EmbedderMaxFaceBiconnectedGraphsLayers.h

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#pragma once
 
#include <ogdf/planarity/embedder/EmbedderMaxFaceBiconnectedGraphs.h>
 
namespace ogdf {
 
 
template<class T>
class EmbedderMaxFaceBiconnectedGraphsLayers : private EmbedderMaxFaceBiconnectedGraphs<T> {
public:
    static void embed(Graph& G, adjEntry& adjExternal, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength, const node& n = nullptr);
 
    using EmbedderMaxFaceBiconnectedGraphs<T>::compute;
    using EmbedderMaxFaceBiconnectedGraphs<T>::computeSize;
 
private:
    using EmbedderMaxFaceBiconnectedGraphs<T>::largestFaceContainingNode;
    using EmbedderMaxFaceBiconnectedGraphs<T>::largestFaceInSkeleton;
 
    /* \brief Computes recursively the thickness of the skeleton graph of all
     *   nodes in the SPQR-tree.
     *
     * \param spqrTree The SPQR-tree of the treated graph.
     * \param mu a node in the SPQR-tree.
     * \param thickness saving the computed results - the thickness of each
     *   skeleton graph.
     * \param nodeLength is saving for each node of the original graph \p G its
     *   length.
     * \param edgeLength is saving the edge lengths of all edges in each skeleton
     *   graph of all tree nodes.
     */
    static void bottomUpThickness(const StaticSPQRTree& spqrTree, const node& mu,
            NodeArray<T>& thickness, const NodeArray<T>& nodeLength,
            const NodeArray<EdgeArray<T>>& edgeLength);
 
    /* \brief ExpandEdge embeds all edges in the skeleton graph \a S into an
     *   existing embedding and calls recursively itself for all virtual edges
     *   in S.
     *
     * \param spqrTree The SPQR-tree of the treated graph.
     * \param treeNodeTreated is an array saving for each SPQR-tree node \p mu
     *   whether it was already treated by any call of ExpandEdge or not. Every
     *   \p mu should only be treated once.
     * \param mu is a node in the SPQR-tree.
     * \param leftNode is the node adjacent to referenceEdge, which should be "left"
     *   in the embedding
     * \param nodeLength is an array saving the lengths of the nodes of \p G.
     * \param edgeLength is saving the edge lengths of all edges in each skeleton
     *   graph of all tree nodes.
     * \param thickness of each skeleton graph.
     * \param newOrder is saving for each node \p n in \p G the new adjacency
     *   list. This is an output parameter.
     * \param adjBeforeNodeArraySource is saving for the source of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param adjBeforeNodeArrayTarget is saving for the target of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param delta_u the distance from the second adjacent face of the reference edge
     *   except the external face to the external face of G.
     * \param delta_d the distance from the external face to the external face of G.
     * \param adjExternal is an adjacency entry in the external face.
     * \param n is only set, if ExpandEdge is called for the first time, because
     *   then there is no virtual edge which has to be expanded, but the max face
     *   has to contain a certain node \p n.
     */
    static void expandEdge(const StaticSPQRTree& spqrTree, NodeArray<bool>& treeNodeTreated,
            const node& mu, const node& leftNode, const NodeArray<T>& nodeLength,
            const NodeArray<EdgeArray<T>>& edgeLength, const NodeArray<T>& thickness,
            NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
            const T& delta_d, adjEntry& adjExternal, const node& n = nullptr);
 
    /* \brief Embeds all edges in the skeleton graph \a S of an S-node of the
     *   SPQR-tree into an existing embedding and calls recursively itself for
     *   all virtual edges in S.
     *
     * \param spqrTree The SPQR-tree of the treated graph.
     * \param treeNodeTreated is an array saving for each SPQR-tree node \p mu
     *   whether it was already treated by any call of ExpandEdge or not. Every
     *   \p mu should only be treated once.
     * \param mu is a node in the SPQR-tree.
     * \param leftNode is the node adjacent to referenceEdge, which should be "left"
     *   in the embedding
     * \param nodeLength is an array saving the lengths of the nodes of \p G.
     * \param edgeLength is saving the edge lengths of all edges in each skeleton
     *   graph of all tree nodes.
     * \param thickness of each skeleton graph.
     * \param newOrder is saving for each node \p n in \p G the new adjacency
     *   list. This is an output parameter.
     * \param adjBeforeNodeArraySource is saving for the source of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param adjBeforeNodeArrayTarget is saving for the target of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param delta_u the distance from the second adjacent face of the reference edge
     *   except the external face to the external face of G.
     * \param delta_d the distance from the external face to the external face of G.
     * \param adjExternal is an adjacency entry in the external face.
     */
    static void expandEdgeSNode(const StaticSPQRTree& spqrTree, NodeArray<bool>& treeNodeTreated,
            const node& mu, const node& leftNode, const NodeArray<T>& nodeLength,
            const NodeArray<EdgeArray<T>>& edgeLength, const NodeArray<T>& thickness,
            NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
            const T& delta_d, adjEntry& adjExternal);
 
    /* \brief Embeds all edges in the skeleton graph \a S of an P-node of the
     *   SPQR-tree into an existing embedding and calls recursively itself for
     *   all virtual edges in S.
     *
     * \param spqrTree The SPQR-tree of the treated graph.
     * \param treeNodeTreated is an array saving for each SPQR-tree node \p mu
     *   whether it was already treated by any call of ExpandEdge or not. Every
     *   \p mu should only be treated once.
     * \param mu is a node in the SPQR-tree.
     * \param leftNode is the node adjacent to referenceEdge, which should be "left"
     *   in the embedding
     * \param nodeLength is an array saving the lengths of the nodes of \p G.
     * \param edgeLength is saving the edge lengths of all edges in each skeleton
     *   graph of all tree nodes.
     * \param thickness of each skeleton graph.
     * \param newOrder is saving for each node \p n in \p G the new adjacency
     *   list. This is an output parameter.
     * \param adjBeforeNodeArraySource is saving for the source of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param adjBeforeNodeArrayTarget is saving for the target of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param delta_u the distance from the second adjacent face of the reference edge
     *   except the external face to the external face of G.
     * \param delta_d the distance from the external face to the external face of G.
     * \param adjExternal is an adjacency entry in the external face.
     */
    static void expandEdgePNode(const StaticSPQRTree& spqrTree, NodeArray<bool>& treeNodeTreated,
            const node& mu, const node& leftNode, const NodeArray<T>& nodeLength,
            const NodeArray<EdgeArray<T>>& edgeLength, const NodeArray<T>& thickness,
            NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
            const T& delta_d, adjEntry& adjExternal);
 
    /* \brief Embeds all edges in the skeleton graph \a S of an R-node of the
     *   SPQR-tree into an existing embedding and calls recursively itself for
     *   all virtual edges in S.
     *
     * \param spqrTree The SPQR-tree of the treated graph.
     * \param treeNodeTreated is an array saving for each SPQR-tree node \p mu
     *   whether it was already treated by any call of ExpandEdge or not. Every
     *   \p mu should only be treated once.
     * \param mu is a node in the SPQR-tree.
     * \param leftNode is the node adjacent to referenceEdge, which should be "left"
     *   in the embedding
     * \param nodeLength is an array saving the lengths of the nodes of \p G.
     * \param edgeLength is saving the edge lengths of all edges in each skeleton
     *   graph of all tree nodes.
     * \param thickness of each skeleton graph.
     * \param newOrder is saving for each node \p n in \p G the new adjacency
     *   list. This is an output parameter.
     * \param adjBeforeNodeArraySource is saving for the source of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param adjBeforeNodeArrayTarget is saving for the target of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param delta_u the distance from the second adjacent face of the reference edge
     *   except the external face to the external face of G.
     * \param delta_d the distance from the external face to the external face of G.
     * \param adjExternal is an adjacency entry in the external face.
     * \param n is only set, if ExpandEdge is called for the first time, because
     *   then there is no virtual edge which has to be expanded, but the max face
     *   has to contain a certain node \p n.
     */
    static void expandEdgeRNode(const StaticSPQRTree& spqrTree, NodeArray<bool>& treeNodeTreated,
            const node& mu, const node& leftNode, const NodeArray<T>& nodeLength,
            const NodeArray<EdgeArray<T>>& edgeLength, const NodeArray<T>& thickness,
            NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
            const T& delta_d, adjEntry& adjExternal, const node& n = nullptr);
 
