EmbedderMaxFaceBiconnectedGraphs.h

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#pragma once
 
#include <ogdf/basic/CombinatorialEmbedding.h>
#include <ogdf/basic/extended_graph_alg.h>
#include <ogdf/decomposition/StaticSPQRTree.h>
 
namespace ogdf {
 
 
template<class T>
class EmbedderMaxFaceBiconnectedGraphs {
public:
    static void embed(Graph& G, adjEntry& adjExternal, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength, const node& n = nullptr);
 
    static void compute(const Graph& G, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree,
            NodeArray<EdgeArray<T>>& edgeLengthSkel);
 
    static T computeSize(const Graph& G, const node& n, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength);
 
    static T computeSize(const Graph& G, const node& n, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree);
 
    static T computeSize(const Graph& G, const node& n, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree,
            const NodeArray<EdgeArray<T>>& edgeLengthSkel);
 
    static T computeSize(const Graph& G, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength);
 
    static T computeSize(const Graph& G, const NodeArray<T>& nodeLength,
            const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree,
            NodeArray<EdgeArray<T>>& edgeLengthSkel);
 
protected:
    static void bottomUpTraversal(StaticSPQRTree& spqrTree, const node& mu,
            const NodeArray<T>& nodeLength, NodeArray<EdgeArray<T>>& edgeLength);
 
    static void topDownTraversal(StaticSPQRTree& spqrTree, const node& mu,
            const NodeArray<T>& nodeLength, NodeArray<EdgeArray<T>>& edgeLength);
 
    static T largestFaceContainingNode(const StaticSPQRTree& spqrTree, const node& mu, const node& n,
            const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength);
 
    static T largestFaceInSkeleton(const StaticSPQRTree& spqrTree, const node& mu,
            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 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 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, NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, 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 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 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, NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, 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 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 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, NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, 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 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 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, NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, adjEntry& adjExternal,
            const node& n);
 
    /* \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 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 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, NodeArray<List<adjEntry>>& newOrder,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
            NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, adjEntry& adjExternal);
};
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphs<T>::embed(Graph& G, adjEntry& adjExternal,
        const NodeArray<T>& nodeLength, const EdgeArray<T>& edgeLength, const node& n /* = 0*/) {
    //Base cases (SPQR-Tree implementation 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 = nullptr;
    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) {
            edge nAdjEdge = adj->theEdge();
            mus[i] = spqrTree.skeletonOfReal(nAdjEdge).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;
    }
    OGDF_ASSERT(bigFaceMu != nullptr);
 
    bigFaceMu = spqrTree.rootTreeAt(bigFaceMu);
 
    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, newOrder,
            adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, adjExternal, n);
 
    for (node v : G.nodes) {
        G.sort(v, newOrder[v]);
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphs<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,
        NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, 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,
                    newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, 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 EmbedderMaxFaceBiconnectedGraphs<T>::expandEdge(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, adjEntry& adjExternal,
        const node& n /*= 0*/) {
    treeNodeTreated[mu] = true;
 
    switch (spqrTree.typeOf(mu)) {
    case SPQRTree::NodeType::SNode:
        expandEdgeSNode(spqrTree, treeNodeTreated, mu, leftNode, nodeLength, edgeLength, newOrder,
                adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, adjExternal);
        break;
    case SPQRTree::NodeType::PNode:
        expandEdgePNode(spqrTree, treeNodeTreated, mu, leftNode, nodeLength, edgeLength, newOrder,
                adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, adjExternal);
        break;
    case SPQRTree::NodeType::RNode:
        expandEdgeRNode(spqrTree, treeNodeTreated, mu, leftNode, nodeLength, edgeLength, newOrder,
                adjBeforeNodeArraySource, adjBeforeNodeArrayTarget, adjExternal, n);
        break;
    default:
        OGDF_ASSERT(false);
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphs<T>::expandEdgeSNode(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, adjEntry& adjExternal) {
    Skeleton& S = spqrTree.skeleton(mu);
    edge referenceEdge = S.referenceEdge();
    adjEntry startAdjEntry = nullptr;
    if (!leftNode) {
        for (edge e : S.getGraph().edges) {
            if (!S.isVirtual(e)) {
                startAdjEntry = e->adjSource();
                break;
            }
        }
        OGDF_ASSERT(startAdjEntry);
    } else if (leftNode->firstAdj()->theEdge() == referenceEdge) {
        startAdjEntry = leftNode->lastAdj();
    } else {
        startAdjEntry = leftNode->firstAdj();
    }
 
