int _IsolateMinorC(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
if (theGraph->G[IC->px].type == VERTEX_HIGH_RXW)
{
int highY = theGraph->G[IC->py].type == VERTEX_HIGH_RYW
? IC->py : IC->y;
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, highY) != OK)
return NOTOK;
}
else
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->x, IC->r) != OK)
return NOTOK;
}
if (_MarkDFSPathsToDescendants(theGraph) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, MIN(IC->ux, IC->uy), IC->r) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
return OK;
}
int _IsolateMinorE4(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
if (IC->px != IC->x)
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->w) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->py, IC->r) != OK)
return NOTOK;
}
else
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->px) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->w, IC->r) != OK)
return NOTOK;
}
if (theGraph->functions.fpMarkDFSPath(theGraph, MIN3(IC->ux, IC->uy, IC->uz),
MAX3(IC->ux, IC->uy, IC->uz)) != OK ||
_MarkDFSPathsToDescendants(theGraph) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
theGraph->IC.minorType |= MINORTYPE_E4;
return OK;
}
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 _IsolateMinorE4(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
if (IC->px != IC->x)
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->w) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->py, IC->r) != OK)
return NOTOK;
}
else
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->px) != OK ||
_MarkPathAlongBicompExtFace(theGraph, IC->w, IC->r) != OK)
return NOTOK;
}
// Note: The x-y path is already marked, due to identifying E as the type of non-planarity minor
if (theGraph->functions.fpMarkDFSPath(theGraph, MIN3(IC->ux, IC->uy, IC->uz),
MAX3(IC->ux, IC->uy, IC->uz)) != OK ||
_MarkDFSPathsToDescendants(theGraph) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
theGraph->IC.minorType |= MINORTYPE_E4;
return OK;
}
int _IsolateMinorC(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
if (gp_GetVertexObstructionType(theGraph, IC->px) == VERTEX_OBSTRUCTIONTYPE_HIGH_RXW)
{
int highY = gp_GetVertexObstructionType(theGraph, IC->py) == VERTEX_OBSTRUCTIONTYPE_HIGH_RYW
? IC->py : IC->y;
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, highY) != OK)
return NOTOK;
}
else
{
if (_MarkPathAlongBicompExtFace(theGraph, IC->x, IC->r) != OK)
return NOTOK;
}
// Note: The x-y path is already marked, due to identifying the type of non-planarity minor
if (_MarkDFSPathsToDescendants(theGraph) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, MIN(IC->ux, IC->uy), IC->r) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
return OK;
}
int _IsolateMinorE(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
/* Minor E1: Isolate a K3,3 homeomorph */
if (IC->z != IC->w)
return _IsolateMinorE1(theGraph);
/* Minor E2: Isolate a K3,3 homeomorph */
if (IC->uz > MAX(IC->ux, IC->uy))
return _IsolateMinorE2(theGraph);
/* Minor E3: Isolate a K3,3 homeomorph */
if (IC->uz < MAX(IC->ux, IC->uy) && IC->ux != IC->uy)
return _IsolateMinorE3(theGraph);
/* Minor E4: Isolate a K3,3 homeomorph */
else if (IC->x != IC->px || IC->y != IC->py)
return _IsolateMinorE4(theGraph);
/* Minor E: Isolate a K5 homeomorph */
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->r) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, MIN3(IC->ux, IC->uy, IC->uz), IC->r) != OK ||
_MarkDFSPathsToDescendants(theGraph) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
return OK;
}
int _IsolateOuterplanarityObstructionE(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
if (_MarkPathAlongBicompExtFace(theGraph, IC->r, IC->r) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, IC->w, IC->dw) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkEdge(theGraph, IC->v, IC->dw) != OK)
return NOTOK;
return OK;
}
int _IsolateMinorD(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
if (_MarkPathAlongBicompExtFace(theGraph, IC->x, IC->y) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, MIN(IC->ux, IC->uy), IC->r) != OK ||
_MarkDFSPathsToDescendants(theGraph) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
return OK;
}
int _IsolateMinorD(graphP theGraph)
{
isolatorContextP IC = &theGraph->IC;
// Note: The x-y and v-z paths are already marked, due to identifying the type of non-planarity minor
if (_MarkPathAlongBicompExtFace(theGraph, IC->x, IC->y) != OK ||
theGraph->functions.fpMarkDFSPath(theGraph, MIN(IC->ux, IC->uy), IC->r) != OK ||
_MarkDFSPathsToDescendants(theGraph) != OK ||
_JoinBicomps(theGraph) != OK ||
_AddAndMarkUnembeddedEdges(theGraph) != OK)
return NOTOK;
return OK;
}
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;
}
