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Filename : two_graphs_common_spanning_trees.hpp
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//          Copyright (C) 2012, Michele Caini.
// Distributed under the Boost Software License, Version 1.0.
//    (See accompanying file LICENSE_1_0.txt or copy at
//          http://www.boost.org/LICENSE_1_0.txt)

//          Two Graphs Common Spanning Trees Algorithm
//      Based on academic article of Mint, Read and Tarjan
//     Efficient Algorithm for Common Spanning Tree Problem
// Electron. Lett., 28 April 1983, Volume 19, Issue 9, p.346-347

#ifndef BOOST_GRAPH_TWO_GRAPHS_COMMON_SPANNING_TREES_HPP
#define BOOST_GRAPH_TWO_GRAPHS_COMMON_SPANNING_TREES_HPP

#include <boost/config.hpp>

#include <boost/bimap.hpp>
#include <boost/type_traits.hpp>
#include <boost/concept/requires.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/undirected_dfs.hpp>
#include <boost/graph/connected_components.hpp>
#include <boost/graph/filtered_graph.hpp>
#include <vector>
#include <stack>
#include <map>

namespace boost
{

namespace detail
{

    template < typename TreeMap, typename PredMap, typename DistMap,
        typename LowMap, typename Buffer >
    struct bridges_visitor : public default_dfs_visitor
    {
        bridges_visitor(TreeMap tree, PredMap pred, DistMap dist, LowMap low,
            Buffer& buffer)
        : mTree(tree), mPred(pred), mDist(dist), mLow(low), mBuffer(buffer)
        {
            mNum = -1;
        }

        template < typename Vertex, typename Graph >
        void initialize_vertex(const Vertex& u, const Graph& g)
        {
            put(mPred, u, u);
            put(mDist, u, -1);
        }

        template < typename Vertex, typename Graph >
        void discover_vertex(const Vertex& u, const Graph& g)
        {
            put(mDist, u, ++mNum);
            put(mLow, u, get(mDist, u));
        }

        template < typename Edge, typename Graph >
        void tree_edge(const Edge& e, const Graph& g)
        {
            put(mPred, target(e, g), source(e, g));
            put(mTree, target(e, g), e);
        }

        template < typename Edge, typename Graph >
        void back_edge(const Edge& e, const Graph& g)
        {
            put(mLow, source(e, g),
                (std::min)(get(mLow, source(e, g)), get(mDist, target(e, g))));
        }

        template < typename Vertex, typename Graph >
        void finish_vertex(const Vertex& u, const Graph& g)
        {
            Vertex parent = get(mPred, u);
            if (get(mLow, u) > get(mDist, parent))
                mBuffer.push(get(mTree, u));
            put(mLow, parent, (std::min)(get(mLow, parent), get(mLow, u)));
        }

        TreeMap mTree;
        PredMap mPred;
        DistMap mDist;
        LowMap mLow;
        Buffer& mBuffer;
        int mNum;
    };

    template < typename Buffer >
    struct cycle_finder : public base_visitor< cycle_finder< Buffer > >
    {
        typedef on_back_edge event_filter;
        cycle_finder() : mBuffer(0) {}
        cycle_finder(Buffer* buffer) : mBuffer(buffer) {}
        template < typename Edge, typename Graph >
        void operator()(const Edge& e, const Graph& g)
        {
            if (mBuffer)
                mBuffer->push(e);
        }
        Buffer* mBuffer;
    };

    template < typename DeletedMap > struct deleted_edge_status
    {
        deleted_edge_status() {}
        deleted_edge_status(DeletedMap map) : mMap(map) {}
        template < typename Edge > bool operator()(const Edge& e) const
        {
            return (!get(mMap, e));
        }
        DeletedMap mMap;
    };

    template < typename InLMap > struct inL_edge_status
    {
        inL_edge_status() {}
        inL_edge_status(InLMap map) : mMap(map) {}
        template < typename Edge > bool operator()(const Edge& e) const
        {
            return get(mMap, e);
        }
        InLMap mMap;
    };

