void UpwardPlanarSubgraphModule::callAndDelete(
GraphCopy &GC,
List<edge> &delOrigEdges)
{
List<edge> delEdges;
call(GC, delEdges);
ListConstIterator<edge> it;
for(it = delEdges.begin(); it.valid(); ++it) {
edge eCopy = *it;
delOrigEdges.pushBack(GC.original(eCopy));
GC.delEdge(eCopy);
}
}
void FUPSSimple::getSpanTree(GraphCopy &GC, List<edge> &delEdges, bool random)
{
if (GC.numberOfNodes() == 1)
return; // nothing to do
node s;
hasSingleSource(GC, s);
NodeArray<bool> visited(GC, false);
EdgeArray<bool> isTreeEdge(GC,false);
List<node> toDo;
//mark the incident edges e1..e_i of super source s and the incident edges of the target node of the edge e1.._e_i as tree edge.
visited[s] = true;
for(adjEntry adj : s->adjEdges) {
isTreeEdge[adj] = true;
visited[adj->theEdge()->target()];
for(adjEntry adjTmp : adj->theEdge()->target()->adjEdges) {
isTreeEdge[adjTmp] = true;
node tgt = adjTmp->theEdge()->target();
if (!visited[tgt]) {
toDo.pushBack(tgt);
visited[tgt] = true;
}
}
}
//traversing with dfs
for(node start : toDo) {
for(adjEntry adj : start->adjEdges) {
node v = adj->theEdge()->target();
if (!visited[v])
dfs_visit(GC, adj->theEdge(), visited, isTreeEdge, random);
}
}
// delete all non tree edgesEdges to obtain a span tree
List<edge> l;
for(edge e : GC.edges) {
if (!isTreeEdge[e])
l.pushBack(e);
}
while (!l.empty()) {
edge e = l.popFrontRet();
delEdges.pushBack(GC.original(e));
GC.delEdge(e);
}
}
void FeasibleUpwardPlanarSubgraph::getSpanTree(GraphCopy &GC, List<edge> &delEdges, bool random, bool multisource)
{
delEdges.clear();
if (GC.numberOfNodes() == 1)
return; // nothing to do
node s;
hasSingleSource(GC, s);
NodeArray<bool> visited(GC, false);
EdgeArray<bool> isTreeEdge(GC,false);
List<node> toDo;
// the original graph is a multisource graph. The sources are connected with the super source s.
// so do not delete the incident edges of s
if (multisource){
// put all incident edges of the source to treeEdges
for(adjEntry adj : s->adjEdges) {
isTreeEdge[adj->theEdge()] = true;
visited[adj->theEdge()->target()];
toDo.pushBack(adj->theEdge()->target());
}
}
else
toDo.pushBack(s);
//traversing with dfs
for(node start : toDo) {
for(adjEntry adj : start->adjEdges) {
node v = adj->theEdge()->target();
if (!visited[v])
dfs_visit(GC, adj->theEdge(), visited, isTreeEdge, random);
}
}
// delete all non tree edgesEdges to obtain a span tree
List<edge> l;
for(edge e : GC.edges) {
if (!isTreeEdge[e])
l.pushBack(e);
}
while (!l.empty()) {
edge e = l.popFrontRet();
delEdges.pushBack(GC.original(e));
GC.delEdge(e);
}
}
Module::ReturnType PlanarSubgraphModule::callAndDelete(
GraphCopy &PG,
const List<edge> &preferedEdges,
List<edge> &delOrigEdges,
bool preferedImplyPlanar)
{
List<edge> delEdges;
ReturnType retValue = call(PG, preferedEdges, delEdges, preferedImplyPlanar);
if(isSolution(retValue))
{
ListConstIterator<edge> it;
for(it = delEdges.begin(); it.valid(); ++it) {
edge eCopy = *it;
delOrigEdges.pushBack(PG.original(eCopy));
PG.delEdge(eCopy);
}
}
return retValue;
}
void UpwardPlanarSubgraphSimple::call(GraphCopy &GC, List<edge> &delEdges)
{
const Graph &G = GC.original();
delEdges.clear();
// We construct an auxiliary graph H which represents the current upward
// planar subgraph.
Graph H;
NodeArray<node> mapToH(G,nullptr);
NodeArray<node> mapToG(H,nullptr);
for(node v : G.nodes)
mapToG[ mapToH[v] = H.newNode() ] = v;
// We currently support only single-source acyclic digraphs ...
node s;
hasSingleSource(G,s);
OGDF_ASSERT(s != 0);
OGDF_ASSERT(isAcyclic(G));
// We start with a spanning tree of G rooted at the single source.
NodeArray<bool> visitedNode(G,false);
SListPure<edge> treeEdges;
dfsBuildSpanningTree(s,treeEdges,visitedNode);
// Mark all edges in the spanning tree so they can be skipped in the
// loop below and add (copies of) them to H.
EdgeArray<bool> visitedEdge(G,false);
SListConstIterator<edge> it;
for(it = treeEdges.begin(); it.valid(); ++it) {
edge eG = *it;
visitedEdge[eG] = true;
H.newEdge(mapToH[eG->source()],mapToH[eG->target()]);
}
// Add subsequently the remaining edges to H and test if the resulting
// graph is still upward planar. If not, remove the edge again from H
// and add it to delEdges.