    /* \brief Writes a given adjacency entry into the newOrder. If the edge
     *   belonging to ae is a virtual edge, it is expanded.
     *
     * \param ae is the adjacency entry which has to be expanded.
     * \param before is the adjacency entry of the node in \p G, before
     *   which ae has to be inserted.
     * \param spqrTree The SPQR-tree of the treated graph.
     * \param treeNodeTreated is an array saving for each SPQR-tree node \p mu
     *   whether it was already treated by any call of ExpandEdge or not. Every
     *   \p mu should only be treated once.
     * \param mu is a node in the SPQR-tree.
     * \param leftNode is the node adjacent to referenceEdge, which should be "left"
     *   in the embedding
     * \param nodeLength is an array saving the lengths of the nodes of \p G.
     * \param edgeLength is saving the edge lengths of all edges in each skeleton
     *   graph of all tree nodes.
     * \param thickness of each skeleton graph.
     * \param newOrder is saving for each node \p n in \p G the new adjacency
     *   list. This is an output parameter.
     * \param adjBeforeNodeArraySource is saving for the source of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param adjBeforeNodeArrayTarget is saving for the target of the reference edge
     *   of the skeleton of mu the adjacency entry, before which new entries have
     *   to be inserted.
     * \param delta_u the distance from the second adjacent face of the reference edge
     *   except the external face to the external face of G.
     * \param delta_d the distance from the external face to the external face of G.
     * \param adjExternal is an adjacency entry in the external face.
     */
    static void adjEntryForNode(adjEntry& ae, ListIterator<adjEntry>& before,
            const StaticSPQRTree& spqrTree, NodeArray<bool>& treeNodeTreated, const node& mu,
            const node& leftNode, const NodeArray<T>& nodeLength,
            const NodeArray<EdgeArray<T>>& edgeLength, const NodeArray<T>& thickness,
            NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
            const T& delta_d, adjEntry& adjExternal);
 
    /* \brief Single source shortest path.
     *
     * \param G directed graph
     * \param s source node
     * \param length length of an edge
     * \param d contains shortest path distances after call
     */
    static bool sssp(const Graph& G, const node& s, const EdgeArray<T>& length, NodeArray<T>& d);
};
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::embed(Graph& G, adjEntry& adjExternal,
        const NodeArray<T>& nodeLength, const EdgeArray<T>& edgeLength, const node& n /* = 0*/) {
    //Base cases (SPQR-Tree-implementatioin would crash with these inputs):
    OGDF_ASSERT(G.numberOfNodes() >= 2);
    if (G.numberOfEdges() <= 2) {
        edge e = G.firstEdge();
        adjExternal = e->adjSource();
        return;
    }
 
    //First step: calculate maximum face and edge lengths for virtual edges
    StaticSPQRTree spqrTree(G);
    NodeArray<EdgeArray<T>> edgeLengthSkel;
    compute(G, nodeLength, edgeLength, &spqrTree, edgeLengthSkel);
 
    //Second step: Embed G
    T biggestFace = -1;
    node bigFaceMu;
    if (n == nullptr) {
        for (node mu : spqrTree.tree().nodes) {
            //Expand all faces in skeleton(mu) and get size of the largest of them:
            T sizeMu = largestFaceInSkeleton(spqrTree, mu, nodeLength, edgeLengthSkel);
            if (sizeMu > biggestFace) {
                biggestFace = sizeMu;
                bigFaceMu = mu;
            }
        }
    } else {
        node* mus = new node[n->degree()];
        int i = 0;
        for (adjEntry adj : n->adjEntries) {
            mus[i] = spqrTree.skeletonOfReal(adj->theEdge()).treeNode();
            bool alreadySeenMu = false;
            for (int j = 0; j < i && !alreadySeenMu; j++) {
                if (mus[i] == mus[j]) {
                    alreadySeenMu = true;
                }
            }
            if (alreadySeenMu) {
                i++;
                continue;
            } else {
                //Expand all faces in skeleton(mu) containing n and get size of
                //the largest of them:
                T sizeInMu =
                        largestFaceContainingNode(spqrTree, mus[i], n, nodeLength, edgeLengthSkel);
                if (sizeInMu > biggestFace) {
                    biggestFace = sizeInMu;
                    bigFaceMu = mus[i];
                }
 
                i++;
            }
        }
        delete[] mus;
    }
 
    bigFaceMu = spqrTree.rootTreeAt(bigFaceMu);
 
    NodeArray<T> thickness(spqrTree.tree());
    bottomUpThickness(spqrTree, bigFaceMu, thickness, nodeLength, edgeLengthSkel);
 
    NodeArray<List<adjEntry>> newOrder(G);
    NodeArray<bool> treeNodeTreated(spqrTree.tree(), false);
    ListIterator<adjEntry> it;
    adjExternal = nullptr;
    NodeArray<ListIterator<adjEntry>> adjBeforeNodeArraySource(spqrTree.tree());
    NodeArray<ListIterator<adjEntry>> adjBeforeNodeArrayTarget(spqrTree.tree());
    expandEdge(spqrTree, treeNodeTreated, bigFaceMu, nullptr, nodeLength, edgeLengthSkel, thickness,
            newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, 0, 0, adjExternal, n);
 
    for (node v : G.nodes) {
        G.sort(v, newOrder[v]);
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::adjEntryForNode(adjEntry& ae,
        ListIterator<adjEntry>& before, const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        const NodeArray<T>& thickness, NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
        const T& delta_d, adjEntry& adjExternal) {
    Skeleton& S = spqrTree.skeleton(mu);
    edge referenceEdge = S.referenceEdge();
    if (S.isVirtual(ae->theEdge())) {
        edge twinE = S.twinEdge(ae->theEdge());
        node twinNT = S.twinTreeNode(ae->theEdge());
#if 0
        Skeleton& twinS = spqrTree.skeleton(twinNT);
#endif
 
        if (!treeNodeTreated[twinNT]) {
            node m_leftNode;
            if (ae->theEdge()->source() == leftNode) {
                m_leftNode = twinE->source();
            } else {
                m_leftNode = twinE->target();
            }
 
            if (ae->theEdge()->source() == ae->theNode()) {
                adjBeforeNodeArraySource[twinNT] = before;
            } else {
                adjBeforeNodeArrayTarget[twinNT] = before;
            }
 
