Prefer to use VS2013 for compiling and testing on AppVeyor

[TortoiseGit.git] / ext / OGDF / src / planarity / BoyerMyrvoldPlanar.cpp

/*
 * $Revision: 2559 $
 *
 * last checkin:
 *   $Author: gutwenger $
 *   $Date: 2012-07-06 15:04:28 +0200 (Fr, 06. Jul 2012) $
 ***************************************************************/

/** \file
 * \brief implementation of the class BoyerMyrvoldPlanar
 *
 * \author Jens Schmidt
 *
 * \par License:
 * This file is part of the Open Graph Drawing Framework (OGDF).
 *
 * \par
 * Copyright (C)<br>
 * See README.txt in the root directory of the OGDF installation for details.
 *
 * \par
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * Version 2 or 3 as published by the Free Software Foundation;
 * see the file LICENSE.txt included in the packaging of this file
 * for details.
 *
 * \par
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * \par
 * You should have received a copy of the GNU General Public
 * License along with this program; if not, write to the Free
 * Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 * Boston, MA 02110-1301, USA.
 *
 * \see  http://www.gnu.org/copyleft/gpl.html
 ***************************************************************/


#include <ogdf/internal/planarity/BoyerMyrvoldPlanar.h>
#include <ogdf/internal/planarity/BoyerMyrvoldInit.h>
#include <ogdf/internal/planarity/FindKuratowskis.h>


namespace ogdf {


// constructor
BoyerMyrvoldPlanar::BoyerMyrvoldPlanar(
        Graph& g,
        bool bundles,
        int embeddingGrade, // see enumeration enumEmbeddingGrade for options
        bool limitStructures, // limits number of structures to embeddingGrade
        SListPure<KuratowskiStructure>& output,
        bool randomDFSTree, // creates a random DFS-Tree, if true
        bool avoidE2Minors) // avoids multiple identical minors (type AE2/E2)
:
m_g(g),
        m_bundles(bundles),
        m_embeddingGrade(embeddingGrade),
        m_limitStructures(limitStructures),
        m_randomDFSTree(randomDFSTree),
        m_avoidE2Minors(avoidE2Minors),

        // BoyerMyrvoldInit members
        m_realVertex(g,0),
        m_dfi(g,0),
        m_nodeFromDFI(-g.numberOfNodes(),g.numberOfNodes(),0),
        m_adjParent(g,0),
        m_leastAncestor(g), // doesn't need initialization
        m_edgeType(g,EDGE_UNDEFINED),
        m_lowPoint(g), // doesn't need initialization
        m_separatedDFSChildList(g),
        m_pNodeInParent(g), // doesn't need initialization

        // Walkup & Walkdown members
        m_visited(g,0),
        m_flipped(g,false),
        m_backedgeFlags(g),
        m_pertinentRoots(g),
        m_output(output)
{
        m_link[CCW].init(g,0);
        m_link[CW].init(g,0);
        m_beforeSCE[CCW].init(g,0);
        m_beforeSCE[CW].init(g,0);
        m_output.clear();
        // apply this only, if FIND-procedure will be called
        if (m_embeddingGrade > doNotFind) {
                m_pointsToRoot.init(g,0);
                m_visitedWithBackedge.init(g,0);
                m_highestSubtreeDFI.init(g); // doesn't need initialization
        }
        m_flippedNodes = 0;
}


// walk upon external face in the given direction, see getSucessorOnExternalFace
// the difference is, that all inactive vertices are skipped, i.e. the returned node
// is active in relation to the node with dfi v
// in the special case of degree-one nodes the direction is not changed
// info returns the dynamic nodetype of the endnode
node BoyerMyrvoldPlanar::activeSuccessor(node w, int& direction, int v, int& info)
{
        OGDF_ASSERT(w!=0);
        OGDF_ASSERT(w->degree()>0);
        OGDF_ASSERT(m_link[CW][w]!=0 && m_link[CCW][w]!=0);
        node next;
        adjEntry adj;

        do {
                adj = m_link[direction][w];
                next = adj->theNode();
                OGDF_ASSERT(next!=0);
                OGDF_ASSERT(next->degree()>0);
                OGDF_ASSERT(m_link[CW][next]!=0 && m_link[CCW][next]!=0);

                if (w->degree() > 1)
                        direction = adj==beforeShortCircuitEdge(next,CCW)->twin();
                w=next;
                info = infoAboutNode(next,v);