SList<Tuple2<node,node> > augmented;
GraphCopySimple graphAcyclicTest(G);
for(edge eG : G.edges)
{
// already treated ?
if(visitedEdge[eG] == true)
continue;
// insert edge into H
edge eH = H.newEdge(mapToH[eG->source()],mapToH[eG->target()]);
node superSink;
SList<edge> augmentedEdges;
if (UpwardPlanarity::upwardPlanarAugment_singleSource(H,superSink,augmentedEdges) == false) {
// if H is no longer upward planar, remove eG from subgraph
H.delEdge(eH);
delEdges.pushBack(eG);
} else {
// add augmented edges as node-pair to tmpAugmented and remove
// all augmented edges from H again
SList<Tuple2<node,node> > tmpAugmented;
SListConstIterator<edge> it;
for(it = augmentedEdges.begin(); it.valid(); ++it) {
node v = mapToG[(*it)->source()];
node w = mapToG[(*it)->target()];
if (v && w)
tmpAugmented.pushBack(Tuple2<node,node>(v,w));
H.delEdge(*it);
}
if (mapToG[superSink] == nullptr)
H.delNode(superSink);
//****************************************************************
// The following is a simple workaround to assure the following
// property of the upward planar subgraph:
// The st-augmented upward planar subgraph plus the edges not
// in the subgraph must be acyclic. (This is a special property
// of the embedding, not the augmentation.)
// The upward-planar embedding function gives us ANY upward-planar
// embedding. We check if the property above holds with this
// embedding. If it doesn't, we have actually no idea if another
// embedding would do.
// The better solution would be to incorporate the acyclicity
// property into the upward-planarity test, but this is compicated.
//****************************************************************
// test if original graph plus augmented edges is still acyclic
if(checkAcyclic(graphAcyclicTest,tmpAugmented) == true) {
augmented = tmpAugmented;
} else {
// if not, remove eG from subgraph
H.delEdge(eH);
delEdges.pushBack(eG);
}
}
}
// remove edges not in the subgraph from GC
ListConstIterator<edge> itE;
for(itE = delEdges.begin(); itE.valid(); ++itE)
GC.delEdge(GC.copy(*itE));
// add augmented edges to GC
SListConstIterator<Tuple2<node,node> > itP;
for(itP = augmented.begin(); itP.valid(); ++itP) {
node v = (*itP).x1();
node w = (*itP).x2();
GC.newEdge(GC.copy(v),GC.copy(w));
}
// add super sink to GC
node sGC = nullptr;
SList<node> sinks;
for(node v : GC.nodes) {
if(v->indeg() == 0)
sGC = v;
if(v->outdeg() == 0)
sinks.pushBack(v);
}
node superSinkGC = GC.newNode();
SListConstIterator<node> itV;
for(itV = sinks.begin(); itV.valid(); ++itV)
GC.newEdge(*itV,superSinkGC);
// add st-edge to GC, so that we now have a planar st-digraph
GC.newEdge(sGC,superSinkGC);
OGDF_ASSERT(isAcyclic(GC));
OGDF_ASSERT(isPlanar(GC));
}
/*
* Construct the realiszer and the Tree T
* rValues = realizer value
* T = Tree
*/
void SchnyderLayout::realizer(
GraphCopy& G,
const List<node>& L,
node a,
node b,
node c,
EdgeArray<int>& rValues,
GraphCopy& T)
{
int i = 0;
edge e;
NodeArray<int> ord(G, 0);
// ordering: b,c,L,a
ord[b] = i++;
ord[c] = i++;
for(node v : L) {
ord[v] = i++; // enumerate V(G)
}
ord[a] = i++;
// remove all edges (they will be re-added later with different orientation)
while (T.numberOfEdges() > 0) {
e = T.firstEdge();
T.delEdge(e);
}
for(node v : L) {
node u = T.copy(G.original(v)); // u is copy of v in T
adjEntry adj = nullptr;
for(adjEntry adjRun : v->adjEdges) {
if (ord[adjRun->twinNode()] > ord[v]) {
adj = adjRun;
break;
}
}
adjEntry adj1 = adj;
while (ord[adj1->twinNode()] > ord[v]) {
adj1 = adj1->cyclicSucc();
}
e = T.newEdge(T.copy(G.original(adj1->twinNode())), u);
rValues[e] = 2;
adjEntry adj2 = adj;
while (ord[adj2->twinNode()] > ord[v]) {
adj2 = adj2->cyclicPred();
}
e = T.newEdge(T.copy(G.original(adj2->twinNode())), u);
rValues[e] = 3;
for (adj = adj1->cyclicSucc(); adj != adj2; adj = adj->cyclicSucc()) {
e = T.newEdge(u, T.copy(G.original(adj->twinNode())));
rValues[e] = 1;
}
}
// special treatement of a,b,c
node a_in_T = T.copy(G.original(a));
node b_in_T = T.copy(G.original(b));
node c_in_T = T.copy(G.original(c));
// all edges to node a get realizer value 1
for(adjEntry adj : a->adjEdges) {
e = T.newEdge(a_in_T, T.copy(G.original(adj->twinNode())));
rValues[e] = 1;
}
// rest of outer triangle (reciprocal linked, realizer values 2 and 3)
e = T.newEdge(b_in_T, a_in_T);
rValues[e] = 2;
e = T.newEdge(b_in_T, c_in_T);
rValues[e] = 2;
e = T.newEdge(c_in_T, a_in_T);
rValues[e] = 3;
e = T.newEdge(c_in_T, b_in_T);
rValues[e] = 3;
}
