/*
 * $Revision: 3977 $
 *
 * last checkin:
 *   $Author: gutwenger $
 *   $Date: 2014-03-25 13:59:42 +0100 (Tue, 25 Mar 2014) $
 ***************************************************************/

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

#ifdef _MSC_VER
#pragma once
#endif

#ifndef OGDF_EMBEDDER_MAX_FACE_BICONNECTED_GRAPHS_Layers_H
#define OGDF_EMBEDDER_MAX_FACE_BICONNECTED_GRAPHS_Layers_H

#include <ogdf/decomposition/StaticSPQRTree.h>
#include <ogdf/basic/CombinatorialEmbedding.h>
#include <ogdf/basic/extended_graph_alg.h>
#include <ogdf/graphalg/ShortestPathWithBFM.h>


namespace ogdf {

//! Computes an embedding of a biconnected graph with maximum external face (plus layers approach).
/**
 * See the paper "Graph Embedding with Minimum Depth and
 * Maximum External Face" by C. Gutwenger and P. Mutzel (2004) for
 * details.
 * The algorithm for maximum external face is combined with the
 * algorithm for maximum external layers which defines how to embed
 * blocks into inner faces. See diploma thesis "Algorithmen zur
 * Bestimmung von guten Graph-Einbettungen f&uuml;r orthogonale
 * Zeichnungen" (in german) by Thorsten Kerkhof (2007) for details.
 */
template<class T>
class EmbedderMaxFaceBiconnectedGraphsLayers
{
public:
	//! Creates an embedder.
	EmbedderMaxFaceBiconnectedGraphsLayers() { }

	/**
	 * \brief Embeds \a G by computing and extending a maximum face in \a G
	 *   containg \a n.
	 * \param G is the original graph.
	 * \param adjExternal is assigned an adjacency entry of the external face.
	 * \param nodeLength stores for each vertex in \a G its length.
	 * \param edgeLength stores for each edge in \a G its length.
	 * \param n is a node of the original graph. If n is given, a maximum face
	 *   containing n is computed, otherwise any maximum face.
	 */
	static void embed(
		Graph& G,
		adjEntry& adjExternal,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength,
		const node& n = 0);

	/**
	 * \brief Computes the component lengths of all virtual edges in spqrTree.
	 * \param G is the original graph.
	 * \param nodeLength is saving for each vertex in \a G its length.
	 * \param edgeLength is saving for each edge in \a G its length.
	 * \param spqrTree is the SPQR-tree of \a G.
	 * \param edgeLengthSkel is saving for each skeleton graph of the SPQR-tree
	 *   all edge lengths.
	 */
	static void compute(
		const Graph& G,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength,
		StaticSPQRTree *spqrTree,
		NodeArray< EdgeArray<T> >& edgeLengthSkel);

	/**
	 * \brief Returns the size of a maximum external face in \a G containing the node \a n.
	 * \param G is the original graph.
	 * \param n is a node of the original graph.
	 * \param nodeLength is saving for each vertex in \a G its length.
	 * \param edgeLength is saving for each edge in \a G its length.
	 * \return The size of a maximum external face in \a G containing the node \a n.
	 */
	static T computeSize(
		const Graph& G,
		const node& n,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength);

	/**
	 * \brief Returns the size of a maximum external face in \a G containing
	 *   the node \a n.
	 *
	 * \param G is the original graph.
	 * \param n is a node of the original graph.
	 * \param nodeLength is saving for each vertex in \a G its length.
	 * \param edgeLength is saving for each edge in \a G its length.
	 * \param spqrTree is the SPQR-tree of G.
	 * \return The size of a maximum external face in \a G containing the node \a n.
	 */
	static T computeSize(
		const Graph& G,
		const node& n,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength,
		StaticSPQRTree *spqrTree);