    adjEntry ae = startAdjEntry;
    if (!adjExternal) {
        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) {
            // NOLINTNEXTLINE(clang-analyzer-core.CallAndMessage): referenceEdge cannot be null
            if (ae->theNode() == referenceEdge->source()) {
                adjBeforeNodeArraySource[mu] = before;
            } else {
                adjBeforeNodeArrayTarget[mu] = before;
            }
        } else {
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    adjExternal);
        }
 
        if (firstStep) {
            beforeSource = before;
            firstStep = false;
        }
 
        ae = ae->twin();
        before = nullptr;
        if (ae->theEdge() == referenceEdge) {
            // NOLINTNEXTLINE(clang-analyzer-core.CallAndMessage): referenceEdge cannot be null
            if (ae->theNode() == referenceEdge->source()) {
                adjBeforeNodeArraySource[mu] = beforeSource;
            } else {
                adjBeforeNodeArrayTarget[mu] = beforeSource;
            }
        } else {
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    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 EmbedderMaxFaceBiconnectedGraphs<T>::expandEdgePNode(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, 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) {
        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;
            }
        }
    }
 
    edge longestEdge = nullptr;
    for (edge e : S.getGraph().edges) {
        if (e == referenceEdge || e == altReferenceEdge) {
            continue;
        }
        if (!longestEdge || edgeLength[mu][e] > edgeLength[mu][longestEdge]) {
            longestEdge = e;
        }
    }
 
    List<edge> rightEdgeOrder;
    ListIterator<adjEntry> beforeAltRefEdge;
 
    //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];
            }
        }
 
        List<edge> edgeList;
        S.getGraph().allEdges(edgeList);
        adjEntry ae;
 
        //if left node, longest edge at first:
        if (i == 0) {
            if (longestEdge->source() == n) {
                ae = longestEdge->adjSource();
            } else {
                ae = longestEdge->adjTarget();
            }
 
            if (referenceEdge && S.isVirtual(longestEdge)) {
                node nu = S.twinTreeNode(longestEdge);
                if (longestEdge->source() == n) {
                    if (referenceEdge->source() == n) {
                        adjBeforeNodeArrayTarget[nu] = adjBeforeNodeArrayTarget[mu];
                    } else {
                        adjBeforeNodeArrayTarget[nu] = adjBeforeNodeArraySource[mu];
                    }
                } else {
                    if (referenceEdge->source() == n) {
                        adjBeforeNodeArraySource[nu] = adjBeforeNodeArrayTarget[mu];
                    } else {
                        adjBeforeNodeArraySource[nu] = adjBeforeNodeArraySource[mu];
                    }
                }
            }
 
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    adjExternal);
        }
 
        //all edges except reference edge and longest edge:
        if (i == 0) {
            //all virtual edges
            for (edge e : edgeList) {
                if (e == referenceEdge || e == longestEdge || e == altReferenceEdge
                        || !S.isVirtual(e)) {
                    continue;
                }
 
                node nu = S.twinTreeNode(e);
                if (referenceEdge != nullptr && e->source() == n) {
                    if (referenceEdge->source() == n) {
                        adjBeforeNodeArrayTarget[nu] = adjBeforeNodeArrayTarget[mu];
                    } else {
                        adjBeforeNodeArrayTarget[nu] = adjBeforeNodeArraySource[mu];
                    }
                } else if (referenceEdge) {
                    if (referenceEdge->source() == n) {
                        adjBeforeNodeArraySource[nu] = adjBeforeNodeArrayTarget[mu];
                    } else {
                        adjBeforeNodeArraySource[nu] = adjBeforeNodeArraySource[mu];
                    }
                }
 
                rightEdgeOrder.pushFront(e);
 
                if (e->source() == n) {
                    ae = e->adjSource();
                } else {
                    ae = e->adjTarget();
                }
 
                adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                        edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                        adjExternal);
            }
 
