node PivotMDS::getRootedPath(const Graph& G)
{
node head = nullptr;
NodeArray<bool> visited(G, false);
SListPure<node> neighbors;
// in every path there are two nodes with degree 1 and
// each node has at most degree 2
for(node v : G.nodes)
{
int degree = 0;
visited[v] = true;
neighbors.pushBack(v);
for(adjEntry adj : v->adjEntries) {
node w = adj->twinNode();
if (!visited[w])
{
neighbors.pushBack(w);
visited[w]=true;
++degree;
}
}
if (degree > 2) {
neighbors.clear();
return nullptr;
}
if (degree == 1) {
head = v;
}
for(node u : neighbors) {
visited[u] = false;
}
neighbors.clear();
}
return head;
}
void PlanarSPQRTree::adoptEmbedding()
{
OGDF_ASSERT_IF(dlExtendedChecking, originalGraph().representsCombEmbedding());
// ordered list of adjacency entries (for one original node) in all
// skeletons (where this node occurs)
NodeArray<SListPure<adjEntry> > adjEdges(tree());
// copy in skeleton of current original node
NodeArray<node> currentCopy(tree(),nullptr);
NodeArray<adjEntry> lastAdj(tree(),nullptr);
SListPure<node> current; // currently processed nodes
for (node vOrig : originalGraph().nodes)
{
for(adjEntry adjOrig : vOrig->adjEdges)
{
edge eOrig = adjOrig->theEdge();
const Skeleton &S = skeletonOfReal(eOrig);
edge eCopy = copyOfReal(eOrig);
adjEntry adjCopy = (S.original(eCopy->source()) == vOrig) ?
eCopy->adjSource() : eCopy->adjTarget();
setPosInEmbedding(adjEdges,currentCopy,lastAdj,current,S,adjCopy);
}
for(node vT : current) {
skeleton(vT).getGraph().sort(currentCopy[vT],adjEdges[vT]);
adjEdges[vT].clear();
currentCopy[vT] = nullptr;
}
current.clear();
}
}
// separate pertinent nodes in the lists of possible different minor-types
void FindKuratowskis::splitInMinorTypes(
const SListPure<adjEntry>& externalFacePath,
int marker)
{
// mark nodes, which are before stopX or behind stopY in CCW-traversal and add
// all extern nodes strictly between stopX and stopY to list
// externE for minor E (pertinent nodes are considered because of the
// position of z left or right of w)
SListConstIterator<adjEntry> itExtern;
SListIterator<WInfo> it = k.wNodes.begin();
node x;
bool between = false;
SListPure<WInfo*> infoList;
SListIterator<WInfo*> itList;
ExternE externEdummy;
// compute list of externE nodes
for (itExtern=externalFacePath.begin(); itExtern.valid(); ++itExtern) {
x = (*itExtern)->theNode();
if (x==k.stopX || x==k.stopY) {
between = (between==false) ? true : false;
} else {
if (!between) {
m_wasHere[x]=marker;
} else {
if (pBM->externallyActive(x,k.V_DFI)) {
externEdummy.theNode = x;
// check minor type B and save extern linkage
if (it.valid() && (*it).w==x &&
!m_pertinentRoots[x].empty() &&
m_lowPoint[m_nodeFromDFI[-m_dfi[m_pertinentRoots[x].back()]]]
< k.V_DFI) {
WInfo& info(*it);
// checking minor type B
info.minorType |= WInfo::B;
// mark extern node for later extraction
externEdummy.startnodes.pushBack(0);
// create externE-list
k.externE.pushBack(externEdummy);
// save extern linkage
info.externEStart = k.externE.rbegin();
info.externEEnd = k.externE.rbegin();
} else {
// create externE-list
externEdummy.startnodes.clear();
k.externE.pushBack(externEdummy);
}
// save for each wNode the first externally active successor
// on the external face
for (itList = infoList.begin(); itList.valid(); ++itList)
(*itList)->firstExternEAfterW = x;
infoList.clear();
}
// get appropriate WInfo
if (it.valid() && (*it).w==x) {
infoList.pushBack(&(*it));
++it;
}
}
}
}
// divide wNodes in different minor types
// avoids multiple computation of the externE range
itExtern = externalFacePath.begin();
SListIterator<ExternE> itExternE = k.externE.begin();
WInfo* oldInfo = NULL;
for (it=k.wNodes.begin(); it.valid(); ++it) {
WInfo& info(*it);
// checking minor type A
if (k.RReal!=k.V) info.minorType |= WInfo::A;
// if a XYPath exists
if (info.highestXYPath!=NULL) {
if (m_wasHere[info.highestXYPath->front()->theNode()]==marker)
info.pxAboveStopX = true;
if (m_wasHere[info.highestXYPath->back()->theNode()]==marker)
info.pyAboveStopY = true;
