Module::ReturnType FeasibleUpwardPlanarSubgraph::call(
const Graph &G,
GraphCopy &FUPS,
adjEntry &extFaceHandle,
List<edge> &delEdges,
bool multisources)
{
FUPS = GraphCopy(G);
delEdges.clear();
node s_orig;
hasSingleSource(G, s_orig);
List<edge> nonTreeEdges_orig;
getSpanTree(FUPS, nonTreeEdges_orig, true, multisources);
CombinatorialEmbedding Gamma(FUPS);
nonTreeEdges_orig.permute(); // random order
//insert nonTreeEdges
while (!nonTreeEdges_orig.empty()) {
// make identical copy GC of Fups
//and insert e_orig in GC
GraphCopy GC = FUPS;
edge e_orig = nonTreeEdges_orig.popFrontRet();
//node a = GC.copy(e_orig->source());
//node b = GC.copy(e_orig->target());
GC.newEdge(e_orig);
if (UpwardPlanarity::upwardPlanarEmbed_singleSource(GC)) { //upward embedded the fups and check feasibility
CombinatorialEmbedding Beta(GC);
//choose a arbitrary feasibel ext. face
FaceSinkGraph fsg(Beta, GC.copy(s_orig));
SList<face> ext_faces;
fsg.possibleExternalFaces(ext_faces);
OGDF_ASSERT(!ext_faces.empty());
Beta.setExternalFace(ext_faces.front());
GraphCopy M = GC; // use a identical copy of GC to constrcut the merge graph of GC
adjEntry extFaceHandle_cur = getAdjEntry(Beta, GC.copy(s_orig), Beta.externalFace());
adjEntry adj_orig = GC.original(extFaceHandle_cur->theEdge())->adjSource();
if (constructMergeGraph(M, adj_orig, nonTreeEdges_orig)) {
FUPS = GC;
extFaceHandle = FUPS.copy(GC.original(extFaceHandle_cur->theEdge()))->adjSource();
continue;
}
else {
//Beta is not feasible
delEdges.pushBack(e_orig);
}
}
else {
// not ok, GC is not feasible
delEdges.pushBack(e_orig);
}
}
return Module::retFeasible;
}
void SchnyderLayout::schnyderEmbedding(
GraphCopy& GC,
GridLayout &gridLayout,
adjEntry adjExternal)
{
NodeArray<int> &xcoord = gridLayout.x();
NodeArray<int> &ycoord = gridLayout.y();
node v;
List<node> L; // (un)contraction order
GraphCopy T = GraphCopy(GC); // the realizer tree (reverse direction of edges!!!)
EdgeArray<int> rValues(T); // the realizer values
// choose outer face a,b,c
adjEntry adja;
if (adjExternal != 0) {
edge eG = adjExternal->theEdge();
edge eGC = GC.copy(eG);
adja = (adjExternal == eG->adjSource()) ? eGC->adjSource() : eGC->adjTarget();
}
else {
adja = GC.firstEdge()->adjSource();
}
adjEntry adjb = adja->faceCyclePred();
adjEntry adjc = adjb->faceCyclePred();
node a = adja->theNode();
node b = adjb->theNode();
node c = adjc->theNode();
node a_in_T = T.copy(GC.original(a));
node b_in_T = T.copy(GC.original(b));
node c_in_T = T.copy(GC.original(c));
contract(GC, a, b, c, L);
realizer(GC, L, a, b, c, rValues, T);
NodeArray<int> t1(T);
NodeArray<int> t2(T);
NodeArray<int> val(T, 1);
NodeArray<int> P1(T);
NodeArray<int> P3(T);
NodeArray<int> v1(T);
NodeArray<int> v2(T);
subtreeSizes(rValues, 1, a_in_T, t1);
subtreeSizes(rValues, 2, b_in_T, t2);
prefixSum(rValues, 1, a_in_T, val, P1);
prefixSum(rValues, 3, c_in_T, val, P3);
// now Pi = depth of all nodes in Tree T(i) (depth[root] = 1)
prefixSum(rValues, 2, b_in_T, t1, v1);
// special treatment for a
v1[a_in_T] = t1[a_in_T];
/*
* v1[v] now is the sum of the
* "count of nodes in t1" minus the "subtree size for node x"
* for every node x on a path from b to v in t2
*/
prefixSum(rValues, 3, c_in_T, t1, val);
// special treatment for a
val[a_in_T] = t1[a_in_T];
/*
* val[v] now is the sum of the
* "count of nodes in t1" minus the "subtree size for node x"
* for every node x on a path from c to v in t3
*/
// r1[v]=v1[v]+val[v]-t1[v] is the number of nodes in region 1 from v
forall_nodes(v, T) {
// calc v1'
v1[v] += val[v] - t1[v] - P3[v];
}