    template < typename Graph, typename Func, typename Seq, typename Map >
    void rec_two_graphs_common_spanning_trees(const Graph& iG,
        bimap< bimaps::set_of< int >,
            bimaps::set_of< typename graph_traits< Graph >::edge_descriptor > >
            iG_bimap,
        Map aiG_inL, Map diG, const Graph& vG,
        bimap< bimaps::set_of< int >,
            bimaps::set_of< typename graph_traits< Graph >::edge_descriptor > >
            vG_bimap,
        Map avG_inL, Map dvG, Func func, Seq inL)
    {
        typedef graph_traits< Graph > GraphTraits;

        typedef typename GraphTraits::vertex_descriptor vertex_descriptor;
        typedef typename GraphTraits::edge_descriptor edge_descriptor;

        typedef typename Seq::size_type seq_size_type;

        int edges = num_vertices(iG) - 1;
        //
        //  [ Michele Caini ]
        //
        //  Using the condition (edges != 0) leads to the accidental submission
        //  of
        //    sub-graphs ((V-1+1)-fake-tree, named here fat-tree).
        //  Remove this condition is a workaround for the problem of fat-trees.
        //  Please do not add that condition, even if it improves performance.
        //
        //  Here is proposed the previous guard (that was wrong):
        //     for(seq_size_type i = 0; (i < inL.size()) && (edges != 0); ++i)
        //
        {
            for (seq_size_type i = 0; i < inL.size(); ++i)
                if (inL[i])
                    --edges;

            if (edges < 0)
                return;
        }

        bool is_tree = (edges == 0);
        if (is_tree)
        {
            func(inL);
        }
        else
        {
            std::map< vertex_descriptor, default_color_type > vertex_color;
            std::map< edge_descriptor, default_color_type > edge_color;

            std::stack< edge_descriptor > iG_buf, vG_buf;
            bool found = false;

            seq_size_type m;
            for (seq_size_type j = 0; j < inL.size() && !found; ++j)
            {
                if (!inL[j] && !get(diG, iG_bimap.left.at(j))
                    && !get(dvG, vG_bimap.left.at(j)))
                {
                    put(aiG_inL, iG_bimap.left.at(j), true);
                    put(avG_inL, vG_bimap.left.at(j), true);

                    undirected_dfs(
                        make_filtered_graph(iG,
                            detail::inL_edge_status< associative_property_map<
                                std::map< edge_descriptor, bool > > >(aiG_inL)),
                        make_dfs_visitor(detail::cycle_finder<
                            std::stack< edge_descriptor > >(&iG_buf)),
                        associative_property_map<
                            std::map< vertex_descriptor, default_color_type > >(
                            vertex_color),
                        associative_property_map<
                            std::map< edge_descriptor, default_color_type > >(
                            edge_color));
                    undirected_dfs(
                        make_filtered_graph(vG,
                            detail::inL_edge_status< associative_property_map<
                                std::map< edge_descriptor, bool > > >(avG_inL)),
                        make_dfs_visitor(detail::cycle_finder<
                            std::stack< edge_descriptor > >(&vG_buf)),
                        associative_property_map<
                            std::map< vertex_descriptor, default_color_type > >(
                            vertex_color),
                        associative_property_map<
                            std::map< edge_descriptor, default_color_type > >(
                            edge_color));

                    if (iG_buf.empty() && vG_buf.empty())
                    {
                        inL[j] = true;
                        found = true;
                        m = j;
                    }
                    else
                    {
                        while (!iG_buf.empty())
                            iG_buf.pop();
                        while (!vG_buf.empty())
                            vG_buf.pop();
                        put(aiG_inL, iG_bimap.left.at(j), false);
                        put(avG_inL, vG_bimap.left.at(j), false);
                    }
                }
            }

            if (found)
            {

                std::stack< edge_descriptor > iG_buf_copy, vG_buf_copy;
                for (seq_size_type j = 0; j < inL.size(); ++j)
                {
                    if (!inL[j] && !get(diG, iG_bimap.left.at(j))
                        && !get(dvG, vG_bimap.left.at(j)))
                    {