	/**
	 * \brief Returns the size of a maximum external face in \a G containing
	 *   the node \a n.
	 *
	 * \param G is the original graph.
	 * \param n is a node of the original graph.
	 * \param nodeLength is saving for each vertex in \a G its length.
	 * \param edgeLength is saving for each edge in \a G its length.
	 * \param spqrTree is the SPQR-tree of G.
	 * \param edgeLengthSkel is saving for each skeleton graph the length
	 *   of each edge.
	 * \return The size of a maximum external face in \a G containing the node \a n.
	 */
	static T computeSize(
		const Graph& G,
		const node& n,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength,
		StaticSPQRTree *spqrTree,
		const NodeArray< EdgeArray<T> >& edgeLengthSkel);

	/**
	 * \brief Returns the size of a maximum external face in \a G.
	 * \param G is the original graph.
	 * \param nodeLength is saving for each vertex in \a G its length.
	 * \param edgeLength is saving for each edge in \a G its length.
	 * \return The size of a maximum external face in \a G.
	 */
	static T computeSize(
		const Graph& G,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength);

	/**
	 * \brief Returns the size of a maximum external face in \a G.
	 *   The SPQR-tree is given. The computed component lengths are
	 *   computed and returned.
	 *
	 * \param G is the original graph.
	 * \param nodeLength is saving for each vertex in \a G its length.
	 * \param edgeLength is saving for each edge in \a G its length.
	 * \param spqrTree is the SPQR-tree of G.
	 * \param edgeLengthSkel is saving for each skeleton graph the length
	 *   of each edge.
	 * \return The size of a maximum external face in \a G.
	 */
	static T computeSize(
		const Graph& G,
		const NodeArray<T>& nodeLength,
		const EdgeArray<T>& edgeLength,
		StaticSPQRTree *spqrTree,
		NodeArray< EdgeArray<T> >& edgeLengthSkel);

private:
	/**
	 * \brief Bottom up traversal of SPQR-tree computing the component length of
	 *   all non-reference edges.
	 * \param spqrTree is the SPQR-tree of \a G.
	 * \param mu is the SPQR-tree node treated in this function call.
	 * \param nodeLength is saving for each node of the original graph \a G its
	 *   length.
	 * \param edgeLength is saving for each skeleton graph the length of each
	 *   edge.
	 */
	static void bottomUpTraversal(
		StaticSPQRTree& spqrTree,
		const node& mu,
		const NodeArray<T>& nodeLength,
		NodeArray< EdgeArray<T> >& edgeLength);

	/**
	 * \brief Top down traversal of SPQR-tree computing the component length of
	 *   all reference edges.
	 * \param spqrTree is the SPQR-tree of \a G.
	 * \param mu is the SPQR-tree node treated in this function call.
	 * \param nodeLength is saving for each node of the original graph \a G its
	 *   length.
	 * \param edgeLength is saving for each skeleton graph the length of each
	 *   edge.
	 */
	static void topDownTraversal(
		StaticSPQRTree& spqrTree,
		const node& mu,
		const NodeArray<T>& nodeLength,
		NodeArray< EdgeArray<T> >& edgeLength);

	/**
	 * \brief Computes the size of a maximum face in the skeleton graph of \a mu
	 *   containing \a n.
	 * \param spqrTree is the SPQR-tree of \a G.
	 * \param mu is the SPQR-tree node treated in this function call.
	 * \param n is a node of the original graph \a G.
	 * \param nodeLength is saving for each node of the original graph \a G its
	 *   length.
	 * \param edgeLength is saving for each skeleton graph the length of each
	 *   edge.
	 */
	static T largestFaceContainingNode(
		const StaticSPQRTree& spqrTree,
		const node& mu,
		const node& n,
		const NodeArray<T>& nodeLength,
		const NodeArray< EdgeArray<T> >& edgeLength);

	/**
	 * \brief Computes the size of a maximum face in the skeleton graph of \a mu.
	 * \param spqrTree is the SPQR-tree of \a G.
	 * \param mu is the SPQR-tree node treated in this function call.
	 * \param nodeLength is saving for each node of the original graph \a G its
	 *   length.
	 * \param edgeLength is saving for each skeleton graph the length of each
	 *   edge.
	 */
	static T largestFaceInSkeleton(
		const StaticSPQRTree& spqrTree,
		const node& mu,
		const NodeArray<T>& nodeLength,
		const NodeArray< EdgeArray<T> >& edgeLength);