            //recursion call:
            expandEdge(spqrTree, treeNodeTreated, twinNT, m_leftNode, nodeLength, edgeLength,
                    thickness, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    delta_u, delta_d, adjExternal);
        }
 
        if (ae->theEdge() == referenceEdge) {
            if (ae->theNode() == ae->theEdge()->source()) {
                ListIterator<adjEntry> tmpBefore = adjBeforeNodeArraySource[mu];
                adjBeforeNodeArraySource[mu] = before;
                before = tmpBefore;
            } else {
                ListIterator<adjEntry> tmpBefore = adjBeforeNodeArrayTarget[mu];
                adjBeforeNodeArrayTarget[mu] = before;
                before = tmpBefore;
            }
        } else 
        {
            if (ae->theNode() == ae->theEdge()->source()) {
                before = adjBeforeNodeArraySource[twinNT];
            } else {
                before = adjBeforeNodeArrayTarget[twinNT];
            }
        }
    } else 
    {
        node origNode = S.original(ae->theNode());
        edge origEdge = S.realEdge(ae->theEdge());
 
        if (origNode == origEdge->source()) {
            if (!before.valid()) {
                before = newOrder[origNode].pushBack(origEdge->adjSource());
            } else {
                before = newOrder[origNode].insertBefore(origEdge->adjSource(), before);
            }
        } else {
            if (!before.valid()) {
                before = newOrder[origNode].pushBack(origEdge->adjTarget());
            } else {
                before = newOrder[origNode].insertBefore(origEdge->adjTarget(), before);
            }
        }
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::expandEdge(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        const NodeArray<T>& thickness, NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
        const T& delta_d, adjEntry& adjExternal, const node& n /*= 0*/) {
    treeNodeTreated[mu] = true;
 
    switch (spqrTree.typeOf(mu)) {
    case SPQRTree::NodeType::SNode:
        expandEdgeSNode(spqrTree, treeNodeTreated, mu, leftNode, nodeLength, edgeLength, thickness,
                newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, delta_u, delta_d,
                adjExternal);
        break;
    case SPQRTree::NodeType::PNode:
        expandEdgePNode(spqrTree, treeNodeTreated, mu, leftNode, nodeLength, edgeLength, thickness,
                newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, delta_u, delta_d,
                adjExternal);
        break;
    case SPQRTree::NodeType::RNode:
        expandEdgeRNode(spqrTree, treeNodeTreated, mu, leftNode, nodeLength, edgeLength, thickness,
                newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, delta_u, delta_d,
                adjExternal, n);
        break;
    default:
        OGDF_ASSERT(false);
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::expandEdgeSNode(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        const NodeArray<T>& thickness, NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
        const T& delta_d, adjEntry& adjExternal) {
    Skeleton& S = spqrTree.skeleton(mu);
    edge referenceEdge = S.referenceEdge();
    adjEntry startAdjEntry = nullptr;
    if (leftNode == nullptr) {
        for (edge e : S.getGraph().edges) {
            if (!S.isVirtual(e)) {
                startAdjEntry = e->adjSource();
                break;
            }
        }
        OGDF_ASSERT(startAdjEntry != nullptr);
    } else if (leftNode->firstAdj()->theEdge() == referenceEdge) {
        startAdjEntry = leftNode->lastAdj();
    } else {
        startAdjEntry = leftNode->firstAdj();
    }
 
    adjEntry ae = startAdjEntry;
    if (adjExternal == nullptr) {
        edge orgEdge = S.realEdge(ae->theEdge());
        if (orgEdge->source() == S.original(ae->theNode())) {
            adjExternal = orgEdge->adjSource()->twin();
        } else {
            adjExternal = orgEdge->adjTarget()->twin();
        }
    }
 
    ListIterator<adjEntry> before;
    if (referenceEdge && leftNode == referenceEdge->source()) {
        before = adjBeforeNodeArraySource[mu];
    } else if (referenceEdge) {
        before = adjBeforeNodeArrayTarget[mu];
    }
    ListIterator<adjEntry> beforeSource;
 
    bool firstStep = true;
    while (firstStep || ae != startAdjEntry) {
        //first treat ae with ae->theNode() is left node, then treat its twin:
        node m_leftNode = ae->theNode();
 
        if (ae->theEdge() == referenceEdge) {
            if (ae->theNode() == referenceEdge->source()) {
                adjBeforeNodeArraySource[mu] = before;
            } else {
                adjBeforeNodeArrayTarget[mu] = before;
            }
        } else {
            if (S.isVirtual(ae->theEdge()) && referenceEdge) {
                node twinTN = S.twinTreeNode(ae->theEdge());
                if (ae->theEdge()->source() == ae->theNode()) {
                    if (ae->theEdge()->target() == referenceEdge->source()) {
                        adjBeforeNodeArrayTarget[twinTN] = adjBeforeNodeArraySource[mu];
                    } else if (ae->theEdge()->target() == referenceEdge->target()) {
                        adjBeforeNodeArrayTarget[twinTN] = adjBeforeNodeArrayTarget[mu];
                    }
                } else {
                    if (ae->theEdge()->source() == referenceEdge->source()) {
                        adjBeforeNodeArraySource[twinTN] = adjBeforeNodeArraySource[mu];
                    } else if (ae->theEdge()->source() == referenceEdge->target()) {
                        adjBeforeNodeArraySource[twinTN] = adjBeforeNodeArrayTarget[mu];
                    }
                }
            }
 
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                    adjBeforeNodeArrayTarget, delta_u, delta_d, adjExternal);
        }
 
        if (firstStep) {
            beforeSource = before;
            firstStep = false;
        }
 
        ae = ae->twin();
        if (!referenceEdge) {
            before = nullptr;
        } else if (ae->theNode() == referenceEdge->source()) {
            before = adjBeforeNodeArraySource[mu];
        } else if (ae->theNode() == referenceEdge->target()) {
            before = adjBeforeNodeArrayTarget[mu];
        } else {
            before = nullptr;
        }
        if (ae->theEdge() == referenceEdge) {
            if (ae->theNode() == referenceEdge->source()) {
                adjBeforeNodeArraySource[mu] = beforeSource;
            } else {
                adjBeforeNodeArrayTarget[mu] = beforeSource;
            }
        } else {
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                    adjBeforeNodeArrayTarget, delta_u, delta_d, adjExternal);
        }
 
        //set new adjacency entry pair (ae and its twin):
        if (ae->theNode()->firstAdj() == ae) {
            ae = ae->theNode()->lastAdj();
        } else {
            ae = ae->theNode()->firstAdj();
        }
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::expandEdgePNode(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        const NodeArray<T>& thickness, NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
        const T& delta_d, adjEntry& adjExternal) {
    //Choose face defined by virtual edge and the longest edge different from it.
    Skeleton& S = spqrTree.skeleton(mu);
    edge referenceEdge = S.referenceEdge();
    edge altReferenceEdge = nullptr;
 
    node m_leftNode = leftNode;
    if (!m_leftNode) {
        List<node> nodeList;
        S.getGraph().allNodes(nodeList);
        m_leftNode = *(nodeList.begin());
    }
    node m_rightNode = m_leftNode->firstAdj()->twinNode();
 
    if (referenceEdge == nullptr) {
        for (edge e : S.getGraph().edges) {
            if (!S.isVirtual(e)) {
                altReferenceEdge = e;
                edge orgEdge = S.realEdge(e);
                if (orgEdge->source() == S.original(m_leftNode)) {
                    adjExternal = orgEdge->adjSource();
                } else {
                    adjExternal = orgEdge->adjTarget();
                }
                break;
            }
        }
    }
 