                        put(aiG_inL, iG_bimap.left.at(j), true);
                        put(avG_inL, vG_bimap.left.at(j), true);

                        undirected_dfs(
                            make_filtered_graph(iG,
                                detail::inL_edge_status<
                                    associative_property_map<
                                        std::map< edge_descriptor, bool > > >(
                                    aiG_inL)),
                            make_dfs_visitor(detail::cycle_finder<
                                std::stack< edge_descriptor > >(&iG_buf)),
                            associative_property_map< std::map<
                                vertex_descriptor, default_color_type > >(
                                vertex_color),
                            associative_property_map< std::map< edge_descriptor,
                                default_color_type > >(edge_color));
                        undirected_dfs(
                            make_filtered_graph(vG,
                                detail::inL_edge_status<
                                    associative_property_map<
                                        std::map< edge_descriptor, bool > > >(
                                    avG_inL)),
                            make_dfs_visitor(detail::cycle_finder<
                                std::stack< edge_descriptor > >(&vG_buf)),
                            associative_property_map< std::map<
                                vertex_descriptor, default_color_type > >(
                                vertex_color),
                            associative_property_map< std::map< edge_descriptor,
                                default_color_type > >(edge_color));

                        if (!iG_buf.empty() || !vG_buf.empty())
                        {
                            while (!iG_buf.empty())
                                iG_buf.pop();
                            while (!vG_buf.empty())
                                vG_buf.pop();
                            put(diG, iG_bimap.left.at(j), true);
                            put(dvG, vG_bimap.left.at(j), true);
                            iG_buf_copy.push(iG_bimap.left.at(j));
                            vG_buf_copy.push(vG_bimap.left.at(j));
                        }

                        put(aiG_inL, iG_bimap.left.at(j), false);
                        put(avG_inL, vG_bimap.left.at(j), false);
                    }
                }

                // REC
                detail::rec_two_graphs_common_spanning_trees< Graph, Func, Seq,
                    Map >(iG, iG_bimap, aiG_inL, diG, vG, vG_bimap, aiG_inL,
                    dvG, func, inL);

                while (!iG_buf_copy.empty())
                {
                    put(diG, iG_buf_copy.top(), false);
                    put(dvG,
                        vG_bimap.left.at(iG_bimap.right.at(iG_buf_copy.top())),
                        false);
                    iG_buf_copy.pop();
                }
                while (!vG_buf_copy.empty())
                {
                    put(dvG, vG_buf_copy.top(), false);
                    put(diG,
                        iG_bimap.left.at(vG_bimap.right.at(vG_buf_copy.top())),
                        false);
                    vG_buf_copy.pop();
                }

                inL[m] = false;
                put(aiG_inL, iG_bimap.left.at(m), false);
                put(avG_inL, vG_bimap.left.at(m), false);

                put(diG, iG_bimap.left.at(m), true);
                put(dvG, vG_bimap.left.at(m), true);

                std::map< vertex_descriptor, edge_descriptor > tree_map;
                std::map< vertex_descriptor, vertex_descriptor > pred_map;
                std::map< vertex_descriptor, int > dist_map, low_map;