            //all real edges
            for (edge e : edgeList) {
                if (e == referenceEdge || e == longestEdge || e == altReferenceEdge
                        || S.isVirtual(e)) {
                    continue;
                }
 
                rightEdgeOrder.pushFront(e);
 
                if (e->source() == n) {
                    ae = e->adjSource();
                } else {
                    ae = e->adjTarget();
                }
 
                adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                        edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                        adjExternal);
            }
        } else {
            for (edge e : rightEdgeOrder) {
                if (e->source() == n) {
                    ae = e->adjSource();
                } else {
                    ae = e->adjTarget();
                }
 
                adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                        edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                        adjExternal);
            }
        }
 
        //if not left node, longest edge:
        if (i == 1) {
            if (longestEdge->source() == n) {
                ae = longestEdge->adjSource();
            } else {
                ae = longestEdge->adjTarget();
            }
 
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, m_leftNode, nodeLength,
                    edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    adjExternal);
        }
 
        //(alternative) reference edge at last:
        if (referenceEdge) {
            if (n == referenceEdge->source()) {
                adjBeforeNodeArraySource[mu] = before;
            } else {
                adjBeforeNodeArrayTarget[mu] = before;
            }
        } else {
            node newLeftNode;
            if (i == 0) {
                newLeftNode = m_leftNode->firstAdj()->twinNode();
            } else {
                newLeftNode = m_leftNode;
            }
 
            if (altReferenceEdge->source() == n) {
                ae = altReferenceEdge->adjSource();
            } else {
                ae = altReferenceEdge->adjTarget();
            }
 
            adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, newLeftNode, nodeLength,
                    edgeLength, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    adjExternal);
 
            if (i == 0 && S.isVirtual(altReferenceEdge)) {
                node nu = S.twinTreeNode(altReferenceEdge);
                if (altReferenceEdge->source() == n) {
                    beforeAltRefEdge = adjBeforeNodeArrayTarget[nu];
                } else {
                    beforeAltRefEdge = adjBeforeNodeArraySource[nu];
                }
            }
        }
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphs<T>::expandEdgeRNode(const StaticSPQRTree& spqrTree,
        NodeArray<bool>& treeNodeTreated, const node& mu, const node& leftNode,
        const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength,
        NodeArray<List<adjEntry>>& newOrder,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArraySource,
        NodeArray<ListIterator<adjEntry>>& adjBeforeNodeArrayTarget, 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;
        }
    }
 
    if (!adjExternal) {
        edge orgEdge = S.realEdge(m_adjExternal->theEdge());
        if (orgEdge->source() == S.original(m_adjExternal->theNode())) {
            adjExternal = orgEdge->adjSource();
        } else {
            adjExternal = orgEdge->adjTarget();
        }
    }
 
    OGDF_ASSERT(maxFaceContEdge);
    adjEntry adjMaxFace = maxFaceContEdge->firstAdj();
 
    //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 (ae->theEdge() == referenceEdge) {
            if (ae->succ()) {
                m_start_ae = ae->succ();
            } else {
                m_start_ae = ae->theNode()->firstAdj();
            }
        } else {
            m_start_ae = ae;
        }
 
        for (adjEntry aeN = m_start_ae; after_ae || aeN != m_start_ae;
                after_ae = after_ae && aeN->succ(),
                      aeN = after_ae ? aeN->succ()
                                     : (!aeN->succ() ? ae->theNode()->firstAdj() : aeN->succ())) {
            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, newOrder, adjBeforeNodeArraySource, adjBeforeNodeArrayTarget,
                    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();
            }
        }
    }
 
    //Simple copy of not treated node's adjacency lists (internal nodes). Setting
    //of left node not necessary, because all nodes are not in external 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()) {
                adjEntryForNode(ae, before, spqrTree, treeNodeTreated, mu, ae->theNode(),
                        nodeLength, edgeLength, newOrder, adjBeforeNodeArraySource,
                        adjBeforeNodeArrayTarget, 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 EmbedderMaxFaceBiconnectedGraphs<T>::compute(const Graph& G, const NodeArray<T>& nodeLength,
        const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree,
        NodeArray<EdgeArray<T>>& edgeLengthSkel) {
    //base cases (SPQR-tree implementation would crash for such graphs):
    if (G.numberOfNodes() <= 1 || G.numberOfEdges() <= 2) {
        return;
    }
 