    //sort edges by length:
    List<edge> graphEdges;
    for (edge e : S.getGraph().edges) {
        if (e == referenceEdge || e == altReferenceEdge) {
            continue;
        }
 
        if (!graphEdges.begin().valid()) {
            graphEdges.pushBack(e);
        } else {
            for (ListIterator<edge> it = graphEdges.begin(); it.valid(); ++it) {
                if (edgeLength[mu][e] > edgeLength[mu][*it]) {
                    graphEdges.insertBefore(e, it);
                    break;
                }
                ListIterator<edge> next = it;
                ++next;
                if (!next.valid()) {
                    graphEdges.pushBack(e);
                    break;
                }
            }
        }
    }
 
    List<edge> rightEdgeOrder;
    ListIterator<adjEntry> beforeAltRefEdge;
    ListIterator<adjEntry> beforeLeft;
 
    //begin with left node and longest edge:
    for (int i = 0; i < 2; ++i) {
        ListIterator<adjEntry> before;
        node n;
        if (i == 0) {
            n = m_leftNode;
        } else {
            n = m_rightNode;
            before = beforeAltRefEdge;
        }
 
        if (referenceEdge) {
            if (n == referenceEdge->source()) {
                before = adjBeforeNodeArraySource[mu];
            } else {
                before = adjBeforeNodeArrayTarget[mu];
            }
        }
 
        adjEntry ae;
 
        //all edges except reference edge:
        if (i == 0) {
            ListIterator<edge> lastPos;
            ListIterator<adjEntry> beforeRight;
            if (referenceEdge) {
                if (referenceEdge->source() == m_rightNode) {
                    beforeRight = adjBeforeNodeArraySource[mu];
                } else { //referenceEdge->target() == rightnode
                    beforeRight = adjBeforeNodeArrayTarget[mu];
                }
            }
            bool insertBeforeLast = false;
            bool oneEdgeInE_a = false;
            T sum_E_a = 0;
            T sum_E_b = 0;
 
            for (int looper = 0; looper < graphEdges.size(); looper++) {
                edge e = *(graphEdges.get(looper));
 
                if (!lastPos.valid()) {
                    lastPos = rightEdgeOrder.pushBack(e);
                } else if (insertBeforeLast) {
                    lastPos = rightEdgeOrder.insertBefore(e, lastPos);
                } else {
                    lastPos = rightEdgeOrder.insertAfter(e, lastPos);
                }
 
                //decide whether to choose face f_a or f_b as f_{mu, mu'}:
                if (delta_u + sum_E_a < delta_d + sum_E_b) {
                    ListIterator<adjEntry> beforeU = before;
 
                    if (e->source() == n) {
                        ae = e->adjSource();
                    } else {
                        ae = e->adjTarget();
                    }
 
                    if (S.isVirtual(e)) {
                        node nu = S.twinTreeNode(e);
 
                        T delta_u_nu = delta_u + sum_E_a;
                        T delta_d_nu = delta_d + sum_E_b;
 
                        //buffer computed embedding:
                        NodeArray<List<adjEntry>> tmp_newOrder(spqrTree.originalGraph());
                        ListIterator<adjEntry> tmp_before;
 
                        adjEntryForNode(ae, tmp_before, spqrTree, treeNodeTreated, mu, m_leftNode,
                                nodeLength, edgeLength, thickness, tmp_newOrder,
                                adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, delta_d_nu,
                                delta_u_nu, adjExternal);
 
                        //copy buffered embedding reversed into newOrder:
                        node leftOrg = S.original(m_leftNode);
                        node rightOrg = S.original(m_rightNode);
                        for (node nOG : spqrTree.originalGraph().nodes) {
                            List<adjEntry> nOG_tmp_adjList = tmp_newOrder[nOG];
                            if (nOG_tmp_adjList.size() == 0) {
                                continue;
                            }
 
                            ListIterator<adjEntry>* m_before;
                            if (nOG == leftOrg) {
                                m_before = &beforeU;
                            } else if (nOG == rightOrg && referenceEdge) {
                                m_before = &beforeRight;
                            } else {
                                m_before = new ListIterator<adjEntry>();
                            }
 
                            for (ListIterator<adjEntry> ae_it = nOG_tmp_adjList.begin();
                                    ae_it.valid(); ++ae_it) {
                                adjEntry adjaEnt = *ae_it;
                                if (!m_before->valid()) {
                                    *m_before = newOrder[nOG].pushBack(adjaEnt);
                                } else {
                                    *m_before = newOrder[nOG].insertBefore(adjaEnt, *m_before);
                                }
 
                                if (nOG == leftOrg || nOG == rightOrg) {
                                    if (S.original(e->source()) == nOG) {
                                        adjBeforeNodeArraySource[nu] = *m_before;
                                    } else {
                                        adjBeforeNodeArrayTarget[nu] = *m_before;
                                    }
                                }
                            }
 
                            if (nOG != leftOrg && (nOG != rightOrg || !referenceEdge)) {
                                delete m_before;
                            }
                        }
 
                        sum_E_a += thickness[nu];
                    } else 
                    {
                        adjEntryForNode(ae, beforeU, spqrTree, treeNodeTreated, mu, m_leftNode,
                                nodeLength, edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                                adjBeforeNodeArrayTarget, 0, 0, adjExternal);
 
                        sum_E_a += 1;
                    }
 
                    insertBeforeLast = false;
                    if (!oneEdgeInE_a) {
                        beforeLeft = beforeU;
                        oneEdgeInE_a = true;
                    }
                } else 
                {
                    if (S.isVirtual(e)) {
                        node nu = S.twinTreeNode(e);
                        if (referenceEdge) {
                            if (e->source() == n) {
                                adjBeforeNodeArrayTarget[nu] = beforeRight;
                            } else {
                                adjBeforeNodeArraySource[nu] = beforeRight;
                            }
                        }
                    }
 
                    T delta_u_nu = delta_u + sum_E_a;
                    T delta_d_nu = delta_d + sum_E_b;
 
                    if (e->source() == n) {
                        ae = e->adjSource();
                    } else {
                        ae = e->adjTarget();
                    }
 
                    adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode,
                            nodeLength, edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                            adjBeforeNodeArrayTarget, delta_u_nu, delta_d_nu, adjExternal);
 
                    if (S.isVirtual(e)) {
                        sum_E_b += thickness[S.twinTreeNode(e)];
                    } else {
                        sum_E_b += 1;
                    }
 
                    insertBeforeLast = true;
                    if (!oneEdgeInE_a) {
                        beforeLeft = before;
                    }
                }
            }
        } else {
            for (ListIterator<edge> it = rightEdgeOrder.begin(); it.valid(); ++it) {
                if ((*it)->source() == n) {
                    ae = (*it)->adjSource();
                } else {
                    ae = (*it)->adjTarget();
                }
 
                adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                        edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                        adjBeforeNodeArrayTarget, 0, 0, adjExternal);
            }
        }
 
        //(alternative) reference edge at last:
        if (referenceEdge) {
            if (i == 0) {
                if (n == referenceEdge->source()) {
                    adjBeforeNodeArraySource[mu] = beforeLeft;
                } else {
                    adjBeforeNodeArrayTarget[mu] = beforeLeft;
                }
            } else {
                if (n == referenceEdge->source()) {
                    adjBeforeNodeArraySource[mu] = before;
                } else {
                    adjBeforeNodeArrayTarget[mu] = before;
                }
            }
        } else {
            if (altReferenceEdge->source() == n) {
                ae = altReferenceEdge->adjSource();
            } else {
                ae = altReferenceEdge->adjTarget();
            }
 
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                    adjBeforeNodeArrayTarget, 0, 0, adjExternal);
        }
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::expandEdgeRNode(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        const NodeArray<T>& thickness, NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, const T& delta_u,
        const T& delta_d, adjEntry& adjExternal, const node& n /* = 0 */) {
    Skeleton& S = spqrTree.skeleton(mu);
    edge referenceEdge = S.referenceEdge();
 