        } while (info==0); // until not inactive
        return next;
}


// merges adjEntries of virtual node w and associated real vertex x according to
// given outgoing directions x_dir and w_dir.
// j is the outgoing traversal direction of the current embedded node.
void BoyerMyrvoldPlanar::mergeBiconnectedComponent(StackPure<int>& stack, const int /* j */)
{
        const int w_dir = stack.pop(); // outgoing direction of w
        const int x_dir = stack.pop(); // outgoing direction of x
        int tmp = stack.pop();
        const node w = m_nodeFromDFI[tmp]; // virtual DFS-Successor of x
        const node w_child = m_nodeFromDFI[-tmp]; // real unique DFS-Child of bicomp with root w
        const node x = m_realVertex[w];

        // set new external face neighbors and save adjEntry, where edges will be merged
        adjEntry mergeEntry;
        Direction dir = (x_dir == CCW) ? before : after;
        mergeEntry = beforeShortCircuitEdge(x,!x_dir)->twin();
        m_link[!x_dir][x] = m_link[!w_dir][w];
        m_beforeSCE[!x_dir][x] = m_beforeSCE[!w_dir][w];

        // merge real and virtual nodes, flip biconnected component root if neccesary
        OGDF_ASSERT(!m_flipped[w_child]);
        adjEntry adj = w->firstAdj();
        edge e;
        if (x_dir==w_dir) {
                // if not flipped
                if (dir==after) {
                        mergeEntry=mergeEntry->cyclicSucc();
                        dir=before;
                }
        } else {
                // if flipped:
                // set unique DFS-child of associated bicomp root node to "flipped"
                m_flipped[w_child] = true;
                ++m_flippedNodes;
                if (dir==before) {
                        mergeEntry = mergeEntry->cyclicPred();
                        dir = after;
                }
        }

        // merge adjEntries
        adjEntry temp;
        while (adj != 0) {
                temp = adj->succ();
                e = adj->theEdge();
                OGDF_ASSERT(e->source() != x && e->target() != x);
                // this allows also self-loops when moving adjacency entries
                if (e->source() == w) {
                        m_g.moveSource(e,mergeEntry,dir);
                } else m_g.moveTarget(e,mergeEntry,dir);
                adj = temp;
        }

        // remove w from pertinent roots of x
        OGDF_ASSERT(!m_pertinentRoots[x].empty());
        OGDF_ASSERT(m_pertinentRoots[x].front() == w);
        m_pertinentRoots[x].popFront();

        // consider x's unique dfs-successor in pertinent bicomp:
        // remove this successor from separatedChildList of x using
        // saved pointer pNodeInParent in constant time
        OGDF_ASSERT(!m_separatedDFSChildList[x].empty());
        OGDF_ASSERT(m_pNodeInParent[w_child].valid());
        m_separatedDFSChildList[x].del(m_pNodeInParent[w_child]);

        // delete virtual vertex, it must not contain any edges any more
        OGDF_ASSERT(w->firstAdj()==0);
        m_nodeFromDFI[m_dfi[w]]=0;
        m_g.delNode(w);
}


// the same as mergeBiconnectedComponent, but without any embedding-related
// operations
void BoyerMyrvoldPlanar::mergeBiconnectedComponentOnlyPlanar(
        StackPure<int>& stack,
        const int /* j */)
{
        const int w_dir = stack.pop(); // outgoing direction of w
        const int x_dir = stack.pop(); // outgoing direction of x
        int tmp = stack.pop();
        const node w = m_nodeFromDFI[tmp]; // virtual DFS-Successor of x
        const node w_child = m_nodeFromDFI[-tmp]; // real unique DFS-Child of bicomp with root w
        const node x = m_realVertex[w];

        // set new external face neighbors and save adjEntry, where edges will be merged
        m_link[!x_dir][x] = m_link[!w_dir][w];
        m_beforeSCE[!x_dir][x] = m_beforeSCE[!w_dir][w];