                detail::bridges_visitor<
                    associative_property_map<
                        std::map< vertex_descriptor, edge_descriptor > >,
                    associative_property_map<
                        std::map< vertex_descriptor, vertex_descriptor > >,
                    associative_property_map<
                        std::map< vertex_descriptor, int > >,
                    associative_property_map<
                        std::map< vertex_descriptor, int > >,
                    std::stack< edge_descriptor > >
                iG_vis(associative_property_map<
                           std::map< vertex_descriptor, edge_descriptor > >(
                           tree_map),
                    associative_property_map<
                        std::map< vertex_descriptor, vertex_descriptor > >(
                        pred_map),
                    associative_property_map<
                        std::map< vertex_descriptor, int > >(dist_map),
                    associative_property_map<
                        std::map< vertex_descriptor, int > >(low_map),
                    iG_buf),
                    vG_vis(associative_property_map<
                               std::map< vertex_descriptor, edge_descriptor > >(
                               tree_map),
                        associative_property_map<
                            std::map< vertex_descriptor, vertex_descriptor > >(
                            pred_map),
                        associative_property_map<
                            std::map< vertex_descriptor, int > >(dist_map),
                        associative_property_map<
                            std::map< vertex_descriptor, int > >(low_map),
                        vG_buf);

                undirected_dfs(
                    make_filtered_graph(iG,
                        detail::deleted_edge_status< associative_property_map<
                            std::map< edge_descriptor, bool > > >(diG)),
                    iG_vis,
                    associative_property_map<
                        std::map< vertex_descriptor, default_color_type > >(
                        vertex_color),
                    associative_property_map<
                        std::map< edge_descriptor, default_color_type > >(
                        edge_color));
                undirected_dfs(
                    make_filtered_graph(vG,
                        detail::deleted_edge_status< associative_property_map<
                            std::map< edge_descriptor, bool > > >(dvG)),
                    vG_vis,
                    associative_property_map<
                        std::map< vertex_descriptor, default_color_type > >(
                        vertex_color),
                    associative_property_map<
                        std::map< edge_descriptor, default_color_type > >(
                        edge_color));

                found = false;
                std::stack< edge_descriptor > iG_buf_tmp, vG_buf_tmp;
                while (!iG_buf.empty() && !found)
                {
                    if (!inL[iG_bimap.right.at(iG_buf.top())])
                    {
                        put(aiG_inL, iG_buf.top(), true);
                        put(avG_inL,
                            vG_bimap.left.at(iG_bimap.right.at(iG_buf.top())),
                            true);

                        undirected_dfs(
                            make_filtered_graph(iG,
                                detail::inL_edge_status<
                                    associative_property_map<
                                        std::map< edge_descriptor, bool > > >(
                                    aiG_inL)),
                            make_dfs_visitor(detail::cycle_finder<
                                std::stack< edge_descriptor > >(&iG_buf_tmp)),
                            associative_property_map< std::map<
                                vertex_descriptor, default_color_type > >(
                                vertex_color),
                            associative_property_map< std::map< edge_descriptor,
                                default_color_type > >(edge_color));
                        undirected_dfs(
                            make_filtered_graph(vG,
                                detail::inL_edge_status<
                                    associative_property_map<
                                        std::map< edge_descriptor, bool > > >(
                                    avG_inL)),
                            make_dfs_visitor(detail::cycle_finder<
                                std::stack< edge_descriptor > >(&vG_buf_tmp)),
                            associative_property_map< std::map<
                                vertex_descriptor, default_color_type > >(
                                vertex_color),
                            associative_property_map< std::map< edge_descriptor,
                                default_color_type > >(edge_color));

                        if (!iG_buf_tmp.empty() || !vG_buf_tmp.empty())
                        {
                            found = true;
                        }
                        else
                        {
                            while (!iG_buf_tmp.empty())
                                iG_buf_tmp.pop();
                            while (!vG_buf_tmp.empty())
                                vG_buf_tmp.pop();
                            iG_buf_copy.push(iG_buf.top());
                        }

                        put(aiG_inL, iG_buf.top(), false);
                        put(avG_inL,
                            vG_bimap.left.at(iG_bimap.right.at(iG_buf.top())),
                            false);
                    }
                    iG_buf.pop();
                }
                while (!vG_buf.empty() && !found)
                {
                    if (!inL[vG_bimap.right.at(vG_buf.top())])
                    {
                        put(avG_inL, vG_buf.top(), true);
                        put(aiG_inL,
                            iG_bimap.left.at(vG_bimap.right.at(vG_buf.top())),
                            true);