    //set length for all real edges in skeletons to length of the original edge
    //and initialize edge lengths for virtual edges with 0:
    edgeLengthSkel.init(spqrTree->tree());
    for (node v : spqrTree->tree().nodes) {
        edgeLengthSkel[v].init(spqrTree->skeleton(v).getGraph());
        for (edge e : spqrTree->skeleton(v).getGraph().edges) {
            if (spqrTree->skeleton(v).isVirtual(e)) {
                edgeLengthSkel[v][e] = 0;
            } else {
                edgeLengthSkel[v][e] = edgeLength[spqrTree->skeleton(v).realEdge(e)];
            }
        }
    }
 
    //set component-length for all non-reference edges:
    bottomUpTraversal(*spqrTree, spqrTree->rootNode(), nodeLength, edgeLengthSkel);
    //set component length for all reference edges:
    topDownTraversal(*spqrTree, spqrTree->rootNode(), nodeLength, edgeLengthSkel);
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::computeSize(const Graph& G, const NodeArray<T>& nodeLength,
        const EdgeArray<T>& edgeLength) {
    //base cases (SPQR-tree implementation would crash for such graphs):
    OGDF_ASSERT(G.numberOfNodes() >= 2);
    if (G.numberOfEdges() == 1) {
        edge e = G.firstEdge();
        return edgeLength[e] + nodeLength[e->source()] + nodeLength[e->target()];
    }
    if (G.numberOfEdges() == 2) {
        edge e1 = G.firstEdge();
        edge e2 = e1->succ();
        return edgeLength[e1] + edgeLength[e2] + nodeLength[e1->source()] + nodeLength[e1->target()];
    }
    StaticSPQRTree spqrTree(G);
    NodeArray<EdgeArray<T>> edgeLengthSkel;
    return computeSize(G, nodeLength, edgeLength, spqrTree, edgeLengthSkel);
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::computeSize(const Graph& G, const NodeArray<T>& nodeLength,
        const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree,
        NodeArray<EdgeArray<T>>& edgeLengthSkel) {
    //base cases (SPQR-tree implementation would crash for such graphs):
    OGDF_ASSERT(G.numberOfNodes() >= 2);
    if (G.numberOfEdges() == 1) {
        edge e = G.firstEdge();
        return edgeLength[e] + nodeLength[e->source()] + nodeLength[e->target()];
    }
    if (G.numberOfEdges() == 2) {
        edge e1 = G.firstEdge();
        edge e2 = e1->succ();
        return edgeLength[e1] + edgeLength[e2] + nodeLength[e1->source()] + nodeLength[e1->target()];
    }
 
    //set length for all real edges in skeletons to length of the original edge
    //and initialize edge lengths for virtual edges with 0:
    OGDF_ASSERT(spqrTree != nullptr);
    edgeLengthSkel.init(spqrTree->tree());
    for (node v : spqrTree->tree().nodes) {
        edgeLengthSkel[v].init(spqrTree->skeleton(v).getGraph());
        for (edge e : spqrTree->skeleton(v).getGraph().edges) {
            if (spqrTree->skeleton(v).isVirtual(e)) {
                edgeLengthSkel[v][e] = 0;
            } else {
                edgeLengthSkel[v][e] = edgeLength[spqrTree->skeleton(v).realEdge(e)];
            }
        }
    }
 
    //set component-length for all non-reference edges:
    bottomUpTraversal(*spqrTree, spqrTree->rootNode(), nodeLength, edgeLengthSkel);
    //set component length for all reference edges:
    topDownTraversal(*spqrTree, spqrTree->rootNode(), nodeLength, edgeLengthSkel);
 