        // merge real and virtual nodes, flipping is not necessary here
        OGDF_ASSERT(!m_flipped[w_child]);
        adjEntry adj = w->firstAdj();
        edge e;
        adjEntry temp;
        while (adj != 0) {
                temp = adj->succ();
                e = adj->theEdge();
                OGDF_ASSERT(e->source() != x && e->target() != x);
                // this allows also self-loops when moving adjacency entries
                if (e->source() == w) {
                        m_g.moveSource(e,x);
                } else m_g.moveTarget(e,x);
                adj = temp;
        }

        // remove w from pertinent roots of x
        OGDF_ASSERT(m_pertinentRoots[x].front() == w);
        m_pertinentRoots[x].popFront();

        // consider x's unique dfs-successor in pertinent bicomp:
        // remove this successor from separatedChildList of x using
        // saved pointer pNodeInParent in constant time
        OGDF_ASSERT(m_pNodeInParent[w_child].valid());
        m_separatedDFSChildList[x].del(m_pNodeInParent[w_child]);

        // delete virtual vertex, it must not contain any edges any more
        OGDF_ASSERT(w->firstAdj()==0);
        m_nodeFromDFI[m_dfi[w]]=0;
        m_g.delNode(w);
}


// embeds backedges from node v with direction v_dir to node w
// with direction w_dir. i is the current embedded node.
void BoyerMyrvoldPlanar::embedBackedges(
        const node v,
        const int v_dir,
        const node w,
        const int w_dir,
        const int /* i */)
{
        OGDF_ASSERT(!m_backedgeFlags[w].empty());
        OGDF_ASSERT(v!=0 && w!=0);
        OGDF_ASSERT(m_link[CCW][v]!=0 && m_link[CW][v]!=0);
        OGDF_ASSERT(m_link[CCW][w]!=0 && m_link[CW][w]!=0);

        // if one edge is a short circuit edge, compute the former underlying adjEntry
        // the adjEntry of v, used for inserting backedges
        adjEntry mergeEntryV = beforeShortCircuitEdge(v,v_dir)->twin();
        Direction insertv = (v_dir==CCW) ? after : before;
        // the adjEntry of w, used for inserting backedges
        adjEntry mergeEntryW = beforeShortCircuitEdge(w,!w_dir)->twin();
        Direction insertw = (w_dir==CCW) ? before : after;

        // the first backedge in the backedgeFlags-list will be
        // the new external face adjEntry
        edge e;
        SListConstIterator<adjEntry> it;
        // save first BackedgeEntry
        adjEntry firstBack = m_backedgeFlags[w].front();
        for (it = m_backedgeFlags[w].begin(); it.valid(); ++it) {
                // embed this backedge
                e = (*it)->theEdge();

                OGDF_ASSERT(w==e->source() || w==e->target());
                //OGDF_ASSERT((*it)->theNode()==m_nodeFromDFI[i]);

                if (e->source() == w) {
                        // insert backedge to v
                        m_g.moveTarget(e,mergeEntryV,insertv);
                        // insert backedge to w
                        m_g.moveSource(e,mergeEntryW,insertw);
                } else {
                        // insert backedge to v
                        m_g.moveSource(e,mergeEntryV,insertv);
                        // insert backedge to w
                        m_g.moveTarget(e,mergeEntryW,insertw);
                }
        }

        // set external face link for this backedge and delete out-dated short
        // circuit links
        m_link[v_dir][v] = firstBack->twin();
        m_beforeSCE[v_dir][v]=0;
        m_link[!w_dir][w] = firstBack;
        m_beforeSCE[!w_dir][w]=0;

        // decrease counter of backedges per bicomp
        if (m_embeddingGrade > doNotFind) {
                node bicompRoot = m_pointsToRoot[m_backedgeFlags[w].front()->theEdge()];
                m_visitedWithBackedge[bicompRoot] -= m_backedgeFlags[w].size();
                OGDF_ASSERT(m_visitedWithBackedge[bicompRoot] >= 0);
        }

        // delete BackedgeFlags
        m_backedgeFlags[w].clear();
}


// the same as embedBackedges, but for the planar check without returned embedding
void BoyerMyrvoldPlanar::embedBackedgesOnlyPlanar(
        const node v,
        const int v_dir,
        const node w,
        const int w_dir,
        const int /* i */)
{
        OGDF_ASSERT(!m_backedgeFlags[w].empty());
        OGDF_ASSERT(m_link[CCW][v]!=0 && m_link[CW][v]!=0);
        OGDF_ASSERT(m_link[CCW][w]!=0 && m_link[CW][w]!=0);