                        undirected_dfs(
                            make_filtered_graph(iG,
                                detail::inL_edge_status<
                                    associative_property_map<
                                        std::map< edge_descriptor, bool > > >(
                                    aiG_inL)),
                            make_dfs_visitor(detail::cycle_finder<
                                std::stack< edge_descriptor > >(&iG_buf_tmp)),
                            associative_property_map< std::map<
                                vertex_descriptor, default_color_type > >(
                                vertex_color),
                            associative_property_map< std::map< edge_descriptor,
                                default_color_type > >(edge_color));
                        undirected_dfs(
                            make_filtered_graph(vG,
                                detail::inL_edge_status<
                                    associative_property_map<
                                        std::map< edge_descriptor, bool > > >(
                                    avG_inL)),
                            make_dfs_visitor(detail::cycle_finder<
                                std::stack< edge_descriptor > >(&vG_buf_tmp)),
                            associative_property_map< std::map<
                                vertex_descriptor, default_color_type > >(
                                vertex_color),
                            associative_property_map< std::map< edge_descriptor,
                                default_color_type > >(edge_color));

                        if (!iG_buf_tmp.empty() || !vG_buf_tmp.empty())
                        {
                            found = true;
                        }
                        else
                        {
                            while (!iG_buf_tmp.empty())
                                iG_buf_tmp.pop();
                            while (!vG_buf_tmp.empty())
                                vG_buf_tmp.pop();
                            vG_buf_copy.push(vG_buf.top());
                        }

                        put(avG_inL, vG_buf.top(), false);
                        put(aiG_inL,
                            iG_bimap.left.at(vG_bimap.right.at(vG_buf.top())),
                            false);
                    }
                    vG_buf.pop();
                }

                if (!found)
                {

                    while (!iG_buf_copy.empty())
                    {
                        inL[iG_bimap.right.at(iG_buf_copy.top())] = true;
                        put(aiG_inL, iG_buf_copy.top(), true);
                        put(avG_inL,
                            vG_bimap.left.at(
                                iG_bimap.right.at(iG_buf_copy.top())),
                            true);
                        iG_buf.push(iG_buf_copy.top());
                        iG_buf_copy.pop();
                    }
                    while (!vG_buf_copy.empty())
                    {
                        inL[vG_bimap.right.at(vG_buf_copy.top())] = true;
                        put(avG_inL, vG_buf_copy.top(), true);
                        put(aiG_inL,
                            iG_bimap.left.at(
                                vG_bimap.right.at(vG_buf_copy.top())),
                            true);
                        vG_buf.push(vG_buf_copy.top());
                        vG_buf_copy.pop();
                    }

                    // REC
                    detail::rec_two_graphs_common_spanning_trees< Graph, Func,
                        Seq, Map >(iG, iG_bimap, aiG_inL, diG, vG, vG_bimap,
                        aiG_inL, dvG, func, inL);

                    while (!iG_buf.empty())
                    {
                        inL[iG_bimap.right.at(iG_buf.top())] = false;
                        put(aiG_inL, iG_buf.top(), false);
                        put(avG_inL,
                            vG_bimap.left.at(iG_bimap.right.at(iG_buf.top())),
                            false);
                        iG_buf.pop();
                    }
                    while (!vG_buf.empty())
                    {
                        inL[vG_bimap.right.at(vG_buf.top())] = false;
                        put(avG_inL, vG_buf.top(), false);
                        put(aiG_inL,
                            iG_bimap.left.at(vG_bimap.right.at(vG_buf.top())),
                            false);
                        vG_buf.pop();
                    }
                }

                put(diG, iG_bimap.left.at(m), false);
                put(dvG, vG_bimap.left.at(m), false);
            }
        }
    }