	/* \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 \a 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 \a mu
	 *   whether it was already treated by any call of ExpandEdge or not. Every
	 *   \a 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 \a 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 \a n in \a 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 \a 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 = 0);

	/* \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 \a mu
	 *   whether it was already treated by any call of ExpandEdge or not. Every
	 *   \a 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 \a 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 \a n in \a 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 \a mu
	 *   whether it was already treated by any call of ExpandEdge or not. Every
	 *   \a 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 \a 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 \a n in \a 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 \a mu
	 *   whether it was already treated by any call of ExpandEdge or not. Every
	 *   \a 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 \a 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 \a n in \a 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 \a 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 = 0);

	/* \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 \a 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 \a mu
	 *   whether it was already treated by any call of ExpandEdge or not. Every
	 *   \a 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 \a 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 \a n in \a 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 == 0)
	{
		node mu;
		forall_nodes(mu, spqrTree.tree())
		{
			//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
	{
		edge nAdjEdge;
		node* mus = new node[n->degree()];
		int i = 0;
		forall_adj_edges(nAdjEdge, n)
		{
			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;
	}

	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 = 0;
	NodeArray< ListIterator<adjEntry> > adjBeforeNodeArraySource(spqrTree.tree());
	NodeArray< ListIterator<adjEntry> > adjBeforeNodeArrayTarget(spqrTree.tree());
	expandEdge(spqrTree, treeNodeTreated, bigFaceMu, 0, nodeLength,
		edgeLengthSkel, thickness, newOrder, adjBeforeNodeArraySource,
		adjBeforeNodeArrayTarget, 0, 0, adjExternal, n);

	node v;
	forall_nodes(v, G)
		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());
		//Skeleton& twinS = spqrTree.skeleton(twinNT);

		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 (!treeNodeTreated[twinNT])

		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 //!(ae->theEdge() == referenceEdge)
		{
			if (ae->theNode() == ae->theEdge()->source())
				before = adjBeforeNodeArraySource[twinNT];
			else
				before = adjBeforeNodeArrayTarget[twinNT];
		}
	}
	else //!(S.isVirtual(ae->theEdge()))
	{
		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);
		}
	} //else //!(S.isVirtual(ae->theEdge()))
}


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::SNode:
		expandEdgeSNode(spqrTree, treeNodeTreated, mu, leftNode,
			nodeLength, edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
			adjBeforeNodeArrayTarget, delta_u, delta_d, adjExternal);
		break;
	case SPQRTree::PNode:
		expandEdgePNode(spqrTree, treeNodeTreated, mu, leftNode,
			nodeLength, edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
			adjBeforeNodeArrayTarget, delta_u, delta_d, adjExternal);
		break;
	case SPQRTree::RNode:
		expandEdgeRNode(spqrTree, treeNodeTreated, mu, leftNode,
			nodeLength, edgeLength, thickness, newOrder, adjBeforeNodeArraySource,
			adjBeforeNodeArrayTarget, delta_u, delta_d, adjExternal, n);
		break;
	OGDF_NODEFAULT
	}
}


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 = 0;
	if (leftNode == 0)
	{
		edge e;
		forall_edges(e, S.getGraph())
		{
			if (!S.isVirtual(e))
			{
				startAdjEntry = e->adjSource();
				break;
			}
		}
		OGDF_ASSERT(startAdjEntry != 0);
	}
	else if (leftNode->firstAdj()->theEdge() == referenceEdge)
		startAdjEntry = leftNode->lastAdj();
	else
		startAdjEntry = leftNode->firstAdj();

	adjEntry ae = startAdjEntry;
	if (adjExternal == 0)
	{
		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 = 0;
		else if (ae->theNode() == referenceEdge->source())
			before = adjBeforeNodeArraySource[mu];
		else if (ae->theNode() == referenceEdge->target())
			before = adjBeforeNodeArrayTarget[mu];
		else
			before = 0;
		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 = NULL;