    T biggestFace = -1;
    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;
        }
    }
 
    return biggestFace;
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::computeSize(const Graph& G, const node& n,
        const NodeArray<T>& nodeLength, const EdgeArray<T>& edgeLength) {
    //base cases (SPQR-tree implementation would crash for such graphs):
    OGDF_ASSERT(G.numberOfNodes() >= 2);
    if (G.numberOfEdges() == 1) {
        edge e = G.firstEdge();
        return edgeLength[e] + nodeLength[e->source()] + nodeLength[e->target()];
    }
    if (G.numberOfEdges() == 2) {
        edge e1 = G.firstEdge();
        edge e2 = e1->succ();
        return edgeLength[e1] + edgeLength[e2] + nodeLength[e1->source()] + nodeLength[e1->target()];
    }
    StaticSPQRTree spqrTree(G);
    NodeArray<EdgeArray<T>> edgeLengthSkel;
    compute(G, nodeLength, edgeLength, &spqrTree, edgeLengthSkel);
    return computeSize(G, n, nodeLength, edgeLength, &spqrTree, edgeLengthSkel);
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::computeSize(const Graph& G, const node& n,
        const NodeArray<T>& nodeLength, const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree) {
    NodeArray<EdgeArray<T>> edgeLengthSkel;
    compute(G, nodeLength, edgeLength, spqrTree, edgeLengthSkel);
    return computeSize(G, n, nodeLength, edgeLength, spqrTree, edgeLengthSkel);
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::computeSize(const Graph& G, const node& n,
        const NodeArray<T>& nodeLength, const EdgeArray<T>& edgeLength, StaticSPQRTree* spqrTree,
        const NodeArray<EdgeArray<T>>& edgeLengthSkel) {
    //base cases (SPQR-tree implementation would crash for such graphs):
    OGDF_ASSERT(G.numberOfNodes() >= 2);
    if (G.numberOfEdges() == 1) {
        edge e = G.firstEdge();
        return edgeLength[e] + nodeLength[e->source()] + nodeLength[e->target()];
    } else if (G.numberOfEdges() == 2) {
        edge e1 = G.firstEdge();
        edge e2 = e1->succ();
        return edgeLength[e1] + edgeLength[e2] + nodeLength[e1->source()] + nodeLength[e1->target()];
    }
 
    node* mus = new node[n->degree()];
    int i = 0;
    T biggestFace = -1;
    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;
            }
 
            i++;
        }
    }
    delete[] mus;
 
    return biggestFace;
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphs<T>::bottomUpTraversal(StaticSPQRTree& spqrTree,
        const node& mu, const NodeArray<T>& nodeLength, NodeArray<EdgeArray<T>>& edgeLength) {
    //Recursion:
    for (adjEntry adj : mu->adjEntries) {
        edge ed = adj->theEdge();
        if (ed->source() == mu) {
            bottomUpTraversal(spqrTree, ed->target(), nodeLength, edgeLength);
        }
    }
 
    for (edge e : spqrTree.skeleton(mu).getGraph().edges) {
        //do not treat real edges here and do not treat reference edges:
        if (!spqrTree.skeleton(mu).isVirtual(e) || e == spqrTree.skeleton(mu).referenceEdge()) {
            continue;
        }
 
        //pertinent node of e in the SPQR-tree:
        node nu = spqrTree.skeleton(mu).twinTreeNode(e);
        //reference edge of nu (virtual edge in nu associated with mu):
        edge er = spqrTree.skeleton(nu).referenceEdge();
        //sum of the lengths of the two poles of mu:
        node refEdgeSource = spqrTree.skeleton(nu).referenceEdge()->source();
        node origRefEdgeSource = spqrTree.skeleton(nu).original(refEdgeSource);
        node refEdgeTarget = spqrTree.skeleton(nu).referenceEdge()->target();
        node origRefEdgeTarget = spqrTree.skeleton(nu).original(refEdgeTarget);
        T ell = nodeLength[origRefEdgeSource] + nodeLength[origRefEdgeTarget];
 
        if (spqrTree.typeOf(nu) == SPQRTree::NodeType::SNode) {
            //size of a face in skeleton(nu) minus ell
            T sizeOfFace = 0;
            for (node nS : spqrTree.skeleton(nu).getGraph().nodes) {
                sizeOfFace += nodeLength[spqrTree.skeleton(nu).original(nS)];
            }
 