} // namespace detail

template < typename Coll, typename Seq > struct tree_collector
{

public:
    BOOST_CONCEPT_ASSERT((BackInsertionSequence< Coll >));
    BOOST_CONCEPT_ASSERT((RandomAccessContainer< Seq >));
    BOOST_CONCEPT_ASSERT((CopyConstructible< Seq >));

    typedef typename Coll::value_type coll_value_type;
    typedef typename Seq::value_type seq_value_type;

    BOOST_STATIC_ASSERT((is_same< coll_value_type, Seq >::value));
    BOOST_STATIC_ASSERT((is_same< seq_value_type, bool >::value));

    tree_collector(Coll& seqs) : mSeqs(seqs) {}

    inline void operator()(Seq seq) { mSeqs.push_back(seq); }

private:
    Coll& mSeqs;
};

template < typename Graph, typename Order, typename Func, typename Seq >
BOOST_CONCEPT_REQUIRES(
    ((RandomAccessContainer< Order >))((IncidenceGraphConcept< Graph >))(
        (UnaryFunction< Func, void, Seq >))(
        (Mutable_RandomAccessContainer< Seq >))(
        (VertexAndEdgeListGraphConcept< Graph >)),
    (void))
two_graphs_common_spanning_trees(const Graph& iG, Order iG_map, const Graph& vG,
    Order vG_map, Func func, Seq inL)
{
    typedef graph_traits< Graph > GraphTraits;

    typedef typename GraphTraits::directed_category directed_category;
    typedef typename GraphTraits::vertex_descriptor vertex_descriptor;
    typedef typename GraphTraits::edge_descriptor edge_descriptor;

    typedef typename GraphTraits::edges_size_type edges_size_type;
    typedef typename GraphTraits::edge_iterator edge_iterator;

    typedef typename Seq::value_type seq_value_type;
    typedef typename Seq::size_type seq_size_type;

    typedef typename Order::value_type order_value_type;
    typedef typename Order::size_type order_size_type;

    BOOST_STATIC_ASSERT((is_same< order_value_type, edge_descriptor >::value));
    BOOST_CONCEPT_ASSERT((Convertible< order_size_type, edges_size_type >));

    BOOST_CONCEPT_ASSERT((Convertible< seq_size_type, edges_size_type >));
    BOOST_STATIC_ASSERT((is_same< seq_value_type, bool >::value));

    BOOST_STATIC_ASSERT((is_same< directed_category, undirected_tag >::value));

    if (num_vertices(iG) != num_vertices(vG))
        return;

    if (inL.size() != num_edges(iG) || inL.size() != num_edges(vG))
        return;

    if (iG_map.size() != num_edges(iG) || vG_map.size() != num_edges(vG))
        return;

    typedef bimaps::bimap< bimaps::set_of< int >,
        bimaps::set_of< order_value_type > >
        bimap_type;
    typedef typename bimap_type::value_type bimap_value;

    bimap_type iG_bimap, vG_bimap;
    for (order_size_type i = 0; i < iG_map.size(); ++i)
        iG_bimap.insert(bimap_value(i, iG_map[i]));
    for (order_size_type i = 0; i < vG_map.size(); ++i)
        vG_bimap.insert(bimap_value(i, vG_map[i]));

    edge_iterator current, last;
    boost::tuples::tie(current, last) = edges(iG);
    for (; current != last; ++current)
        if (iG_bimap.right.find(*current) == iG_bimap.right.end())
            return;
    boost::tuples::tie(current, last) = edges(vG);
    for (; current != last; ++current)
        if (vG_bimap.right.find(*current) == vG_bimap.right.end())
            return;

    std::stack< edge_descriptor > iG_buf, vG_buf;

    std::map< vertex_descriptor, edge_descriptor > tree_map;
    std::map< vertex_descriptor, vertex_descriptor > pred_map;
    std::map< vertex_descriptor, int > dist_map, low_map;

