
gp_AttachFirstArc(theGraph, I, J);
gp_SetDirection(theGraph, J, EDGEFLAG_DIRECTION_INONLY);
}
}
return ErrorCode;
}
int _MarkZtoRPath(graphP theGraph)
{
int ZPrevArc, ZNextArc, Z, R, Px, Py;
/* Initialize */
R = theGraph->IC.r;
Px = theGraph->IC.px;
Py = theGraph->IC.py;
theGraph->IC.z = NIL;
/* Begin at Px and search its adjacency list for the edge leading to
the first internal vertex of the X-Y path. */
Z = Px;
ZNextArc = gp_GetLastArc(theGraph, Z);
while (ZNextArc != gp_GetFirstArc(theGraph, Z))
{
if (theGraph->G[ZNextArc].visited) break;
ZNextArc = gp_GetPrevArc(theGraph, ZNextArc);
}
if (!theGraph->G[ZNextArc].visited)
return NOTOK;
/* For each internal vertex Z, determine whether it has a path to root. */
while (theGraph->G[ZNextArc].visited)
{
ZPrevArc = gp_GetTwinArc(theGraph, ZNextArc);
ZNextArc = gp_GetPrevArcCircular(theGraph, ZPrevArc);
}
ZPrevArc = gp_GetTwinArc(theGraph, ZNextArc);
Z = theGraph->G[ZPrevArc].v;
/* If there is no Z to R path, return */
if (Z == Py) return OK;
/* Otherwise, store Z in the isolation context */
theGraph->IC.z = Z;
/* Walk the proper face starting with (Z, ZNextArc) until we reach R, marking
the vertices and edges encountered along the way, then Return OK. */
while (Z != R)
{
/* If we ever encounter a non-internal vertex (other than the root R),
then corruption has occured, so we return NOTOK */
if (theGraph->G[Z].type != TYPE_UNKNOWN)
return NOTOK;
/* Go to the next vertex indicated by ZNextArc */
Z = theGraph->G[ZNextArc].v;
/* Mark the next vertex and the edge leading to it as visited. */
theGraph->G[ZNextArc].visited = 1;
theGraph->G[ZPrevArc].visited = 1;
theGraph->G[Z].visited = 1;
/* Go to the next edge in the proper face */
ZNextArc = gp_GetPrevArcCircular(theGraph, ZPrevArc);
ZPrevArc = gp_GetTwinArc(theGraph, ZNextArc);
}
/* Found Z to R path, so indicate as much to caller */
return OK;
}
int _MarkHighestXYPath(graphP theGraph)
{
int J, Z;
int R, X, Y, W;
int stackBottom1, stackBottom2;
/* Initialization */
R = theGraph->IC.r;
X = theGraph->IC.x;
Y = theGraph->IC.y;
W = theGraph->IC.w;
theGraph->IC.px = theGraph->IC.py = NIL;
/* Save the stack bottom before we start hiding internal edges, so
we will know how many edges to restore */
stackBottom1 = sp_GetCurrentSize(theGraph->theStack);
/* Remove the internal edges incident to vertex R */
if (_HideInternalEdges(theGraph, R) != OK)
return NOTOK;
/* Now we're going to use the stack to collect the vertices of potential
* X-Y paths, so we need to store where the hidden internal edges are
* located because we must, at times, pop the collected vertices if
* the path being collected doesn't work out. */
stackBottom2 = sp_GetCurrentSize(theGraph->theStack);
/* Walk the proper face containing R to find and mark the highest
X-Y path. Note that if W is encountered, then there is no
intervening X-Y path, so we would return FALSE in that case. */
Z = R;
// This setting of J is the arc equivalent of prevLink=1
// As loop progresses, J indicates the arc used to enter Z, not the exit arc
J = gp_GetLastArc(theGraph, R);
while (theGraph->G[Z].type != VERTEX_HIGH_RYW &&
theGraph->G[Z].type != VERTEX_LOW_RYW)
{
/* Advance J and Z along the proper face containing R */
J = gp_GetPrevArcCircular(theGraph, J);
Z = theGraph->G[J].v;
J = gp_GetTwinArc(theGraph, J);
/* If Z is already visited, then pop everything since the last time
we visited Z because its all part of a separable component. */
if (theGraph->G[Z].visited)
{
if (_PopAndUnmarkVerticesAndEdges(theGraph, Z, stackBottom2) != OK)
return NOTOK;
}
/* If we have not visited this vertex before... */
else
{
/* If we find W, then there is no X-Y path. Never happens
for Kuratowski subgraph isolator, but this routine is
also used to test for certain X-Y paths.