        // the last backedge in the backedgeFlags-list will be
        // the new external face adjEntry
        edge e;
        SListIterator<adjEntry> it;
        // save last BackedgeEntry
        adjEntry lastBack = m_backedgeFlags[w].back();
        for(it=m_backedgeFlags[w].begin();it.valid();++it) {
                // embed backedge
                e = (*it)->theEdge();

                //OGDF_ASSERT((*it)->theNode()==m_nodeFromDFI[i]);
                OGDF_ASSERT(w==e->source() || w==e->target());

                if (e->source() == w) {
                        // insert backedge to v
                        m_g.moveTarget(e,v);
                } else {
                        // insert backedge to v
                        m_g.moveSource(e,v);
                }
        }

        // set external face link for this backedge and delete out-dated short
        // circuit links
        m_link[v_dir][v] = lastBack->twin();
        m_beforeSCE[v_dir][v]=0;
        m_link[!w_dir][w] = lastBack;
        m_beforeSCE[!w_dir][w]=0;

        // delete BackedgeFlags
        m_backedgeFlags[w].clear();
}


// create short circuit edge from node v with direction v_dir to node w with outgoing
// direction w_dir.
void BoyerMyrvoldPlanar::createShortCircuitEdge(
        const node v,
        const int v_dir,
        const node w,
        const int w_dir)
{
        // save former neighbors
        if (m_beforeSCE[v_dir][v]==0) m_beforeSCE[v_dir][v]=m_link[v_dir][v];
        if (m_beforeSCE[!w_dir][w]==0) m_beforeSCE[!w_dir][w]=m_link[!w_dir][w];
        // set new short circuit edge
        adjEntry temp = m_beforeSCE[!w_dir][w]->twin();
        m_link[!w_dir][w] = m_beforeSCE[v_dir][v]->twin();
        m_link[v_dir][v] = temp;
}


// Walkup
// finds pertinent subgraph for descendant w of v.
// marks visited nodes with marker and returns the last traversed node.
node BoyerMyrvoldPlanar::walkup(
        const node v,
        const node w,
        const int marker,
        const edge back)
{
        const int i = m_dfi[v];
        node x = w;
        node y = w;
        node temp;
        int x_dir = CW;
        int y_dir = CCW;

        while (m_visited[x]!=marker && m_visited[y]!=marker)
        {
                m_visited[x] = marker;
                m_visited[y] = marker;
                if (m_embeddingGrade > doNotFind) {
                        m_visitedWithBackedge[x] = back->index();
                        m_visitedWithBackedge[y] = back->index();
                }

                // is x or y root vertex?
                if (m_realVertex[x] != 0) {
                        temp=x;
                } else if (m_realVertex[y] != 0) {
                        temp=y;
                } else temp=0;

                if (temp != 0) {
                        // put pertinent root into the list of its non-virtual vertex.
                        // the insert-position is either front or back of the list, this
                        // depends on the external activity of the pertinent root's
                        // biconnected component.

                        x = m_realVertex[temp];
                        y = x;

                        OGDF_ASSERT(m_visited[x]==marker || m_pertinentRoots[x].empty());
                        // push pertinent root
                        if (m_lowPoint[m_nodeFromDFI[-m_dfi[temp]]] < i) {
                                m_pertinentRoots[x].pushBack(temp);
                        } else m_pertinentRoots[x].pushFront(temp);
                        // found v, finish walkup and return last traversed node
                        if (x==v) {
                                m_visited[x] = marker;
                                return temp;
                        }
                } else {
                        // traverse to external face successors
                        x = successorOnExternalFace(x,x_dir);
                        y = successorOnExternalFace(y,y_dir);
                }
        }

        // return last traversed node
        return (m_visited[x] == marker) ? x : y;
}


// Walkdown
// for DFS-child w of the current processed vertex v': embed all backedges
// to the virtual node v of v'
// returns 1, iff the embedding process found a stopping configuration
int BoyerMyrvoldPlanar::walkdown(
        const int i, // dfi of rootvertex v'
        const node v, // v is virtual node of v'
        FindKuratowskis *findKuratowskis)
{
        StackPure<int> stack;
        node stopX = 0;

        bool stoppingNodesFound = 0; // 0=false,1=true,2=break

        // in both directions
        // j=current outgoing direction of current embedded node v
        for (int j = CCW; j <= CW; ++j) {
                int w_dir = j; // direction of traversal of node w

                node w = successorOnExternalFace(v,w_dir); // current node

                while (w != v) {
                        // assert, that CCW[] and CW[] return that adjEntry of the neighbor
                        OGDF_ASSERT(beforeShortCircuitEdge(w,w_dir)->twinNode()==w);