    detail::bridges_visitor< associative_property_map< std::map<
                                 vertex_descriptor, edge_descriptor > >,
        associative_property_map<
            std::map< vertex_descriptor, vertex_descriptor > >,
        associative_property_map< std::map< vertex_descriptor, int > >,
        associative_property_map< std::map< vertex_descriptor, int > >,
        std::stack< edge_descriptor > >
    iG_vis(associative_property_map<
               std::map< vertex_descriptor, edge_descriptor > >(tree_map),
        associative_property_map<
            std::map< vertex_descriptor, vertex_descriptor > >(pred_map),
        associative_property_map< std::map< vertex_descriptor, int > >(
            dist_map),
        associative_property_map< std::map< vertex_descriptor, int > >(low_map),
        iG_buf),
        vG_vis(associative_property_map<
                   std::map< vertex_descriptor, edge_descriptor > >(tree_map),
            associative_property_map<
                std::map< vertex_descriptor, vertex_descriptor > >(pred_map),
            associative_property_map< std::map< vertex_descriptor, int > >(
                dist_map),
            associative_property_map< std::map< vertex_descriptor, int > >(
                low_map),
            vG_buf);

    std::map< vertex_descriptor, default_color_type > vertex_color;
    std::map< edge_descriptor, default_color_type > edge_color;

    undirected_dfs(iG, iG_vis,
        associative_property_map<
            std::map< vertex_descriptor, default_color_type > >(vertex_color),
        associative_property_map<
            std::map< edge_descriptor, default_color_type > >(edge_color));
    undirected_dfs(vG, vG_vis,
        associative_property_map<
            std::map< vertex_descriptor, default_color_type > >(vertex_color),
        associative_property_map<
            std::map< edge_descriptor, default_color_type > >(edge_color));

    while (!iG_buf.empty())
    {
        inL[iG_bimap.right.at(iG_buf.top())] = true;
        iG_buf.pop();
    }
    while (!vG_buf.empty())
    {
        inL[vG_bimap.right.at(vG_buf.top())] = true;
        vG_buf.pop();
    }

    std::map< edge_descriptor, bool > iG_inL, vG_inL;
    associative_property_map< std::map< edge_descriptor, bool > > aiG_inL(
        iG_inL),
        avG_inL(vG_inL);

    for (seq_size_type i = 0; i < inL.size(); ++i)
    {
        if (inL[i])
        {
            put(aiG_inL, iG_bimap.left.at(i), true);
            put(avG_inL, vG_bimap.left.at(i), true);
        }
        else
        {
            put(aiG_inL, iG_bimap.left.at(i), false);
            put(avG_inL, vG_bimap.left.at(i), false);
        }
    }

    undirected_dfs(
        make_filtered_graph(iG,
            detail::inL_edge_status<
                associative_property_map< std::map< edge_descriptor, bool > > >(
                aiG_inL)),
        make_dfs_visitor(
            detail::cycle_finder< std::stack< edge_descriptor > >(&iG_buf)),
        associative_property_map<
            std::map< vertex_descriptor, default_color_type > >(vertex_color),
        associative_property_map<
            std::map< edge_descriptor, default_color_type > >(edge_color));
    undirected_dfs(
        make_filtered_graph(vG,
            detail::inL_edge_status<
                associative_property_map< std::map< edge_descriptor, bool > > >(
                avG_inL)),
        make_dfs_visitor(
            detail::cycle_finder< std::stack< edge_descriptor > >(&vG_buf)),
        associative_property_map<
            std::map< vertex_descriptor, default_color_type > >(vertex_color),
        associative_property_map<
            std::map< edge_descriptor, default_color_type > >(edge_color));

    if (iG_buf.empty() && vG_buf.empty())
    {

        std::map< edge_descriptor, bool > iG_deleted, vG_deleted;
        associative_property_map< std::map< edge_descriptor, bool > > diG(
            iG_deleted);
        associative_property_map< std::map< edge_descriptor, bool > > dvG(
            vG_deleted);

