FM / graph

/usr/include/boost/graph

Name	Size	Mode	Actions
detail/	-	0755	rm
distributed/	-	0755	rm
parallel/	-	0755	rm
planar_detail/	-	0755	rm
property_maps/	-	0755	rm
accounting.hpp	876	0644	edit dl rm
adjacency_iterator.hpp	2899	0644	edit dl rm
adjacency_list.hpp	13692	0644	edit dl rm
adjacency_list_io.hpp	11849	0644	edit dl rm
adjacency_matrix.hpp	45743	0644	edit dl rm
adj_list_serialize.hpp	4523	0644	edit dl rm
astar_search.hpp	26736	0644	edit dl rm
bandwidth.hpp	2992	0644	edit dl rm
bc_clustering.hpp	5937	0644	edit dl rm
bellman_ford_shortest_paths.hpp	8229	0644	edit dl rm
betweenness_centrality.hpp	26290	0644	edit dl rm
biconnected_components.hpp	16701	0644	edit dl rm
bipartite.hpp	13492	0644	edit dl rm
boyer_myrvold_planar_test.hpp	9849	0644	edit dl rm
boykov_kolmogorov_max_flow.hpp	47342	0644	edit dl rm
breadth_first_search.hpp	14751	0644	edit dl rm
bron_kerbosch_all_cliques.hpp	11736	0644	edit dl rm
buffer_concepts.hpp	2429	0644	edit dl rm
chrobak_payne_drawing.hpp	8641	0644	edit dl rm
circle_layout.hpp	1924	0644	edit dl rm
closeness_centrality.hpp	6057	0644	edit dl rm
clustering_coefficient.hpp	5726	0644	edit dl rm
compressed_sparse_row_graph.hpp	69887	0644	edit dl rm
connected_components.hpp	4134	0644	edit dl rm
copy.hpp	21225	0644	edit dl rm
core_numbers.hpp	13663	0644	edit dl rm
create_condensation_graph.hpp	3159	0644	edit dl rm
cuthill_mckee_ordering.hpp	5992	0644	edit dl rm
cycle_canceling.hpp	6645	0644	edit dl rm
dag_shortest_paths.hpp	6064	0644	edit dl rm
degree_centrality.hpp	4236	0644	edit dl rm
depth_first_search.hpp	15430	0644	edit dl rm
dijkstra_shortest_paths.hpp	23687	0644	edit dl rm
dijkstra_shortest_paths_no_color_map.hpp	9620	0644	edit dl rm
dimacs.hpp	10448	0644	edit dl rm
directed_graph.hpp	24214	0644	edit dl rm
dll_import_export.hpp	892	0644	edit dl rm
dominator_tree.hpp	17553	0644	edit dl rm
eccentricity.hpp	4611	0644	edit dl rm
edge_coloring.hpp	6809	0644	edit dl rm
edge_connectivity.hpp	6796	0644	edit dl rm
edge_list.hpp	9948	0644	edit dl rm
edmonds_karp_max_flow.hpp	10177	0644	edit dl rm
edmunds_karp_max_flow.hpp	982	0644	edit dl rm
erdos_renyi_generator.hpp	7257	0644	edit dl rm
exception.hpp	1466	0644	edit dl rm
exterior_property.hpp	4289	0644	edit dl rm
filtered_graph.hpp	20098	0644	edit dl rm
find_flow_cost.hpp	1859	0644	edit dl rm
floyd_warshall_shortest.hpp	8510	0644	edit dl rm
fruchterman_reingold.hpp	17325	0644	edit dl rm
geodesic_distance.hpp	8015	0644	edit dl rm
graphml.hpp	13460	0644	edit dl rm
graphviz.hpp	33503	0644	edit dl rm
graph_archetypes.hpp	11008	0644	edit dl rm
graph_as_tree.hpp	4532	0644	edit dl rm
graph_concepts.hpp	19785	0644	edit dl rm
graph_mutability_traits.hpp	4995	0644	edit dl rm
graph_selectors.hpp	1274	0644	edit dl rm
graph_stats.hpp	4394	0644	edit dl rm
graph_traits.hpp	13065	0644	edit dl rm
graph_utility.hpp	16182	0644	edit dl rm
grid_graph.hpp	33830	0644	edit dl rm
gursoy_atun_layout.hpp	13248	0644	edit dl rm
hawick_circuits.hpp	14593	0644	edit dl rm
howard_cycle_ratio.hpp	23107	0644	edit dl rm
incremental_components.hpp	8224	0644	edit dl rm
isomorphism.hpp	26308	0644	edit dl rm
is_kuratowski_subgraph.hpp	10260	0644	edit dl rm
is_straight_line_drawing.hpp	7230	0644	edit dl rm
iteration_macros.hpp	11659	0644	edit dl rm
iteration_macros_undef.hpp	673	0644	edit dl rm
johnson_all_pairs_shortest.hpp	7646	0644	edit dl rm
kamada_kawai_spring_layout.hpp	28048	0644	edit dl rm
king_ordering.hpp	12101	0644	edit dl rm
kruskal_min_spanning_tree.hpp	5743	0644	edit dl rm
labeled_graph.hpp	30914	0644	edit dl rm
leda_graph.hpp	28789	0644	edit dl rm
lookup_edge.hpp	1894	0644	edit dl rm
loop_erased_random_walk.hpp	4436	0644	edit dl rm
make_biconnected_planar.hpp	3513	0644	edit dl rm
make_connected.hpp	2645	0644	edit dl rm
make_maximal_planar.hpp	7578	0644	edit dl rm
matrix_as_graph.hpp	7227	0644	edit dl rm