                        // if backedgeFlag is set
                        if (!m_backedgeFlags[w].empty()) {
                                if (m_embeddingGrade != doNotEmbed) {
                                        // compute entire embedding
                                        while (!stack.empty()) mergeBiconnectedComponent(stack,j);
                                        // embed the backedge
                                        embedBackedges(v,j,w,w_dir,i);
                                } else {
                                        // compute only planarity, not the entire embedding
                                        while (!stack.empty()) mergeBiconnectedComponentOnlyPlanar(stack,j);
                                        // embed the backedge
                                        embedBackedgesOnlyPlanar(v,j,w,w_dir,i);
                                }
                        }

                        // if pertinentRoots of w is not empty
                        if (!m_pertinentRoots[w].empty()) {
                                // append pertinent root of w and direction of entry in w to stack
                                // y is root of pertinent child bicomp
                                node root = m_pertinentRoots[w].front();
                                stack.push(m_dfi[root]);

                                // append outgoing direction of entry in w to stack
                                OGDF_ASSERT(w->degree() > 0);
                                stack.push(w_dir);

                                // get active successor in pertinent bicomp
                                // variables for recognizing the right direction after descending to a bicomp
                                int x_dir = CCW;
                                int y_dir = CW;
                                int infoX, infoY; // gives information about the type of endnode in that direction
                                node x = activeSuccessor(root,x_dir,i,infoX);
                                node y = activeSuccessor(root,y_dir,i,infoY);

                                OGDF_ASSERT(x != root && y != root);
                                createShortCircuitEdge(root,CCW,x,x_dir);
                                createShortCircuitEdge(root,CW,y,y_dir);

                                // push counterclockwise resp. clockwise active successor
                                // in pertinent bicomp
                                if (infoX == infoY) {
                                        // if both attributes are externally active and non-pertinent,
                                        // save stopping nodes
                                        if (infoX==3) {
                                                OGDF_ASSERT(x != y);
                                                if (m_embeddingGrade <= doNotFind) return true;

                                                // extract Kuratowskis
                                                stoppingNodesFound = 1;
                                                // check, if we have found enough kuratowski structures
                                                if (m_embeddingGrade > 0 &&
                                                                findKuratowskis->getAllKuratowskis().size() >= m_embeddingGrade) {
                                                        return 2;
                                                }
                                                findKuratowskis->addKuratowskiStructure(m_nodeFromDFI[i],root,x,y);

                                                // go to the pertinent starting node on father bicomp
                                                stack.pop(); // delete new w_dir from stack
                                                w = m_realVertex[m_nodeFromDFI[stack.pop()]]; // x itself
                                                // refresh pertinentRoots information
                                                m_pertinentRoots[w].popFront();

                                                // if more pertinent child bicomps exist on the same root,
                                                // let the walkdown either embed it or find a new kuratowski structure
                                                while (!stack.empty() && !pertinent(w)) {
                                                        // last real root
                                                        node lastActiveNode = w;

                                                        // not in V-bicomp:
                                                        // go to the unvisited active node on father bicomp
                                                        w_dir = stack.pop(); // outgoing direction of w
                                                        x_dir = stack.pop(); // outgoing direction of x
                                                        w = m_nodeFromDFI[stack.top()]; // w, virtual node

                                                        node otherActiveNode = m_link[!w_dir][w]->theNode();