// checking minor type C
if (info.pxAboveStopX || info.pyAboveStopY)
info.minorType |= WInfo::C;
// checking minor type D
if (info.zPath!=NULL) info.minorType |= WInfo::D;
// checking minor type E
if (!k.externE.empty()) {
node t;
// compute valid range of externE-nodes in linear time
if (oldInfo!=NULL && info.highestXYPath==oldInfo->highestXYPath) {
// found the same highestXYPath as before
info.externEStart = oldInfo->externEStart;
info.externEEnd = oldInfo->externEEnd;
if (oldInfo->minorType & WInfo::E) info.minorType |= WInfo::E;
} else {
// compute range of a new highestXYPath
node px;
if (info.pxAboveStopX) px = k.stopX;
else px = info.highestXYPath->front()->theNode();
node py;
if (info.pyAboveStopY) py = k.stopY;
else py = info.highestXYPath->back()->theNode();
while ((*itExtern)->theNode() != px) ++itExtern;
t = (*(++itExtern))->theNode();
node start = NULL;
node end = NULL;
while (t != py) {
if (pBM->externallyActive(t,k.V_DFI)) {
if (start==NULL) start = t;
end = t;
}
t = (*(++itExtern))->theNode();
}
if (start != NULL) {
while ((*itExternE).theNode != start) ++itExternE;
info.externEStart = itExternE;
// mark node to extract external subgraph later
(*itExternE).startnodes.pushBack(0);
node temp = start;
while (temp != end) {
temp = (*++itExternE).theNode;
// mark node to extract external subgraph later
(*itExternE).startnodes.pushBack(0);
}
info.externEEnd = itExternE;
info.minorType |= WInfo::E;
}
oldInfo = &info;
}
}
}
/*
// use this to find special kuratowski-structures
if ((info.minorType & (WInfo::A|WInfo::B|WInfo::C|WInfo::D|WInfo::E)) ==
(WInfo::A|WInfo::B|WInfo::C|WInfo::D|WInfo::E)) {
char t; cin >> t;
}
*/
}
// extract the externalSubgraph of all saved externally active nodes
// exclude the already extracted minor b-types
#ifdef OGDF_DEBUG
int visited = m_nodeMarker+1;
#endif
for (itExternE=k.externE.begin(); itExternE.valid(); ++itExternE) {
if ((*itExternE).startnodes.empty()) continue;
ExternE& externE(*itExternE);
externE.startnodes.clear();
if (m_bundles) {
OGDF_ASSERT(m_wasHere[externE.theNode] < visited);
extractExternalSubgraphBundles(externE.theNode,k.V_DFI,
k.externalSubgraph,++m_nodeMarker);
} else {
extractExternalSubgraph(externE.theNode,k.V_DFI,externE.startnodes,
externE.endnodes);
SListIterator<int> itInt;
SListPure<edge> dummy;
for (itInt = externE.startnodes.begin(); itInt.valid(); ++itInt)
externE.externalPaths.pushBack(dummy);
}
}
}
// extract external facepath in direction CCW and split the highest facepath
// in highest xy-paths. marker marks the node, highMarker is used to check,
// whether the node was visited before by the highest facepath traversal.
// highMarker+1 identifies the nodes that are zNodes.
void FindKuratowskis::extractExternalFacePath(
SListPure<adjEntry>& externalFacePath,
const ListPure<adjEntry>& highestFacePath,
int marker,
int highMarker)
{
int dir = CCW;
// x traverses the external facepath
node x = pBM->successorWithoutShortCircuit(k.R,dir);
externalFacePath.pushBack(pBM->beforeShortCircuitEdge(k.R,CCW));
m_wasHere[k.R] = marker;
while (x != k.R) {
// set visited sign on nodes that are both on the highest and external facepath
if (m_wasHere[x]>=highMarker) m_wasHere[x] = marker;
externalFacePath.pushBack(pBM->beforeShortCircuitEdge(x,dir));
x = pBM->successorWithoutShortCircuit(x,dir);
}
dir = CCW;
x = pBM->successorWithoutShortCircuit(k.R,dir);
ListConstIterator<adjEntry> highIt = highestFacePath.begin();
OGDF_ASSERT(x == (*highIt)->theNode());
SListPure<adjEntry> XYPathList;
SListPure<adjEntry> zList;
WInfo info;
adjEntry adj = pBM->beforeShortCircuitEdge(k.R,CCW);
adjEntry temp;
while (x != k.R) {
// go along the highest face path until next visited sign
OGDF_ASSERT(adj->theNode()==x);
if (m_wasHere[x] == marker) {
XYPathList.clear();
zList.clear();
info.w = NULL;
info.minorType = 0;
info.highestXYPath = NULL;
info.zPath = NULL;
info.pxAboveStopX = false;
info.pyAboveStopY = false;
info.externEStart = NULL;
info.externEEnd = NULL;