	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();

	edge e;
	if (!referenceEdge) {
		forall_edges(e, S.getGraph()) {
			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;
	forall_edges(e, S.getGraph())
	{
		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);
						node nOG;
						forall_nodes(nOG, spqrTree.originalGraph())
						{
							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 = OGDF_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;
						} //forall_nodes(nOG, spqrTree.originalGraph())

						sum_E_a += thickness[nu];
					}
					else //!(S.isVirtual(e))
					{
						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 //!(delta_u + sum_E_a <= delta_d + sum_E_b)
				{
					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 = NULL;
	List<node> maxFaceNodes;
	planarEmbed(S.getGraph());
	CombinatorialEmbedding combinatorialEmbedding(S.getGraph());
	T bigFaceSize = -1;
	adjEntry m_adjExternal = 0;
	face f;
	forall_faces(f, combinatorialEmbedding) {
		bool containsVirtualEdgeOrN = false;
		adjEntry this_m_adjExternal = 0;
		T sizeOfFace = 0;
		List<node> faceNodes;
		adjEntry ae;
		forall_face_adj(ae, f) {
			faceNodes.pushBack(ae->theNode());
			if ((n == 0 && (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;
		adjEntry aeExtFace;
		forall_face_adj(aeExtFace, maxFaceContEdge)
		{
			if (aeExtFace->theEdge() == succ_virtualEdge_leftNode->theEdge())
			{
				succVELNAEInExtFace = true;
				break;
			}
		}

		if (!succVELNAEInExtFace)
		{
			node v;
			forall_nodes(v, S.getGraph())
			{
				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()) ? false : true,
			ae = after_start_ae ? ae->faceCycleSucc()
			: (!ae->faceCycleSucc() ? adjMaxFace : ae->faceCycleSucc()))
	{
		firstStep = false;
		//node nodeG = S.original(ae->theNode());
		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()) ? false : true,
			 aeN = after_ae ? aeN->succ()
				 : (!aeN->succ() ? ae->theNode()->firstAdj() : aeN->succ()),
				 numOfHits = (aeN == m_stop_ae) ? numOfHits + 1 : numOfHits)
		{
			node m_leftNode = 0;
			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 = 0;
				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();
			}
		} //for (adjEntry aeN = m_start_ae; [...]
	} //for (adjEntry ae = start_ae; [...]

	//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;

	node v;
	forall_nodes(v, S.getGraph())
	{
		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());
						node nBG;
						forall_nodes(nBG, S.getGraph())
						{
							adjEntry ae_nBG;
							forall_adj(ae_nBG, nBG)
								adjacencyList[nBG].pushBack(ae_nBG);
						}

						NodeArray< List<adjEntry> > adjEntryTreated(S.getGraph());
						forall_nodes(nBG, S.getGraph())
						{
							adjEntry adj;
							forall_adj(adj, nBG)
							{
								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 (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)
											{
												if (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++;
						} //for (ListIterator< List<adjEntry> > it = faces.begin(); it.valid(); it++)

						//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);
						}
					} //if (!DGcomputed)

					//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:
					//node m_leftNode = v;
					node m_rightNode = ae->twinNode();
					node leftOrg = v_original;
					node rightOrg = S.original(m_rightNode);
					node nOG;
					forall_nodes(nOG, spqrTree.originalGraph())
					{
						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 = OGDF_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;
					} //forall_nodes(nOG, spqrTree.originalGraph())
				}
				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>::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());
	node v;
	forall_nodes(v, spqrTree->tree())
	{
		edgeLengthSkel[v].init(spqrTree->skeleton(v).getGraph());
		edge e;
		forall_edges(e, spqrTree->skeleton(v).getGraph())
		{
			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 EmbedderMaxFaceBiconnectedGraphsLayers<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()];
	}
	else 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 EmbedderMaxFaceBiconnectedGraphsLayers<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()];
	}
	else 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:
	edgeLengthSkel.init(spqrTree->tree());
	node v;
	forall_nodes(v, spqrTree->tree())
	{
		edgeLengthSkel[v].init(spqrTree->skeleton(v).getGraph());
		edge e;
		forall_edges(e, spqrTree->skeleton(v).getGraph())
		{
			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;
	node mu;
	forall_nodes(mu, spqrTree->tree())
	{
		//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 EmbedderMaxFaceBiconnectedGraphsLayers<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()];
	}
	else 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 EmbedderMaxFaceBiconnectedGraphsLayers<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 EmbedderMaxFaceBiconnectedGraphsLayers<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()];
	}