            for (edge eS : spqrTree.skeleton(nu).getGraph().edges) {
                sizeOfFace += edgeLength[nu][eS];
            }
 
            edgeLength[mu][e] = sizeOfFace - ell;
        } else if (spqrTree.typeOf(nu) == SPQRTree::NodeType::PNode) {
            //length of the longest edge different from er in skeleton(nu)
            edge longestEdge = nullptr;
            for (edge ed : spqrTree.skeleton(nu).getGraph().edges) {
                if (ed != er && (!longestEdge || edgeLength[nu][ed] > edgeLength[nu][longestEdge])) {
                    longestEdge = ed;
                }
            }
            edgeLength[mu][e] = edgeLength[nu][longestEdge];
        } else if (spqrTree.typeOf(nu) == SPQRTree::NodeType::RNode) {
            //size of the largest face containing er in skeleton(nu) minus ell
            //Calculate an embedding of the graph (it exists only two which are
            //mirror-symmetrical):
            planarEmbed(spqrTree.skeleton(nu).getGraph());
            CombinatorialEmbedding combinatorialEmbedding(spqrTree.skeleton(nu).getGraph());
            T biggestFaceSize = -1;
            for (face f : combinatorialEmbedding.faces) {
                T sizeOfFace = 0;
                bool containsEr = false;
                for (adjEntry ae : f->entries) {
                    if (ae->theEdge() == er) {
                        containsEr = true;
                    }
                    sizeOfFace += edgeLength[nu][ae->theEdge()]
                            + nodeLength[spqrTree.skeleton(nu).original(ae->theNode())];
                }
 
                if (containsEr && sizeOfFace > biggestFaceSize) {
                    biggestFaceSize = sizeOfFace;
                }
            }
 
            edgeLength[mu][e] = biggestFaceSize - ell;
        } else { //should never happen
            edgeLength[mu][e] = 1;
        }
    }
}
 
template<class T>
void EmbedderMaxFaceBiconnectedGraphs<T>::topDownTraversal(StaticSPQRTree& spqrTree, const node& mu,
        const NodeArray<T>& nodeLength, NodeArray<EdgeArray<T>>& edgeLength) {
    //S: skeleton of mu
    Skeleton& S = spqrTree.skeleton(mu);
 
    //Get all reference edges of the children nu of mu and set their component length:
    for (adjEntry adj : mu->adjEntries) {
        edge ed = adj->theEdge();
        if (ed->source() != mu) {
            continue;
        }
 
        node nu = ed->target();
        edge referenceEdgeOfNu = spqrTree.skeleton(nu).referenceEdge();
        edge eSnu = spqrTree.skeleton(nu).twinEdge(referenceEdgeOfNu);
        if (spqrTree.typeOf(mu) == SPQRTree::NodeType::SNode) {
            //Let L be the sum of the length of all vertices and edges in S. The component
            //length of the reference edge of nu is L minus the length of e_{S, nu} minus
            //the lengths of the two vertices incident to e_{S, nu}.
            T L = 0;
            for (edge ed2 : S.getGraph().edges) {
                L += edgeLength[mu][ed2];
            }
            for (node no : S.getGraph().nodes) {
                L += nodeLength[S.original(no)];
            }
 
            edgeLength[nu][referenceEdgeOfNu] = L - edgeLength[mu][eSnu]
                    - nodeLength[S.original(eSnu->source())] - nodeLength[S.original(eSnu->target())];
        } else if (spqrTree.typeOf(mu) == SPQRTree::NodeType::PNode) {
            //The component length of the reference edge of nu is the length of the longest
            //edge in S different from e_{S, nu}.
            edge longestEdge = nullptr;
            for (edge ed2 : S.getGraph().edges) {
                if (ed2 != eSnu
                        && (!longestEdge || edgeLength[mu][ed2] > edgeLength[mu][longestEdge])) {
                    longestEdge = ed2;
                }
            }
            edgeLength[nu][referenceEdgeOfNu] = edgeLength[mu][longestEdge];
        } else if (spqrTree.typeOf(mu) == SPQRTree::NodeType::RNode) {
            //Let f be the largest face in S containing e_{S, nu}. The component length of
            //the reference edge of nu is the size of f minus the length of e_{S, nu} minus
            //the lengths of the two vertices incident to e_{S, nu}.
 