info.firstExternEAfterW = NULL;
}
// push in wNodes-list
if (pBM->pertinent(x)) {
info.w = x;
k.wNodes.pushBack(info);
}
// compute next highestXYPath
if (m_wasHere[x] == marker &&
m_wasHere[pBM->constSuccessorWithoutShortCircuit(x,dir)] != marker) {
// traverse highFacePath to x
while ((*highIt)->theNode() != x) ++highIt;
OGDF_ASSERT(highIt.valid());
XYPathList.pushBack(adj);
OGDF_ASSERT((*highIt.succ())->theNode() !=
pBM->constSuccessorWithoutShortCircuit(x,dir));
// traverse highFacePath to next marker
do {
++highIt;
if (!highIt.valid()) break;
temp = *highIt;
XYPathList.pushBack(temp);
// check, if node is z-node and push one single z-node
if (m_wasHere[temp->theNode()]==highMarker+1 && zList.empty())
zList.pushBack(temp);
} while (m_wasHere[temp->theNode()] != marker);
// save highestXY-Path
OGDF_ASSERT(!XYPathList.empty());
k.highestXYPaths.pushBack(XYPathList);
info.highestXYPath = &k.highestXYPaths.back();
// compute path from zNode to V and save it
if (!zList.empty()) {
OGDF_ASSERT(zList.size()==1); // just one zNode for now
temp = zList.back();
do {
do {
temp = temp->cyclicSucc();
OGDF_ASSERT(m_dfi[temp->twinNode()]==m_dfi[k.R] ||
m_dfi[temp->twinNode()]>=m_dfi[k.RReal]);
} while (m_edgeType[temp->theEdge()]==EDGE_BACK_DELETED);
temp = temp->twin();
zList.pushBack(temp);
} while (temp->theNode() != k.R);
k.zPaths.pushBack(zList);
info.zPath = &k.zPaths.back();
}
}
// go on
adj = pBM->beforeShortCircuitEdge(x,dir);
x = pBM->successorWithoutShortCircuit(x,dir);
}
}
// start DFS-traversal
void BoyerMyrvoldInit::computeDFS()
{
// compute random edge costs
EdgeArray<int> costs;
EdgeComparer comp;
if(m_randomness > 0 && m_edgeCosts != nullptr) {
costs.init(m_g);
int minCost = std::numeric_limits<int>::max();
int maxCost = std::numeric_limits<int>::min();
for(edge e : m_g.edges) {
minCost = min(minCost, (*m_edgeCosts)[e]);
maxCost = min(maxCost, (*m_edgeCosts)[e]);
}
std::uniform_real_distribution<> urd(-1, 1);
for(edge e : m_g.edges) {
costs[e] = minCost + (int)((1 - m_randomness) * ((*m_edgeCosts)[e] - minCost) + m_randomness * (maxCost - minCost) * urd(m_rand));
}
comp.setCosts(&costs);
} else if(m_edgeCosts != nullptr) {
comp.setCosts(m_edgeCosts);
}
StackPure<adjEntry> stack;
int nextDFI = 1;
const int numberOfNodes = m_g.numberOfNodes();
SListPure<adjEntry> adjList;
SListPure<node> list;
m_g.allNodes(list);
// get random dfs-tree, if wanted
if (m_randomness > 0) {
list.permute();
}
for (node v : list) {
if (v->degree() == 0) {
m_dfi[v] = nextDFI;
m_leastAncestor[v] = nextDFI;
m_nodeFromDFI[nextDFI] = v;
++nextDFI;
} else {
adjList.clear();
m_g.adjEntries(v, adjList);
adjList.quicksort(comp);
m_g.sort(v, adjList);
stack.push(v->firstAdj());
}
}
while (nextDFI <= numberOfNodes) {
OGDF_ASSERT(!stack.empty());
adjEntry prnt = stack.pop();
node v = prnt->theNode();
// check, if node v was visited before.
if (m_dfi[v] != 0) continue;
// parentNode=nullptr on first node on connected component
node parentNode = prnt->twinNode();
if (m_dfi[parentNode] == 0) parentNode = nullptr;
// if not, mark node as visited and initialize NodeArrays
m_dfi[v] = nextDFI;
m_leastAncestor[v] = nextDFI;
m_nodeFromDFI[nextDFI] = v;
++nextDFI;
// push all adjacent nodes onto stack
for(adjEntry adj : v->adjEdges) {
edge e = adj->theEdge();
if (adj == prnt && parentNode != nullptr) continue;
// check for self-loops and dfs- and dfs-parallel edges
node w = adj->twinNode();
if (m_dfi[w] == 0) {
m_edgeType[e] = EDGE_DFS;
m_adjParent[w] = adj;
m_link[CW][w] = adj;
m_link[CCW][w] = adj;
// found new dfs-edge: preorder
stack.push(adj->twin());
} else if (w == v) {
// found self-loop
m_edgeType[e] = EDGE_SELFLOOP;
} else {
// node w already has been visited and is an dfs-ancestor of v
OGDF_ASSERT(m_dfi[w] < m_dfi[v]);
if (w == parentNode) {
// found parallel edge of dfs-parent-edge
m_edgeType[e] = EDGE_DFS_PARALLEL;
} else {
// found backedge
m_edgeType[e] = EDGE_BACK;
// set least Ancestor
if (m_dfi[w] < m_leastAncestor[v])
m_leastAncestor[v] = m_dfi[w];
}
}
}
}
}