    //compute biggest face containing the reference edge:
    face maxFaceContEdge = nullptr;
    List<node> maxFaceNodes;
    planarEmbed(S.getGraph());
    CombinatorialEmbedding combinatorialEmbedding(S.getGraph());
    T bigFaceSize = -1;
    adjEntry m_adjExternal = nullptr;
    for (face f : combinatorialEmbedding.faces) {
        bool containsVirtualEdgeOrN = false;
        adjEntry this_m_adjExternal = nullptr;
        T sizeOfFace = 0;
        List<node> faceNodes;
        for (adjEntry ae : f->entries) {
            faceNodes.pushBack(ae->theNode());
            if ((n == nullptr && (ae->theEdge() == referenceEdge || !referenceEdge))
                    || S.original(ae->theNode()) == n) {
                containsVirtualEdgeOrN = true;
                if (referenceEdge) {
                    this_m_adjExternal = ae;
                }
            }
 
            if (!referenceEdge && !S.isVirtual(ae->theEdge())) {
                this_m_adjExternal = ae;
            }
 
            sizeOfFace += edgeLength[mu][ae->theEdge()] + nodeLength[S.original(ae->theNode())];
        }
 
        if (containsVirtualEdgeOrN && this_m_adjExternal && sizeOfFace > bigFaceSize) {
            maxFaceNodes = faceNodes;
            bigFaceSize = sizeOfFace;
            maxFaceContEdge = f;
            m_adjExternal = this_m_adjExternal;
        }
    }
    OGDF_ASSERT(maxFaceContEdge);
 
    if (!adjExternal) {
        edge orgEdge = S.realEdge(m_adjExternal->theEdge());
        if (orgEdge->source() == S.original(m_adjExternal->theNode())) {
            adjExternal = orgEdge->adjSource();
        } else {
            adjExternal = orgEdge->adjTarget();
        }
    }
 
    adjEntry adjMaxFace = m_adjExternal;
 
    //if embedding is mirror symmetrical embedding of desired embedding,
    //invert adjacency list of all nodes:
    if (referenceEdge) {
        //successor of adjEntry of virtual edge in adjacency list of leftNode:
        adjEntry succ_virtualEdge_leftNode;
        if (leftNode == referenceEdge->source()) {
            succ_virtualEdge_leftNode = referenceEdge->adjSource()->succ();
        } else {
            succ_virtualEdge_leftNode = referenceEdge->adjTarget()->succ();
        }
        if (!succ_virtualEdge_leftNode) {
            succ_virtualEdge_leftNode = leftNode->firstAdj();
        }
 
        bool succVELNAEInExtFace = false;
        for (adjEntry aeExtFace : maxFaceContEdge->entries) {
            if (aeExtFace->theEdge() == succ_virtualEdge_leftNode->theEdge()) {
                succVELNAEInExtFace = true;
                break;
            }
        }
 
        if (!succVELNAEInExtFace) {
            for (node v : S.getGraph().nodes) {
                List<adjEntry> newAdjOrder;
                for (adjEntry ae = v->firstAdj(); ae; ae = ae->succ()) {
                    newAdjOrder.pushFront(ae);
                }
                S.getGraph().sort(v, newAdjOrder);
            }
            adjMaxFace = adjMaxFace->twin();
        }
    }
 
    NodeArray<bool> nodeTreated(S.getGraph(), false);
    adjEntry start_ae;
    if (referenceEdge) {
        start_ae = adjMaxFace;
        do {
            if (start_ae->theEdge() == referenceEdge) {
                start_ae = start_ae->faceCycleSucc();
                break;
            }
            start_ae = start_ae->faceCycleSucc();
        } while (start_ae != adjMaxFace);
    } else {
        start_ae = adjMaxFace;
    }
 
    //For every edge a buffer saving adjacency entries written in embedding step
    //for nodes on the maximum face, needed in step for other nodes.
    EdgeArray<List<adjEntry>> buffer(S.getGraph());
 
    bool firstStep = true;
    bool after_start_ae = true;
    for (adjEntry ae = start_ae; firstStep || ae != start_ae;
            after_start_ae = after_start_ae && ae->succ(),
                  ae = after_start_ae ? ae->faceCycleSucc()
                                      : (!ae->faceCycleSucc() ? adjMaxFace : ae->faceCycleSucc())) {
        firstStep = false;
#if 0
        node nodeG = S.original(ae->theNode());
#endif
        nodeTreated[ae->theNode()] = true;
 
        //copy adjacency list of nodes into newOrder:
        ListIterator<adjEntry> before;
        edge vE = (ae->theEdge() == referenceEdge) ? referenceEdge : ae->theEdge();
        node nu = (ae->theEdge() == referenceEdge) ? mu : S.twinTreeNode(ae->theEdge());
        if (S.isVirtual(vE)) {
            if (ae->theNode() == vE->source()) {
                before = adjBeforeNodeArraySource[nu];
            } else {
                before = adjBeforeNodeArrayTarget[nu];
            }
        }
 
        bool after_ae = true;
        adjEntry m_start_ae;
        if (referenceEdge) {
            if (ae->theNode() == referenceEdge->source()) {
                m_start_ae = referenceEdge->adjSource();
            } else if (ae->theNode() == referenceEdge->target()) {
                m_start_ae = referenceEdge->adjTarget();
            } else {
                m_start_ae = ae;
            }
        } else {
            m_start_ae = ae;
        }
 
        adjEntry m_stop_ae;
        bool hit_stop_twice = false;
        int numOfHits = 0;
        if (referenceEdge
                && (ae->theNode() == referenceEdge->source()
                        || ae->theNode() == referenceEdge->target())) {
            if (m_start_ae->succ()) {
                m_stop_ae = m_start_ae->succ();
            } else {
                m_stop_ae = m_start_ae->theNode()->firstAdj();
                hit_stop_twice = true;
            }
        } else {
            m_stop_ae = m_start_ae;
        }
 
        for (adjEntry aeN = m_start_ae;
                after_ae || (hit_stop_twice && numOfHits != 2) || aeN != m_stop_ae;
                after_ae = after_ae && aeN->succ(),
                      aeN = after_ae ? aeN->succ()
                                     : (!aeN->succ() ? ae->theNode()->firstAdj() : aeN->succ()),
                      numOfHits = (aeN == m_stop_ae) ? numOfHits + 1 : numOfHits) {
            node m_leftNode = nullptr;
            if (S.isVirtual(aeN->theEdge()) && aeN->theEdge() != referenceEdge) {
                //Compute left node of aeN->theNode(). First get adjacency entry in ext. face
                //(if edge is in ext. face) and compare face cycle successor with successor
                //in node adjacency list. If it is the same, it is the right node, otherwise
                //the left.
                adjEntry aeExtFace = nullptr;
                bool succInExtFace = false;
                bool aeNInExtFace = false;
                adjEntry aeNSucc = (aeN->succ()) ? aeN->succ() : ae->theNode()->firstAdj();
                aeExtFace = adjMaxFace;
                do {
                    if (aeExtFace->theEdge() == aeNSucc->theEdge()) {
                        succInExtFace = true;
                        if (aeNInExtFace) {
                            break;
                        }
                    }
                    if (aeExtFace->theEdge() == aeN->theEdge()) {
                        aeNInExtFace = true;
                        if (succInExtFace) {
                            break;
                        }
                    }
                    aeExtFace = aeExtFace->faceCycleSucc();
                } while (aeExtFace != adjMaxFace);
                if (aeNInExtFace && succInExtFace) {
                    m_leftNode = aeN->twinNode();
                } else {
                    m_leftNode = aeN->theNode();
                }
 