	edge nAdjEdges;
	node* mus = new node[n->degree()];
	int i = 0;
	T biggestFace = -1;
	forall_adj_edges(nAdjEdges, n)
	{
		mus[i] = spqrTree->skeletonOfReal(nAdjEdges).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 EmbedderMaxFaceBiconnectedGraphsLayers<T>::bottomUpTraversal(
	StaticSPQRTree& spqrTree,
	const node& mu,
	const NodeArray<T>& nodeLength,
	NodeArray< EdgeArray<T> >& edgeLength)
{
	//Recursion:
	edge ed;
	forall_adj_edges(ed, mu)
	{
		if (ed->source() == mu)
			bottomUpTraversal(spqrTree, ed->target(), nodeLength, edgeLength);
	}

	edge e;
	forall_edges(e, spqrTree.skeleton(mu).getGraph())
	{
		//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::SNode)
		{
			//size of a face in skeleton(nu) minus ell
			T sizeOfFace = 0;
			node nS;
			forall_nodes(nS, spqrTree.skeleton(nu).getGraph())
				sizeOfFace += nodeLength[spqrTree.skeleton(nu).original(nS)];

			edge eS;
			forall_edges(eS, spqrTree.skeleton(nu).getGraph())
				sizeOfFace += edgeLength[nu][eS];

			edgeLength[mu][e] = sizeOfFace - ell;
		}
		else if (spqrTree.typeOf(nu) == SPQRTree::PNode)
		{
			//length of the longest edge different from er in skeleton(nu)
			edge longestEdge = NULL;
			forall_edges(ed, spqrTree.skeleton(nu).getGraph()) {
				if (!(ed == er)
				 && (!longestEdge || edgeLength[nu][ed] > edgeLength[nu][longestEdge])) {
					longestEdge = ed;
				}
			}
			edgeLength[mu][e] = edgeLength[nu][longestEdge];
		}
		else if (spqrTree.typeOf(nu) == SPQRTree::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;
			face f;
			forall_faces(f, combinatorialEmbedding)
			{
				T sizeOfFace = 0;
				bool containsEr = false;
				adjEntry ae;
				forall_face_adj(ae, f)
				{
					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 EmbedderMaxFaceBiconnectedGraphsLayers<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:
	edge ed;
	forall_adj_edges(ed, mu)
	{
		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::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;
			edge ed2;
			forall_edges(ed2, S.getGraph())
				L += edgeLength[mu][ed2];
			node no;
			forall_nodes(no, S.getGraph())
				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::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 ed2;
			edge longestEdge = NULL;
			forall_edges(ed2, S.getGraph())
			{
				if (ed2 != eSnu
				 && (!longestEdge || edgeLength[mu][ed2] > edgeLength[mu][longestEdge])) {
					longestEdge = ed2;
				}
			}
			edgeLength[nu][referenceEdgeOfNu] = edgeLength[mu][longestEdge];
		}
		else if (spqrTree.typeOf(mu) == SPQRTree::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;
			face f;
			forall_faces(f, combinatorialEmbedding)
			{
				T sizeOfFace = 0;
				bool containsESnu = false;
				adjEntry ae;
				forall_face_adj(ae, f)
				{
					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 EmbedderMaxFaceBiconnectedGraphsLayers<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::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;
		face f;
		forall_faces(f, combinatorialEmbedding)
		{
			T sizeOfFace = 0;
			bool containingN = false;
			bool m_containsARealEdge = false;
			adjEntry ae;
			forall_face_adj(ae, f)
			{
				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::PNode)
	{
		//Find the two longest edges, they define the largest face containg n.
		edge edgeWalker;
		edge longestEdges[2] = {0, 0};
		forall_edges(edgeWalker, spqrTree.skeleton(mu).getGraph()) {
			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::SNode)
	{
		//The largest face containing n is any face in the single existing embedding of S.
		T sizeOfFace = 0;
		node nS;
		forall_nodes(nS, spqrTree.skeleton(mu).getGraph())
			sizeOfFace += nodeLength[spqrTree.skeleton(mu).original(nS)];