So, we clean up and bail out in that case. */
if (Z == W)
{
if (_PopAndUnmarkVerticesAndEdges(theGraph, NIL, stackBottom2) != OK)
return NOTOK;
break;
}
/* If we found another vertex along the RXW path, then blow off
all the vertices we visited so far because they're not part of
the obstructing path */
if (theGraph->G[Z].type == VERTEX_HIGH_RXW ||
theGraph->G[Z].type == VERTEX_LOW_RXW)
{
theGraph->IC.px = Z;
if (_PopAndUnmarkVerticesAndEdges(theGraph, NIL, stackBottom2) != OK)
return NOTOK;
}
/* Push the current vertex onto the stack of vertices visited
since the last RXW vertex was encountered */
sp_Push(theGraph->theStack, J);
sp_Push(theGraph->theStack, Z);
/* Mark the vertex Z as visited as well as its edge of entry
(except the entry edge for P_x).*/
theGraph->G[Z].visited = 1;
if (Z != theGraph->IC.px)
{
theGraph->G[J].visited = 1;
theGraph->G[gp_GetTwinArc(theGraph, J)].visited = 1;
}
/* If we found an RYW vertex, then we have successfully finished
identifying the highest X-Y path, so we record the point of
attachment and break the loop. */
if (theGraph->G[Z].type == VERTEX_HIGH_RYW ||
theGraph->G[Z].type == VERTEX_LOW_RYW)
{
theGraph->IC.py = Z;
break;
}
}
}
/* Remove any remaining vertex-edge pairs on the top of the stack, then
Restore the internal edges incident to R that were previously removed. */
sp_SetCurrentSize(theGraph->theStack, stackBottom2);
if (_RestoreInternalEdges(theGraph, stackBottom1) != OK)
return NOTOK;
/* Return the result */
return theGraph->IC.py==NIL ? FALSE : TRUE;
}
int _K33Search_CreateFwdArcLists(graphP theGraph)
{
K33SearchContext *context = NULL;
gp_FindExtension(theGraph, K33SEARCH_ID, (void *)&context);
if (context == NULL)
return NOTOK;
// For isolating a K_{3,3} homeomorph, we need the forward edges
// of each vertex to be in sorted order by DFI of descendants.
// Otherwise we just drop through to the normal processing...
if (theGraph->embedFlags == EMBEDFLAGS_SEARCHFORK33)
{
int I, Jcur, Jnext, ancestor;
// for each vertex v in order, we follow each of its back edges
// to the twin forward edge in an ancestor u, then we move
// the forward edge to the fwdArcList of u. Since this loop
// processes vertices in order, the fwdArcList of each vertex
// will be in order by the neighbor indicated by the forward edges.
for (I=0; I < theGraph->N; I++)
{
// Skip this vertex if it has no edges
Jnext = gp_GetLastArc(theGraph, I);
if (!gp_IsArc(theGraph, Jnext))
continue;
// Skip the forward edges, which are in succession at the
// end of the arc list (last and its predecessors)
while (theGraph->G[Jnext].type == EDGE_FORWARD)
Jnext = gp_GetPrevArc(theGraph, Jnext);
// Now we want to put all the back arcs in a backArcList, too.
// Since we've already skipped past the forward arcs, we continue
// with the predecessor arcs until we either run out of arcs or
// we find a DFS child arc (the DFS child arcs are in succession
// at the beginning of the arc list, so when a child arc is
// encountered in the predecessor direction, then there won't be
// any more back arcs.
while (gp_IsArc(theGraph, Jnext) &&
theGraph->G[Jnext].type != EDGE_DFSCHILD)
{
Jcur = Jnext;
Jnext = gp_GetPrevArc(theGraph, Jnext);
if (theGraph->G[Jcur].type == EDGE_BACK)
{
// Remove the back arc from I's adjacency list
gp_DetachArc(theGraph, Jcur);
// Put the back arc in the backArcList
if (context->V[I].backArcList == NIL)
{
context->V[I].backArcList = Jcur;
gp_SetPrevArc(theGraph, Jcur, Jcur);
gp_SetNextArc(theGraph, Jcur, Jcur);
}
else
{
gp_AttachArc(theGraph, NIL, context->V[I].backArcList, 1, Jcur);
}
// Determine the ancestor of vertex I to which Jcur connects
ancestor = theGraph->G[Jcur].v;
// Go to the forward arc in the ancestor
Jcur = gp_GetTwinArc(theGraph, Jcur);
// Remove the forward arc from the ancestor's adjacency list
gp_DetachArc(theGraph, Jcur);
// Add the forward arc to the end of the fwdArcList.
if (theGraph->V[ancestor].fwdArcList == NIL)
{
theGraph->V[ancestor].fwdArcList = Jcur;
gp_SetPrevArc(theGraph, Jcur, Jcur);
gp_SetNextArc(theGraph, Jcur, Jcur);
}
else
{
gp_AttachArc(theGraph, NIL, theGraph->V[ancestor].fwdArcList, 1, Jcur);
}
}
}
}
// Since the fwdArcLists have been created, we do not fall through
// to run the superclass implementation
return OK;
}
// If we're not actually running a K3,3 search, then we just run the
// superclass implementation
return context->functions.fpCreateFwdArcLists(theGraph);
}