                node twinTN = S.twinTreeNode(aeN->theEdge());
                if (referenceEdge) {
                    if (aeN->theEdge()->source() == aeN->theNode()) {
                        if (aeN->theEdge()->target() == referenceEdge->source()) {
                            adjBeforeNodeArrayTarget[twinTN] = adjBeforeNodeArraySource[mu];
                        } else if (aeN->theEdge()->target() == referenceEdge->target()) {
                            adjBeforeNodeArrayTarget[twinTN] = adjBeforeNodeArrayTarget[mu];
                        }
                    } else {
                        if (aeN->theEdge()->source() == referenceEdge->source()) {
                            adjBeforeNodeArraySource[twinTN] = adjBeforeNodeArraySource[mu];
                        } else if (aeN->theEdge()->source() == referenceEdge->target()) {
                            adjBeforeNodeArraySource[twinTN] = adjBeforeNodeArrayTarget[mu];
                        }
                    }
                }
            }
 
            adjEntryForNode(aeN, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                    adjBeforeNodeArrayTarget, 0, 0, adjExternal);
 
            //if the other node adjacent to the current treated edge is not in the
            //max face, put written edges into an buffer and clear the adjacency
            //list of that node.
            if (!maxFaceNodes.search(aeN->twinNode()).valid()) {
                node orig_aeN_twin_theNode = S.original(aeN->twinNode());
                buffer[aeN->theEdge()] = newOrder[orig_aeN_twin_theNode];
                newOrder[orig_aeN_twin_theNode].clear();
            }
        }
    }
 
    //Copy of not treated node's adjacency lists (internal nodes). Setting
    //of left node depending on minimal distance to external face of the
    //face defined by left node.
    bool DGcomputed = false;
    int f_ext_id = 0;
    int f_ref_id = 0;
    Graph DG;
    ArrayBuffer<node> fPG_to_nDG;
    NodeArray<List<adjEntry>> adjacencyList;
    List<List<adjEntry>> faces;
    NodeArray<T> dist_f_ref;
    NodeArray<T> dist_f_ext;
    AdjEntryArray<int> ae_to_face;
 
    for (node v : S.getGraph().nodes) {
        if (nodeTreated[v]) {
            continue;
        }
 
        node v_original = S.original(v);
        nodeTreated[v] = true;
        ListIterator<adjEntry> before;
        for (adjEntry ae = v->firstAdj(); ae; ae = ae->succ()) {
            if (buffer[ae->theEdge()].empty()) {
                T delta_u_nu = 0;
                T delta_d_nu = 0;
                bool frauenlinks = false;
                if (S.isVirtual(ae->theEdge())) {
                    if (!DGcomputed) {
                        ae_to_face.init(S.getGraph());
                        EdgeArray<T> edgeLengthDG(DG);
                        DGcomputed = true;
 
                        //compute dual graph of skeleton graph:
                        adjacencyList.init(S.getGraph());
                        for (node nBG : S.getGraph().nodes) {
                            for (adjEntry ae_nBG : nBG->adjEntries) {
                                adjacencyList[nBG].pushBack(ae_nBG);
                            }
                        }
 
                        NodeArray<List<adjEntry>> adjEntryTreated(S.getGraph());
                        for (node nBG : S.getGraph().nodes) {
                            for (adjEntry adj : nBG->adjEntries) {
                                if (adjEntryTreated[nBG].search(adj).valid()) {
                                    continue;
                                }
 
                                List<adjEntry> newFace;
                                adjEntry adj2 = adj;
                                do {
                                    newFace.pushBack(adj2);
                                    ae_to_face[adj2] = faces.size();
                                    adjEntryTreated[adj2->theNode()].pushBack(adj2);
                                    List<adjEntry>& ladj = adjacencyList[adj2->twinNode()];
                                    adj2 = *ladj.cyclicPred(ladj.search(adj2->twin()));
                                } while (adj2 != adj);
                                faces.pushBack(newFace);
                            }
                        }
 
                        for (ListIterator<List<adjEntry>> it = faces.begin(); it.valid(); ++it) {
                            fPG_to_nDG.push(DG.newNode());
                        }
 
                        NodeArray<List<node>> adjFaces(DG);
                        int i = 0;
                        for (ListIterator<List<adjEntry>> it = faces.begin(); it.valid(); ++it) {
                            int f1_id = i;
                            for (ListIterator<adjEntry> it2 = (*it).begin(); it2.valid(); ++it2) {
                                int f2_id = 0;
                                int j = 0;
                                for (ListIterator<List<adjEntry>> it3 = faces.begin(); it3.valid();
                                        ++it3) {
                                    bool do_break = false;
                                    for (ListIterator<adjEntry> it4 = (*it3).begin(); it4.valid();
                                            ++it4) {
                                        if ((*it4) == (*it2)->twin()) {
                                            f2_id = j;
                                            do_break = true;
                                            break;
                                        }
                                    }
                                    if (do_break) {
                                        break;
                                    }
                                    j++;
                                }
 
                                if (f1_id != f2_id
                                        && !adjFaces[fPG_to_nDG[f1_id]].search(fPG_to_nDG[f2_id]).valid()
                                        && !adjFaces[fPG_to_nDG[f2_id]].search(fPG_to_nDG[f1_id]).valid()) {
                                    adjFaces[fPG_to_nDG[f1_id]].pushBack(fPG_to_nDG[f2_id]);
                                    edge e1 = DG.newEdge(fPG_to_nDG[f1_id], fPG_to_nDG[f2_id]);
                                    edge e2 = DG.newEdge(fPG_to_nDG[f2_id], fPG_to_nDG[f1_id]);
 
                                    //set edge length:
                                    T e_length = -1;
                                    for (auto f1 : *it) {
                                        edge e = f1->theEdge();
                                        for (auto f2 : *faces.get(f2_id)) {
                                            if (f2->theEdge() == e
                                                    && (e_length == -1
                                                            || edgeLength[mu][e] < e_length)) {
                                                e_length = edgeLength[mu][e];
                                            }
                                        }
                                    }
                                    edgeLengthDG[e1] = e_length;
                                    edgeLengthDG[e2] = e_length;
                                }
 
                                if (*it2 == adjMaxFace) {
                                    f_ext_id = f1_id;
                                }
                                if (referenceEdge && *it2 == adjMaxFace->twin()) {
                                    f_ref_id = f1_id;
                                }
                            }
                            i++;
                        }
 
                        //compute shortest path from every face to the external face:
                        node f_ext_DG = fPG_to_nDG[f_ext_id];
                        dist_f_ext.init(DG);
                        sssp(DG, f_ext_DG, edgeLengthDG, dist_f_ext);
                        if (referenceEdge) {
                            node f_ref_DG = fPG_to_nDG[f_ref_id];
                            dist_f_ref.init(DG);
                            sssp(DG, f_ref_DG, edgeLengthDG, dist_f_ref);
                        }
                    }
 
                    //choose face with minimal shortest path:
                    T min1, min2;
                    T pi_f_0_f_ext = dist_f_ext[fPG_to_nDG[ae_to_face[ae]]];
                    T pi_f_1_f_ext = dist_f_ext[fPG_to_nDG[ae_to_face[ae->twin()]]];
                    if (referenceEdge) {
                        T pi_f_0_f_ref = dist_f_ref[fPG_to_nDG[ae_to_face[ae]]];
                        T pi_f_1_f_ref = dist_f_ref[fPG_to_nDG[ae_to_face[ae->twin()]]];
 