		edge eS;
		forall_edges(eS, spqrTree.skeleton(mu).getGraph())
		{
			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 EmbedderMaxFaceBiconnectedGraphsLayers<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::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;
		face f;
		forall_faces(f, combinatorialEmbedding)
		{
			bool m_containsARealEdge = false;
			T sizeOfFace = 0;
			adjEntry ae;
			forall_face_adj(ae, f)
			{
				//node originalNode = spqrTree.skeleton(mu).original(ae->theNode());
				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::PNode)
	{
		//Find the two longest edges, they define the largest face.
		edge edgeWalker;
		edge longestEdges[2] = {0, 0};
		forall_edges(edgeWalker, spqrTree.skeleton(mu).getGraph()) {
			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::SNode)
	{
		//The largest face is any face in the single existing embedding of S.
		T sizeOfFace = 0;
		node nS;
		forall_nodes(nS, spqrTree.skeleton(mu).getGraph())
			sizeOfFace += nodeLength[spqrTree.skeleton(mu).original(nS)];

		edge eS;
		forall_edges(eS, spqrTree.skeleton(mu).getGraph())
		{
			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>
void EmbedderMaxFaceBiconnectedGraphsLayers<T>::bottomUpThickness(
	const StaticSPQRTree& spqrTree,
	const node& mu,
	NodeArray<T>& thickness,
	const NodeArray<T>& nodeLength,
	const NodeArray< EdgeArray<T> >& edgeLength)
{
	//recursion:
	edge e_mu_to_nu;
	forall_adj_edges(e_mu_to_nu, mu)
	{
		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());
	edge eSG;
	forall_edges(eSG, S.getGraph())
	{
		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::SNode:
		{
			//thickness(mu) = min_{edges e != referenceEdge} dLength(e)
			T min_dLength = -1;
			forall_edges(eSG, S.getGraph())
			{
				if (eSG == referenceEdge)
					continue;
				if (min_dLength == -1 || dLength[eSG] < min_dLength)
					min_dLength = dLength[eSG];
			}
			thickness[mu] = min_dLength;
		} break;
	case SPQRTree::PNode:
		{
			//thickness(mu) = sum_{edges e != referenceEdge} dLength(e)
			T sumof_dLength = 0;
			forall_edges(eSG, S.getGraph())
			{
				if (eSG == referenceEdge)
					continue;
				sumof_dLength += dLength[eSG];
			}
			thickness[mu] = sumof_dLength;
		} break;
	case SPQRTree::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;

			node nBG;
			forall_nodes(nBG, S.getGraph())
			{
				adjEntry ae_nBG;
				forall_adj(ae_nBG, nBG)
					adjacencyList[nBG].pushBack(ae_nBG);
			}

			NodeArray< List<adjEntry> > adjEntryTreated(S.getGraph());
			forall_nodes(nBG, S.getGraph())
			{
				adjEntry adj;
				forall_adj(adj, nBG)
				{
					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);
				}
			} //forall_nodes(nBG, blockG[bT])

			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)
								{
									if (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;
				} //for (ListIterator<adjEntry> it2 = (*it).begin(); it2.valid(); it2++)
				i++;
			} //for (ListIterator< List<adjEntry> > it = faces.begin(); it.valid(); it++)

			//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;
	OGDF_NODEFAULT
	}
}


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);
	node v;
	edge e;
	forall_nodes (v, G)
		d[v] = infinity;

	d[s] = 0;
	for (int i = 1; i < G.numberOfNodes(); ++i)
	{
		forall_edges (e, G)
		{
			//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:
	forall_edges (e, G)
	{
		if (d[e->target()] > d[e->source()] + length[e])
			return false;
	}

	return true;
}


} // end namespace ogdf

#endif