            //Calculate an embedding of the graph (it exists only two which are
            //mirror-symmetrical):
            planarEmbed(S.getGraph());
            CombinatorialEmbedding combinatorialEmbedding(S.getGraph());
            T biggestFaceSize = -1;
            for (face f : combinatorialEmbedding.faces) {
                T sizeOfFace = 0;
                bool containsESnu = false;
                for (adjEntry ae : f->entries) {
                    if (ae->theEdge() == eSnu) {
                        containsESnu = true;
                    }
                    sizeOfFace +=
                            edgeLength[mu][ae->theEdge()] + nodeLength[S.original(ae->theNode())];
                }
                if (containsESnu && sizeOfFace > biggestFaceSize) {
                    biggestFaceSize = sizeOfFace;
                }
            }
            edgeLength[nu][referenceEdgeOfNu] = biggestFaceSize - edgeLength[mu][eSnu]
                    - nodeLength[S.original(eSnu->source())] - nodeLength[S.original(eSnu->target())];
        } else { //should never happen
            edgeLength[nu][referenceEdgeOfNu] = 0;
        }
 
        //Recursion:
        topDownTraversal(spqrTree, ed->target(), nodeLength, edgeLength);
    }
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::largestFaceContainingNode(const StaticSPQRTree& spqrTree,
        const node& mu, const node& n, const NodeArray<T>& nodeLength,
        const NodeArray<EdgeArray<T>>& edgeLength) {
    bool containsARealEdge = false;
    if (spqrTree.typeOf(mu) == SPQRTree::NodeType::RNode) {
        //The largest face containing n is the largest face containg n in any embedding of S.
        planarEmbed(spqrTree.skeleton(mu).getGraph());
        CombinatorialEmbedding combinatorialEmbedding(spqrTree.skeleton(mu).getGraph());
        T biggestFaceSize = -1;
        for (face f : combinatorialEmbedding.faces) {
            T sizeOfFace = 0;
            bool containingN = false;
            bool m_containsARealEdge = false;
            for (adjEntry ae : f->entries) {
                if (spqrTree.skeleton(mu).original(ae->theNode()) == n) {
                    containingN = true;
                }
                if (!spqrTree.skeleton(mu).isVirtual(ae->theEdge())) {
                    m_containsARealEdge = true;
                }
                sizeOfFace += edgeLength[mu][ae->theEdge()];
                sizeOfFace += nodeLength[spqrTree.skeleton(mu).original(ae->theNode())];
            }
            if (containingN && sizeOfFace > biggestFaceSize) {
                biggestFaceSize = sizeOfFace;
                containsARealEdge = m_containsARealEdge;
            }
        }
 
        if (!containsARealEdge) {
            return -1;
        }
        return biggestFaceSize;
    } else if (spqrTree.typeOf(mu) == SPQRTree::NodeType::PNode) {
        //Find the two longest edges, they define the largest face containg n.
        edge longestEdges[2] = {nullptr, nullptr};
        for (edge edgeWalker : spqrTree.skeleton(mu).getGraph().edges) {
            if (!longestEdges[1] || edgeLength[mu][edgeWalker] > edgeLength[mu][longestEdges[1]]) {
                if (!longestEdges[0] || edgeLength[mu][edgeWalker] > edgeLength[mu][longestEdges[0]]) {
                    longestEdges[1] = longestEdges[0];
                    longestEdges[0] = edgeWalker;
                } else {
                    longestEdges[1] = edgeWalker;
                }
            }
        }
 
        if (!spqrTree.skeleton(mu).isVirtual(longestEdges[0])
                || !spqrTree.skeleton(mu).isVirtual(longestEdges[1])) {
            containsARealEdge = true;
        }
 