        boost::tuples::tie(current, last) = edges(iG);
        for (; current != last; ++current)
            put(diG, *current, false);
        boost::tuples::tie(current, last) = edges(vG);
        for (; current != last; ++current)
            put(dvG, *current, false);

        for (seq_size_type j = 0; j < inL.size(); ++j)
        {
            if (!inL[j])
            {
                put(aiG_inL, iG_bimap.left.at(j), true);
                put(avG_inL, vG_bimap.left.at(j), true);

                undirected_dfs(
                    make_filtered_graph(iG,
                        detail::inL_edge_status< associative_property_map<
                            std::map< edge_descriptor, bool > > >(aiG_inL)),
                    make_dfs_visitor(
                        detail::cycle_finder< std::stack< edge_descriptor > >(
                            &iG_buf)),
                    associative_property_map<
                        std::map< vertex_descriptor, default_color_type > >(
                        vertex_color),
                    associative_property_map<
                        std::map< edge_descriptor, default_color_type > >(
                        edge_color));
                undirected_dfs(
                    make_filtered_graph(vG,
                        detail::inL_edge_status< associative_property_map<
                            std::map< edge_descriptor, bool > > >(avG_inL)),
                    make_dfs_visitor(
                        detail::cycle_finder< std::stack< edge_descriptor > >(
                            &vG_buf)),
                    associative_property_map<
                        std::map< vertex_descriptor, default_color_type > >(
                        vertex_color),
                    associative_property_map<
                        std::map< edge_descriptor, default_color_type > >(
                        edge_color));

                if (!iG_buf.empty() || !vG_buf.empty())
                {
                    while (!iG_buf.empty())
                        iG_buf.pop();
                    while (!vG_buf.empty())
                        vG_buf.pop();
                    put(diG, iG_bimap.left.at(j), true);
                    put(dvG, vG_bimap.left.at(j), true);
                }

                put(aiG_inL, iG_bimap.left.at(j), false);
                put(avG_inL, vG_bimap.left.at(j), false);
            }
        }

        int cc = 0;

        std::map< vertex_descriptor, int > com_map;
        cc += connected_components(
            make_filtered_graph(iG,
                detail::deleted_edge_status< associative_property_map<
                    std::map< edge_descriptor, bool > > >(diG)),
            associative_property_map< std::map< vertex_descriptor, int > >(
                com_map));
        cc += connected_components(
            make_filtered_graph(vG,
                detail::deleted_edge_status< associative_property_map<
                    std::map< edge_descriptor, bool > > >(dvG)),
            associative_property_map< std::map< vertex_descriptor, int > >(
                com_map));

        if (cc != 2)
            return;

        // REC
        detail::rec_two_graphs_common_spanning_trees< Graph, Func, Seq,
            associative_property_map< std::map< edge_descriptor, bool > > >(
            iG, iG_bimap, aiG_inL, diG, vG, vG_bimap, aiG_inL, dvG, func, inL);
    }
}

template < typename Graph, typename Func, typename Seq >
BOOST_CONCEPT_REQUIRES(
    ((IncidenceGraphConcept< Graph >))((EdgeListGraphConcept< Graph >)), (void))
two_graphs_common_spanning_trees(
    const Graph& iG, const Graph& vG, Func func, Seq inL)
{
    typedef graph_traits< Graph > GraphTraits;

    typedef typename GraphTraits::edge_descriptor edge_descriptor;
    typedef typename GraphTraits::edge_iterator edge_iterator;

    std::vector< edge_descriptor > iGO, vGO;
    edge_iterator curr, last;

    boost::tuples::tie(curr, last) = edges(iG);
    for (; curr != last; ++curr)
        iGO.push_back(*curr);

    boost::tuples::tie(curr, last) = edges(vG);
    for (; curr != last; ++curr)
        vGO.push_back(*curr);

    two_graphs_common_spanning_trees(iG, iGO, vG, vGO, func, inL);
}

} // namespace boost

#endif // BOOST_GRAPH_TWO_GRAPHS_COMMON_SPANNING_TREES_HPP