                                                        OGDF_ASSERT(otherActiveNode == constActiveSuccessor(w,!w_dir,i,infoX));
                                                        OGDF_ASSERT(externallyActive(otherActiveNode,i));
                                                        OGDF_ASSERT(lastActiveNode == m_link[w_dir][w]->theNode());
                                                        if (pertinent(otherActiveNode)) {
                                                                // push adapted information about actual bicomp in stack
                                                                stack.push(x_dir);
                                                                stack.push(!w_dir);
                                                                // go on with walkdown on unvisited active node
                                                                w_dir = !w_dir;
                                                                break;
                                                        } else {
                                                                // delete old root
                                                                stack.pop();
                                                                // if there are two stopping vertices, that are not pertinent
                                                                // there could be another kuratowski structure
                                                                if (lastActiveNode != otherActiveNode &&
                                                                                wNodesExist(w,lastActiveNode,otherActiveNode)) {
                                                                        // check, if we have found enough kuratowski structures
                                                                        if (m_embeddingGrade > 0 &&
                                                                                        findKuratowskis->getAllKuratowskis().size() >= m_embeddingGrade) {
                                                                                return 2;
                                                                        }
                                                                        // different stopping nodes:
                                                                        // try to extract kuratowski structure and put the two
                                                                        // stopping nodes in the right traversal order
                                                                        if (w_dir==CCW) {
                                                                                findKuratowskis->addKuratowskiStructure(m_nodeFromDFI[i],
                                                                                                                w,lastActiveNode,otherActiveNode);
                                                                        } else {
                                                                                findKuratowskis->addKuratowskiStructure(m_nodeFromDFI[i],
                                                                                                                w,otherActiveNode,lastActiveNode);
                                                                        }
                                                                }

                                                                // refresh pertinentRoots information
                                                                w = m_realVertex[w]; // x
                                                                m_pertinentRoots[w].popFront();
                                                                w_dir = x_dir;
                                                        }
                                                }
                                        }
                                        // if both attributes are the same: minimize flips
                                        else if (w_dir==CCW) {
                                                w = x;
                                                w_dir = x_dir;
                                                stack.push(CCW);

                                        } else {
                                                w = y;
                                                w_dir = y_dir;
                                                stack.push(CW);
                                        }
                                } else if (infoX <= infoY) {
                                        // push x
                                        w=x; w_dir=x_dir;
                                        stack.push(CCW);

                                } else {
                                        // push y
                                        w=y; w_dir=y_dir;
                                        stack.push(CW);
                                }

                        } else if (inactive(w,i)) {
                                // w is an inactive vertex
                                w = successorOnExternalFace(w,w_dir);

                        } else {
                                // w must be a stopping vertex
                                OGDF_ASSERT(externallyActive(w,i));
                                OGDF_ASSERT(m_lowPoint[m_nodeFromDFI[-m_dfi[v]]] < i);

                                // embed shortCircuitEdge
                                /*if (stack.empty())*/ createShortCircuitEdge(v,j,w,w_dir);

                                // only save single stopping nodes, if we don't have already one
                                if (j==CCW) {
                                        stopX = w;
                                } else if (w != stopX) {
                                        OGDF_ASSERT(stopX!=0);

                                        if (m_embeddingGrade <= doNotFind) return false;
                                        // check, if some backedges were not embedded (=> nonplanar)
                                        // note, that this is performed at most one time per virtual root
                                        if (m_visitedWithBackedge[v] > 0) {
                                                // some backedges are left on this bicomp
                                                stoppingNodesFound = 1;
                                                // check, if we have found enough kuratowski structures
                                                if (m_embeddingGrade > 0 &&
                                                                findKuratowskis->getAllKuratowskis().size() >= m_embeddingGrade) {
                                                        return 2;
                                                }
                                                findKuratowskis->addKuratowskiStructure(m_nodeFromDFI[i],v,stopX,w);
                                        }
                                }

                                break; // while
                        }
                } // while

                stack.clear();
        } // for

        return stoppingNodesFound;
}

// embed graph m_g node by node in descending DFI-order beginning with dfi i
bool BoyerMyrvoldPlanar::embed()
{
        bool nonplanar=false; // true, if graph is not planar

        //FindKuratowskis findKuratowskis(this);
        FindKuratowskis* findKuratowskis =
                (m_embeddingGrade <= doNotFind) ? 0 : new FindKuratowskis(this);

        for (int i = m_nodeFromDFI.high(); i >= 1; --i)
        {
                const node v = m_nodeFromDFI[i];

                // call Walkup
                // for all sources of backedges of v: find pertinent subgraph

                adjEntry adj;
                forall_adj(adj,v) {
                        node w = adj->twinNode(); // dfs-descendant of v
                        edge e = adj->theEdge();
                        if (m_dfi[w] > i && m_edgeType[e] == EDGE_BACK) {
                                m_backedgeFlags[w].pushBack(adj);