                        if (delta_u + pi_f_0_f_ref < delta_d + pi_f_0_f_ext) {
                            min1 = delta_u + pi_f_0_f_ref;
                        } else {
                            min1 = delta_d + pi_f_0_f_ext;
                        }
 
                        if (delta_u + pi_f_1_f_ref < delta_d + pi_f_1_f_ext) {
                            min2 = delta_u + pi_f_1_f_ref;
                        } else {
                            min2 = delta_d + pi_f_1_f_ext;
                        }
 
                        if (min1 > min2) {
                            delta_u_nu = delta_u;
                            if (pi_f_0_f_ref < pi_f_0_f_ext) {
                                delta_u_nu += pi_f_0_f_ref;
                            } else {
                                delta_u_nu += pi_f_0_f_ext;
                            }
                            delta_d_nu = delta_d;
                            if (pi_f_1_f_ref < pi_f_1_f_ext) {
                                delta_d_nu += pi_f_1_f_ref;
                            } else {
                                delta_d_nu += pi_f_1_f_ext;
                            }
                        } else {
                            frauenlinks = true;
                            delta_u_nu = delta_u;
                            if (pi_f_1_f_ref < pi_f_1_f_ext) {
                                delta_u_nu += pi_f_1_f_ref;
                            } else {
                                delta_u_nu += pi_f_1_f_ext;
                            }
                            delta_d_nu = delta_d;
                            if (pi_f_0_f_ref < pi_f_0_f_ext) {
                                delta_d_nu += pi_f_0_f_ref;
                            } else {
                                delta_d_nu += pi_f_0_f_ext;
                            }
                        }
                    } else {
                        min1 = delta_d + pi_f_0_f_ext;
                        min2 = delta_d + pi_f_1_f_ext;
 
                        if (min1 > min2) {
                            delta_u_nu = delta_u + pi_f_0_f_ext;
                            delta_d_nu = delta_d + pi_f_1_f_ext;
                        } else {
                            frauenlinks = true;
                            delta_u_nu = delta_u + pi_f_1_f_ext;
                            delta_d_nu = delta_d + pi_f_0_f_ext;
                        }
                    }
                }
 
                if (frauenlinks) {
                    node nu = S.twinTreeNode(ae->theEdge());
 
                    //buffer computed embedding:
                    NodeArray<List<adjEntry>> tmp_newOrder(spqrTree.originalGraph());
                    ListIterator<adjEntry> tmp_before;
 
                    adjEntryForNode(ae, tmp_before, spqrTree, treeNodeTreated, mu, v, nodeLength,
                            edgeLength, thickness, tmp_newOrder, adjBeforeNodeArraySource,
                            adjBeforeNodeArrayTarget, delta_u_nu, delta_d_nu, adjExternal);
 
                    //copy buffered embedding reversed into newOrder:
#if 0
                    node m_leftNode = v;
#endif
                    node m_rightNode = ae->twinNode();
                    node leftOrg = v_original;
                    node rightOrg = S.original(m_rightNode);
                    for (node nOG : spqrTree.originalGraph().nodes) {
                        List<adjEntry> nOG_tmp_adjList = tmp_newOrder[nOG];
                        if (nOG_tmp_adjList.size() == 0) {
                            continue;
                        }
 
                        ListIterator<adjEntry>* m_before;
                        if (nOG == leftOrg) {
                            m_before = &before;
                        } else {
                            m_before = new ListIterator<adjEntry>();
                        }
 
                        for (ListIterator<adjEntry> ae_it = nOG_tmp_adjList.begin(); ae_it.valid();
                                ++ae_it) {
                            adjEntry adjaEnt = *ae_it;
                            if (!m_before->valid()) {
                                *m_before = newOrder[nOG].pushBack(adjaEnt);
                            } else {
                                *m_before = newOrder[nOG].insertBefore(adjaEnt, *m_before);
                            }
 
                            if (nOG == leftOrg || nOG == rightOrg) {
                                if (S.original(ae->theEdge()->source()) == nOG) {
                                    adjBeforeNodeArraySource[nu] = *m_before;
                                } else {
                                    adjBeforeNodeArrayTarget[nu] = *m_before;
                                }
                            }
                        }
 
                        if (nOG != leftOrg) {
                            delete m_before;
                        }
                    }
                } else {
                    adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, v, nodeLength,
                            edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
                            adjBeforeNodeArrayTarget, delta_u_nu, delta_d_nu, adjExternal);
                }
 
                if (!nodeTreated[ae->twinNode()]) {
                    node orig_ae_twin_theNode = S.original(ae->twinNode());
                    buffer[ae->theEdge()] = newOrder[orig_ae_twin_theNode];
                    newOrder[orig_ae_twin_theNode].clear();
                }
            } else {
                buffer[ae->theEdge()].reverse();
                for (ListIterator<adjEntry> it = buffer[ae->theEdge()].begin(); it.valid(); ++it) {
                    if (!before.valid()) {
                        before = newOrder[v_original].pushFront(*it);
                    } else {
                        before = newOrder[v_original].insertBefore(*it, before);
                    }
                }
            }
        }
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::bottomUpThickness(const StaticSPQRTree& spqrTree,
        const node& mu, NodeArray<T>& thickness, const NodeArray<T>& nodeLength,
        const NodeArray<EdgeArray<T>>& edgeLength) {
    //recursion:
    for (adjEntry adj : mu->adjEntries) {
        edge e_mu_to_nu = adj->theEdge();
        if (e_mu_to_nu->source() != mu) {
            continue;
        } else {
            node nu = e_mu_to_nu->target();
            bottomUpThickness(spqrTree, nu, thickness, nodeLength, edgeLength);
        }
    }
 
    Skeleton& S = spqrTree.skeleton(mu);
    edge referenceEdge = S.referenceEdge();
 
    if (!referenceEdge) { //root of SPQR-tree
        thickness[mu] = 0;
        return;
    }
 
    //set dLengths for all edges in skeleton graph:
    EdgeArray<T> dLength(S.getGraph());
    for (edge eSG : S.getGraph().edges) {
        if (eSG == referenceEdge) {
            continue;
        }
 
        if (S.isVirtual(eSG)) {
            node twinTN = S.twinTreeNode(eSG);
            dLength[eSG] = thickness[twinTN];
        } else {
            dLength[eSG] = edgeLength[mu][eSG];
        }
    }
 
