int _IsolateOuterplanarObstruction(graphP theGraph, int v, int R)
{
int RetVal;
/* A subgraph homeomorphic to K_{2,3} or K_4 will be isolated by using the visited
flags, set=keep edge/vertex and clear=omit. Here we initialize to omit all, then we
subsequently set visited on all edges and vertices in the homeomorph. */
_ClearVisitedFlags(theGraph);
/* Next we determineg which of the non-outerplanarity Minors was encountered
and the principal bicomp on which the isolator will focus attention. */
if (_ChooseTypeOfNonOuterplanarityMinor(theGraph, v, R) != OK)
return NOTOK;
/* Find the path connecting the pertinent vertex w with the current vertex v */
if (theGraph->IC.minorType & MINORTYPE_B)
{
isolatorContextP IC = &theGraph->IC;
int SubtreeRoot = gp_GetVertexLastPertinentRootChild(theGraph, IC->w);
if (_FindUnembeddedEdgeToSubtree(theGraph, IC->v, SubtreeRoot, &IC->dw) != TRUE)
return NOTOK;
}
else
{
isolatorContextP IC = &theGraph->IC;
if (_FindUnembeddedEdgeToCurVertex(theGraph, IC->w, &IC->dw) != TRUE)
return NOTOK;
}
/* For minor E, we need to find and mark an X-Y path */
if (theGraph->IC.minorType & MINORTYPE_E)
{
if (_MarkHighestXYPath(theGraph) != TRUE)
return NOTOK;
}
/* Call the appropriate isolator */
if (theGraph->IC.minorType & MINORTYPE_A)
RetVal = _IsolateOuterplanarityObstructionA(theGraph);
else if (theGraph->IC.minorType & MINORTYPE_B)
RetVal = _IsolateOuterplanarityObstructionB(theGraph);
else if (theGraph->IC.minorType & MINORTYPE_E)
RetVal = _IsolateOuterplanarityObstructionE(theGraph);
else
RetVal = NOTOK;
/* Delete the unmarked edges and vertices, and return */
if (RetVal == OK)
RetVal = _DeleteUnmarkedVerticesAndEdges(theGraph);
return RetVal;
}
int _IsolateOuterplanarityObstructionE3orE4(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
int u, d, XorY;
/* Minor E3 */
if (FUTUREPERTINENT(theGraph, theGraph->IC.x, theGraph->IC.v) ||
FUTUREPERTINENT(theGraph, theGraph->IC.y, theGraph->IC.v))
{
if (_MarkHighestXYPath(theGraph) != TRUE)
return NOTOK;
if (FUTUREPERTINENT(theGraph, theGraph->IC.x, theGraph->IC.v))
XorY = theGraph->IC.x;
else XorY = theGraph->IC.y;
/* The cases of X externally active and Y externally active
are the same except for the bicomp external face marking
(because parameter order is important) */
if (XorY == theGraph->IC.x)
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->x, IC->w) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->y, IC->r) != OK)
return NOTOK;
}
else
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->x) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->w, IC->y) != OK)
return NOTOK;
}
if (_FindUnembeddedEdgeToCurVertex(theGraph, IC->w, &IC->dw) != TRUE)
return NOTOK;
if (_FindUnembeddedEdgeToAncestor(theGraph, XorY, &u, &d) != TRUE)
return NOTOK;
if (theGraph->functions.fpMarkDFSPath(theGraph, u, IC->v) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, XorY, d) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, IC->w, IC->dw) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkEdge(theGraph, u, d) != OK ||
_AddAndMarkEdge(theGraph, IC->v, IC->dw) != OK)
return NOTOK;
return OK;
}
/* Otherwise, isolate Minor E4 (reduce to minor A) */
if (_FindUnembeddedEdgeToAncestor(theGraph, IC->w, &u, &d) != TRUE)
return NOTOK;
IC->v = u;
IC->dw = d;
return _IsolateOuterplanarityObstructionA(theGraph);
}
int _IsolateOuterplanarityObstructionE1orE2(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
int XPrevLink = 1;
if (_MarkHighestXYPath(theGraph) != TRUE)
return NOTOK;
/* Isolate E1 */
if (theGraph->IC.px != theGraph->IC.x)
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->w) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->py, IC->r) != OK)
return NOTOK;
}
else if (theGraph->IC.py != theGraph->IC.y)
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->x) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->w, IC->r) != OK)
return NOTOK;
}
/* Isolate E2 */
else if (IC->w != _GetNextVertexOnExternalFace(theGraph, IC->x, &XPrevLink))
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->y) != OK)
return NOTOK;
}
else
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->x, IC->r) != OK)
return NOTOK;
}
/* Final bits are in common */
if (_FindUnembeddedEdgeToCurVertex(theGraph, IC->w, &IC->dw) != TRUE ||
theGraph->functions.fpMarkDFSPath(theGraph, IC->w, IC->dw) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkEdge(theGraph, IC->v, IC->dw) != OK)
return NOTOK;
return OK;
}
int _ChooseTypeOfNonplanarityMinor(graphP theGraph, int I, int R)
{
int N, X, Y, W, Px, Py, Z, DFSChild, RootId;
/* Create the initial non-planarity minor state in the isolator context */
if (_InitializeNonplanarityContext(theGraph, I, R) != OK)
return NOTOK;
N = theGraph->N;
R = theGraph->IC.r;
X = theGraph->IC.x;
Y = theGraph->IC.y;
W = theGraph->IC.w;
/* If the root copy is not a root copy of the current vertex I,
then the Walkdown terminated because it couldn't find
a viable path along a child bicomp, which is Minor A. */
if (theGraph->V[R - N].DFSParent != I)
{
theGraph->IC.minorType |= MINORTYPE_A;
return OK;
}
/* If W has an externally active pertinent child bicomp, then
we've found Minor B */
if (theGraph->V[W].pertinentBicompList != NIL)
{
RootId = LCGetPrev(theGraph->BicompLists,
theGraph->V[W].pertinentBicompList, NIL);
DFSChild = RootId;
if (theGraph->V[DFSChild].Lowpoint < I)
{
theGraph->IC.minorType |= MINORTYPE_B;
return OK;
}
}
/* Find the highest obstructing X-Y path */
if (_MarkHighestXYPath(theGraph) != TRUE)
return NOTOK;
Px = theGraph->IC.px;
Py = theGraph->IC.py;
/* If either point of attachment is 'high' (P_x closer to R than X
or P_y closer to R than Y along external face), then we've
matched Minor C. */
if (theGraph->G[Px].type == VERTEX_HIGH_RXW ||
theGraph->G[Py].type == VERTEX_HIGH_RYW)
{
theGraph->IC.minorType |= MINORTYPE_C;
return OK;
}
/* For Minor D, we search for a path from an internal
vertex Z along the X-Y path up to the root R of the bicomp. */
if (_MarkZtoRPath(theGraph) != OK)
return NOTOK;
if (theGraph->IC.z != NIL)
{
theGraph->IC.minorType |= MINORTYPE_D;
return OK;
}
/* For Minor E, we search for an externally active vertex Z
below the points of attachment of the X-Y path */
Z = _FindExtActivityBelowXYPath(theGraph);
if (Z != NIL)
{
theGraph->IC.z = Z;
theGraph->IC.minorType |= MINORTYPE_E;
return OK;
}
return NOTOK;
}