                                node x = walkup(v,w,i,e);
                                if (m_embeddingGrade <= doNotFind) continue;

                                // divide children bicomps
                                if (m_realVertex[x] == v) {
                                        m_pointsToRoot[e] = x;
                                        // set backedgenumber to 1 on this root
                                        m_visitedWithBackedge[x] = 1;
                                } else {
                                        x = m_pointsToRoot[m_visitedWithBackedge[x]];
                                        m_pointsToRoot[e] = x;
                                        // increase backedgenumber on this root
                                        OGDF_ASSERT(m_visitedWithBackedge[x]>=1);
                                        ++m_visitedWithBackedge[x];
                                }
                        }
                }

                // call Walkdown
                // for every pertinent subtrees with children w of v as roots
                // embed all backedges to v
                SListPure<node>& pert(m_pertinentRoots[v]);
                while (!pert.empty()) {
                        OGDF_ASSERT(pert.front()->degree()==1);
                        int result = walkdown(i,pert.popFrontRet(),findKuratowskis);
                        if (result == 2) {
                                m_output = findKuratowskis->getAllKuratowskis();
                                delete findKuratowskis;
                                return false;
                        } else if (result == 1) {
                                // found stopping configuration
                                nonplanar = true;
                                if (m_embeddingGrade <= doNotFind) return false;
                        }
                }

                // if !embed, check, if there are any backedges left
                if (m_embeddingGrade <= doNotFind) {
                        forall_adj(adj,v) {
                                if (m_edgeType[adj->theEdge()] == EDGE_BACK &&
                                                m_dfi[adj->twinNode()] > m_dfi[v])
                                        return false; // nonplanar
                        }
                }
        }

        // embed and flip bicomps, if necessary
        if (nonplanar) {
                if(findKuratowskis)
                        m_output = findKuratowskis->getAllKuratowskis();
        } else
                postProcessEmbedding(); // flip graph and embed self-loops, etc.

        delete findKuratowskis;
        return !nonplanar;
}


// merge unprocessed virtual nodes such as the dfs-roots
void BoyerMyrvoldPlanar::mergeUnprocessedNodes()
{
        node v = m_g.firstNode();
        while (v) {
                node next = v->succ();
                if (m_dfi[v] < 0) {
                        node w = m_realVertex[v];
                        adjEntry adj = v->firstAdj();
                        // copy all adjEntries to non-virtual node
                        while (adj) {
                                edge e = adj->theEdge();
                                adj = adj->succ();
                                if (e->source()==v) {
                                        m_g.moveSource(e,w);
                                } else m_g.moveTarget(e,w);
                        }
                        m_nodeFromDFI[m_dfi[v]]=0;
                        m_g.delNode(v);
                }
                v = next;
        }
}


// flips all nodes of the bicomp with unique real root-child c as necessary.
// in addition all connected components with dfs-root c without virtual
// nodes are allowed. this function can be used to reverse the flip, too!
// marker has to be an non-existing int in array visited.
// if wholeGraph ist true, all bicomps of all connected components will be traversed.
// if deleteFlipFlags ist true, the flipping flags will be deleted after flipping
void BoyerMyrvoldPlanar::flipBicomp(
        int c,
        int marker,
        NodeArray<int>& visited,
        bool wholeGraph,
        bool deleteFlipFlags)
{
        if (m_flippedNodes == 0) {
                if (wholeGraph) mergeUnprocessedNodes();
                return;
        }

        StackPure<int> stack; // stack for dfs-traversal
        node v;
        int temp;
        adjEntry adj;

        if (wholeGraph) {
                mergeUnprocessedNodes();
                for (int i = 1; i <= m_g.numberOfNodes(); ++i)
                        stack.push(-i);
        }

        // flip bicomps, if the flipped-flag is set
        bool flip;
        stack.push(-c); // negative numbers: flip=false, otherwise flip=true
        while (!stack.empty()) {
                temp = stack.pop();
                if (temp < 0) {
                        flip = false;
                        v = m_nodeFromDFI[-temp];
                } else {
                        flip = true;
                        v = m_nodeFromDFI[temp];
                }
                if (wholeGraph) {
                        if (visited[v]==marker) continue;
                        // mark visited nodes
                        visited[v] = marker;
                }