    //compute thickness of skeleton(mu):
    switch (spqrTree.typeOf(mu)) {
    case SPQRTree::NodeType::SNode: {
        //thickness(mu) = min_{edges e != referenceEdge} dLength(e)
        T min_dLength = -1;
        for (edge eSG : S.getGraph().edges) {
            if (eSG == referenceEdge) {
                continue;
            }
            if (min_dLength == -1 || dLength[eSG] < min_dLength) {
                min_dLength = dLength[eSG];
            }
        }
        thickness[mu] = min_dLength;
    } break;
    case SPQRTree::NodeType::PNode: {
        //thickness(mu) = sum_{edges e != referenceEdge} dLength(e)
        T sumof_dLength = 0;
        for (edge eSG : S.getGraph().edges) {
            if (eSG == referenceEdge) {
                continue;
            }
            sumof_dLength += dLength[eSG];
        }
        thickness[mu] = sumof_dLength;
    } break;
    case SPQRTree::NodeType::RNode: {
        /* Let f^ref_0, ... , f^ref_k be the faces sharing at least one edge with
             * f_ref - the face adjacent to the reference edge not equal to the
             * external face f_ext. Compute the dual graph and set edge lengths for
             * two faces f_i, f_j, i != j, with at least one shared edge, to the
             * minimal dLength of the shared edges of f_i and f_j. Remove the node
             * related to face f_ref. thickness(mu) is then the length of the shortest
             * path from any of the faces f^ref_0, ... , f^ref_k to f_ext plus 1.
             */
        CombinatorialEmbedding CE(S.getGraph());
        adjEntry ae_f_ext = referenceEdge->adjSource();
        adjEntry ae_f_ref = referenceEdge->adjTarget();
        T faceSize_f_ext = 0;
        adjEntry ae_f_ext_walker = ae_f_ext;
        do {
            faceSize_f_ext += nodeLength[S.original(ae_f_ext_walker->theNode())]
                    + edgeLength[mu][ae_f_ext_walker->theEdge()];
            ae_f_ext_walker = ae_f_ext_walker->faceCycleSucc();
        } while (ae_f_ext_walker != ae_f_ext);
        T faceSize_f_ref = 0;
        adjEntry ae_f_ref_walker = ae_f_ref;
        do {
            faceSize_f_ref += nodeLength[S.original(ae_f_ref_walker->theNode())]
                    + edgeLength[mu][ae_f_ref_walker->theEdge()];
            ae_f_ref_walker = ae_f_ref_walker->faceCycleSucc();
        } while (ae_f_ref_walker != ae_f_ref);
        if (faceSize_f_ext < faceSize_f_ref) {
            adjEntry ae_tmp = ae_f_ext;
            ae_f_ext = ae_f_ref;
            ae_f_ref = ae_tmp;
        }
 
        //compute dual graph:
        Graph DG;
        ArrayBuffer<node> fPG_to_nDG;
        NodeArray<List<adjEntry>> adjacencyList(S.getGraph());
        List<List<adjEntry>> faces;
        NodeArray<int> distances;
        EdgeArray<T> edgeLengthDG(DG);
        int f_ref_id = -1;
        int f_ext_id = -1;
 
        for (node nBG : S.getGraph().nodes) {
            for (adjEntry ae_nBG : nBG->adjEntries) {
                adjacencyList[nBG].pushBack(ae_nBG);
            }
        }
 
        NodeArray<List<adjEntry>> adjEntryTreated(S.getGraph());
        for (node nBG : S.getGraph().nodes) {
            for (adjEntry adj : nBG->adjEntries) {
                if (adjEntryTreated[nBG].search(adj).valid()) {
                    continue;
                }
 
                List<adjEntry> newFace;
                adjEntry adj2 = adj;
                do {
                    newFace.pushBack(adj2);
                    adjEntryTreated[adj2->theNode()].pushBack(adj2);
                    List<adjEntry>& ladj = adjacencyList[adj2->twinNode()];
                    adj2 = *ladj.cyclicPred(ladj.search(adj2->twin()));
                } while (adj2 != adj);
                faces.pushBack(newFace);
            }
        }
 
        for (ListIterator<List<adjEntry>> it = faces.begin(); it.valid(); ++it) {
            fPG_to_nDG.push(DG.newNode());
        }
 
        NodeArray<List<node>> adjFaces(DG);
        int i = 0;
        for (ListIterator<List<adjEntry>> it = faces.begin(); it.valid(); ++it) {
            int f1_id = i;
            for (ListIterator<adjEntry> it2 = (*it).begin(); it2.valid(); ++it2) {
                int f2_id = 0;
                int j = 0;
                for (ListIterator<List<adjEntry>> it3 = faces.begin(); it3.valid(); ++it3) {
                    bool do_break = false;
                    for (ListIterator<adjEntry> it4 = (*it3).begin(); it4.valid(); ++it4) {
                        if ((*it4) == (*it2)->twin()) {
                            f2_id = j;
                            do_break = true;
                            break;
                        }
                    }
                    if (do_break) {
                        break;
                    }
                    j++;
                }
 
                if (f1_id != f2_id && !adjFaces[fPG_to_nDG[f1_id]].search(fPG_to_nDG[f2_id]).valid()
                        && !adjFaces[fPG_to_nDG[f2_id]].search(fPG_to_nDG[f1_id]).valid()) {
                    adjFaces[fPG_to_nDG[f1_id]].pushBack(fPG_to_nDG[f2_id]);
                    adjFaces[fPG_to_nDG[f2_id]].pushBack(fPG_to_nDG[f1_id]);
                    edge e1 = DG.newEdge(fPG_to_nDG[f1_id], fPG_to_nDG[f2_id]);
                    edge e2 = DG.newEdge(fPG_to_nDG[f2_id], fPG_to_nDG[f1_id]);
 
                    //set edge length:
                    T e_length = -1;
                    for (ListIterator<adjEntry> it_f1 = (*it).begin(); it_f1.valid(); ++it_f1) {
                        edge e = (*it_f1)->theEdge();
                        for (ListIterator<adjEntry> it_f2 = (*(faces.get(f2_id))).begin();
                                it_f2.valid(); ++it_f2) {
                            if ((*it_f2)->theEdge() == e
                                    && (e_length == -1 || edgeLength[mu][e] < e_length)) {
                                e_length = edgeLength[mu][e];
                            }
                        }
                    }
                    edgeLengthDG[e1] = e_length;
                    edgeLengthDG[e2] = e_length;
                }
 
                if (*it2 == ae_f_ext) {
                    f_ext_id = f1_id;
                }
                if (*it2 == ae_f_ref) {
                    f_ref_id = f1_id;
                }
            }
            i++;
        }
 
        //the faces sharing at least one edge with f_ref:
        node nDG_f_ref = fPG_to_nDG[f_ref_id];
        List<node>& f_ref_adj_faces = adjFaces[nDG_f_ref];
 
        //remove node related to f_ref from dual graph:
        DG.delNode(fPG_to_nDG[f_ref_id]);
 
        //compute shortest path and set thickness:
        NodeArray<T> dist(DG);
        node nDG_f_ext = fPG_to_nDG[f_ext_id];
        sssp(DG, nDG_f_ext, edgeLengthDG, dist);
        T minDist = -1;
        for (ListIterator<node> it_adj_faces = f_ref_adj_faces.begin(); it_adj_faces.valid();
                ++it_adj_faces) {
            node fDG = *it_adj_faces;
            if (fDG != nDG_f_ext) {
                T d = dist[fDG];
                if (minDist == -1 || d < minDist) {
                    minDist = d;
                }
            }
        }
        thickness[mu] = minDist + 1;
    } break;
    default:
        OGDF_ASSERT(false);
    }
}
 
template<class T>
bool EmbedderMaxFaceBiconnectedGraphsLayers<T>::sssp(const Graph& G, const node& s,
        const EdgeArray<T>& length, NodeArray<T>& d) {
    const T infinity = 20000000; // big number. danger. think about it.
 
    //Initialize-Single-Source(G, s):
    d.init(G);
    for (node v : G.nodes) {
        d[v] = infinity;
    }
 
    d[s] = 0;
    for (int i = 1; i < G.numberOfNodes(); ++i) {
        for (edge e : G.edges) {
            //relax(u, v, w): // e == (u, v), length == w
            if (d[e->target()] > d[e->source()] + length[e]) {
                d[e->target()] = d[e->source()] + length[e];
            }
        }
    }
 
    //check for negative cycle:
    for (edge e : G.edges) {
        if (d[e->target()] > d[e->source()] + length[e]) {
            return false;
        }
    }
 
    return true;
}
 
}