        if (!containsARealEdge) {
            return -1;
        }
 
        return edgeLength[mu][longestEdges[0]] + edgeLength[mu][longestEdges[1]];
    } else if (spqrTree.typeOf(mu) == SPQRTree::NodeType::SNode) {
        //The largest face containing n is any face in the single existing embedding of S.
        T sizeOfFace = 0;
        for (node nS : spqrTree.skeleton(mu).getGraph().nodes) {
            sizeOfFace += nodeLength[spqrTree.skeleton(mu).original(nS)];
        }
 
        for (edge eS : spqrTree.skeleton(mu).getGraph().edges) {
            if (!spqrTree.skeleton(mu).isVirtual(eS)) {
                containsARealEdge = true;
            }
            sizeOfFace += edgeLength[mu][eS];
        }
 
        if (!containsARealEdge) {
            return -1;
        }
 
        return sizeOfFace;
    }
 
    //should never end here...
    return 42;
}
 
template<class T>
T EmbedderMaxFaceBiconnectedGraphs<T>::largestFaceInSkeleton(const StaticSPQRTree& spqrTree,
        const node& mu, const NodeArray<T>& nodeLength, const NodeArray<EdgeArray<T>>& edgeLength) {
    bool containsARealEdge = false;
    if (spqrTree.typeOf(mu) == SPQRTree::NodeType::RNode) {
        //The largest face is a largest face in any embedding of S.
        planarEmbed(spqrTree.skeleton(mu).getGraph());
        CombinatorialEmbedding combinatorialEmbedding(spqrTree.skeleton(mu).getGraph());
        T biggestFaceSize = -1;
        for (face f : combinatorialEmbedding.faces) {
            bool m_containsARealEdge = false;
            T sizeOfFace = 0;
            for (adjEntry ae : f->entries) {
#if 0
                node originalNode = spqrTree.skeleton(mu).original(ae->theNode());
#endif
                if (!spqrTree.skeleton(mu).isVirtual(ae->theEdge())) {
                    m_containsARealEdge = true;
                }
                sizeOfFace += edgeLength[mu][ae->theEdge()]
                        + nodeLength[spqrTree.skeleton(mu).original(ae->theNode())];
            }
 
            if (sizeOfFace > biggestFaceSize) {
                biggestFaceSize = sizeOfFace;
                containsARealEdge = m_containsARealEdge;
            }
        }
 
        if (!containsARealEdge) {
            return -1;
        }
 
        return biggestFaceSize;
    } else if (spqrTree.typeOf(mu) == SPQRTree::NodeType::PNode) {
        //Find the two longest edges, they define the largest face.
        edge longestEdges[2] = {nullptr, nullptr};
        for (edge edgeWalker : spqrTree.skeleton(mu).getGraph().edges) {
            if (!longestEdges[1] || edgeLength[mu][edgeWalker] > edgeLength[mu][longestEdges[1]]) {
                if (!longestEdges[0] || edgeLength[mu][edgeWalker] > edgeLength[mu][longestEdges[0]]) {
                    longestEdges[1] = longestEdges[0];
                    longestEdges[0] = edgeWalker;
                } else {
                    longestEdges[1] = edgeWalker;
                }
            }
        }
 
        if (!spqrTree.skeleton(mu).isVirtual(longestEdges[0])
                || !spqrTree.skeleton(mu).isVirtual(longestEdges[1])) {
            containsARealEdge = true;
        }
 
        if (!containsARealEdge) {
            return -1;
        }
 
        return edgeLength[mu][longestEdges[0]] + edgeLength[mu][longestEdges[1]];
    } else if (spqrTree.typeOf(mu) == SPQRTree::NodeType::SNode) {
        //The largest face is any face in the single existing embedding of S.
        T sizeOfFace = 0;
        for (node nS : spqrTree.skeleton(mu).getGraph().nodes) {
            sizeOfFace += nodeLength[spqrTree.skeleton(mu).original(nS)];
        }
 
        for (edge eS : spqrTree.skeleton(mu).getGraph().edges) {
            if (!spqrTree.skeleton(mu).isVirtual(eS)) {
                containsARealEdge = true;
            }
            sizeOfFace += edgeLength[mu][eS];
        }
 
        if (!containsARealEdge) {
            return -1;
        }
 
        return sizeOfFace;
    }
 
    //should never end here...
    return 42;
}
 
}