                // flip adjEntries of node, if necessary
                if (m_flipped[v]) {
                        flip = !flip;

                        // don't do this, if all flips on nodes of this bicomp will be reversed
                        if (deleteFlipFlags) {
                                m_flipped[v] = false;
                                --m_flippedNodes;
                                OGDF_ASSERT(m_flippedNodes >= 0);
                        }
                }
                if (flip) {
                        m_g.reverseAdjEdges(v);
                        if (deleteFlipFlags) {
                                adjEntry tmp = m_link[CCW][v];
                                m_link[CCW][v] = m_link[CW][v];
                                m_link[CW][v] = tmp;

                                tmp = m_beforeSCE[CCW][v];
                                m_beforeSCE[CCW][v] = m_beforeSCE[CW][v];
                                m_beforeSCE[CW][v] = tmp;
                        }
                }

                // go along the dfs-edges
                forall_adj(adj,v) {
                        temp = m_dfi[adj->twinNode()];
                        OGDF_ASSERT(m_edgeType[adj->theEdge()] != EDGE_UNDEFINED);
                        if (temp > m_dfi[v] && m_edgeType[adj->theEdge()]==EDGE_DFS) {
                                stack.push(flip ? temp : -temp);
                        }
                }
        }
}


// postprocess the embedding, so that all unprocessed virtual vertices are
// merged with their non-virtual counterpart. Furthermore all bicomps
// are flipped, if necessary and parallel edges and self-loops are embedded.
void BoyerMyrvoldPlanar::postProcessEmbedding()
{
        StackPure<int> stack; // stack for dfs-traversal
        node v,w;
        adjEntry adj;
        int temp;

        mergeUnprocessedNodes();

        // flip bicomps, if the flipped-flag is set, i.e. postprocessing in
        // reverse dfi-order
        bool flip;
        for(int i=1; i<=m_g.numberOfNodes(); ++i) {
                if (m_visited[m_nodeFromDFI[i]] == -1) continue;
                stack.push(-i); // negative numbers: flip=false, otherwise flip=true

                while (!stack.empty()) {
                        temp = stack.pop();
                        if (temp < 0) {
                                flip=false;
                                v = m_nodeFromDFI[-temp];
                        } else {
                                flip=true;
                                v = m_nodeFromDFI[temp];
                        }
                        if (m_visited[v]==-1) continue;
                        // mark visited nodes with visited[v]==-1
                        m_visited[v] = -1;

                        // flip adjEntries of node, if necessary
                        if (m_flipped[v]) {
                                m_flipped[v] = false;
                                flip = !flip;
                        }
                        if (flip) m_g.reverseAdjEdges(v);

                        adj=v->firstAdj();
                        while (adj) {
                                w = adj->twinNode();
                                temp = m_edgeType[adj->theEdge()];
                                if (temp==EDGE_DFS) {
                                        // go along the dfs-edges
                                        stack.push(flip ? m_dfi[w] : -m_dfi[w]);
                                        adj=adj->succ();
                                } else if (temp==EDGE_SELFLOOP) {
                                        // embed self-loops
                                        m_g.moveAdjBefore(adj->twin(),adj);
                                        adj=adj->succ();
                                } else if (temp==EDGE_DFS_PARALLEL &&
                                                        m_adjParent[v]!=0 &&
                                                        w == m_adjParent[v]->theNode()) {
                                        // embed edges that are parallel to dfs-edges
                                        // it is only possible to deal with the parallel edges to the
                                        // parent, since children nodes could be flipped later
                                        adjEntry tmp = adj->succ();
                                        m_g.moveAdjAfter(adj,m_adjParent[v]->twin());
                                        m_g.moveAdjBefore(adj->twin(),m_adjParent[v]);
                                        adj = tmp;
                                } else adj=adj->succ();
                        }
                }
        }
}


// tests Graph m_g for planarity
// if graph should be embedded, a planar embedding or a kuratowski subdivision
// of m_g is returned in addition, depending on whether m_g is planar
bool BoyerMyrvoldPlanar::start()
{
        BoyerMyrvoldInit bmi(this);
        bmi.computeDFS();
        bmi.computeLowPoints();
        bmi.computeDFSChildLists();

        // call the embedding procedure
        return embed();
}


}