maximum_adjacency_search.hpp	15125	0644	edit dl rm
maximum_weighted_matching.hpp	49722	0644	edit dl rm
max_cardinality_matching.hpp	31000	0644	edit dl rm
mcgregor_common_subgraphs.hpp	43470	0644	edit dl rm
mesh_graph_generator.hpp	5616	0644	edit dl rm
metis.hpp	10982	0644	edit dl rm
metric_tsp_approx.hpp	10809	0644	edit dl rm
minimum_degree_ordering.hpp	27087	0644	edit dl rm
named_function_params.hpp	39639	0644	edit dl rm
named_graph.hpp	20614	0644	edit dl rm
neighbor_bfs.hpp	11763	0644	edit dl rm
numeric_values.hpp	1814	0644	edit dl rm
one_bit_color_map.hpp	3277	0644	edit dl rm
overloading.hpp	1584	0644	edit dl rm
page_rank.hpp	6164	0644	edit dl rm
planar_canonical_ordering.hpp	7203	0644	edit dl rm
planar_face_traversal.hpp	6020	0644	edit dl rm
plod_generator.hpp	7708	0644	edit dl rm
point_traits.hpp	782	0644	edit dl rm
prim_minimum_spanning_tree.hpp	2960	0644	edit dl rm
profile.hpp	1327	0644	edit dl rm
properties.hpp	12417	0644	edit dl rm
property_iter_range.hpp	4345	0644	edit dl rm
push_relabel_max_flow.hpp	34737	0644	edit dl rm
random.hpp	9672	0644	edit dl rm
random_layout.hpp	988	0644	edit dl rm
random_spanning_tree.hpp	5775	0644	edit dl rm
read_dimacs.hpp	12080	0644	edit dl rm
relax.hpp	4400	0644	edit dl rm
reverse_graph.hpp	22402	0644	edit dl rm
rmat_graph_generator.hpp	19291	0644	edit dl rm
r_c_shortest_paths.hpp	30673	0644	edit dl rm
sequential_vertex_coloring.hpp	4562	0644	edit dl rm
simple_point.hpp	628	0644	edit dl rm
sloan_ordering.hpp	15540	0644	edit dl rm
smallest_last_ordering.hpp	5458	0644	edit dl rm
small_world_generator.hpp	3670	0644	edit dl rm
ssca_graph_generator.hpp	6564	0644	edit dl rm
stanford_graph.hpp	20126	0644	edit dl rm
stoer_wagner_min_cut.hpp	12415	0644	edit dl rm
strong_components.hpp	13009	0644	edit dl rm
st_connected.hpp	2852	0644	edit dl rm
subgraph.hpp	39996	0644	edit dl rm
successive_shortest_path_nonnegative_weights.hpp	10413	0644	edit dl rm
tiernan_all_cycles.hpp	12547	0644	edit dl rm
topological_sort.hpp	2611	0644	edit dl rm
topology.hpp	20389	0644	edit dl rm
transitive_closure.hpp	14260	0644	edit dl rm
transitive_reduction.hpp	5326	0644	edit dl rm
transpose_graph.hpp	1198	0644	edit dl rm
tree_traits.hpp	1338	0644	edit dl rm
two_bit_color_map.hpp	3510	0644	edit dl rm
two_graphs_common_spanning_trees.hpp	34996	0644	edit dl rm
undirected_dfs.hpp	10672	0644	edit dl rm
undirected_graph.hpp	25276	0644	edit dl rm
use_mpi.hpp	437	0644	edit dl rm
vector_as_graph.hpp	10474	0644	edit dl rm
vertex_and_edge_range.hpp	5528	0644	edit dl rm
vf2_sub_graph_iso.hpp	48585	0644	edit dl rm
visitors.hpp	11318	0644	edit dl rm
wavefront.hpp	3932	0644	edit dl rm
write_dimacs.hpp	2889	0644	edit dl rm

Edit: /usr/include/boost/graph/minimum_degree_ordering.hpp (27087B)

//-*-c++-*-
//=======================================================================
// Copyright 1997-2001 University of Notre Dame.
// Authors: Lie-Quan Lee, Jeremy Siek
//
// 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)
//=======================================================================
//
#ifndef BOOST_GRAPH_MINIMUM_DEGREE_ORDERING_HPP
#define BOOST_GRAPH_MINIMUM_DEGREE_ORDERING_HPP

#include <vector>
#include <boost/assert.hpp>
#include <boost/config.hpp>
#include <boost/pending/bucket_sorter.hpp>
#include <boost/detail/numeric_traits.hpp> // for integer_traits
#include <boost/graph/graph_traits.hpp>
#include <boost/property_map/property_map.hpp>

namespace boost
{

namespace detail
{

//
    // Given a set of n integers (where the integer values range from
    // zero to n-1), we want to keep track of a collection of stacks
    // of integers. It so happens that an integer will appear in at
    // most one stack at a time, so the stacks form disjoint sets.
    // Because of these restrictions, we can use one big array to
    // store all the stacks, intertwined with one another.
    // No allocation/deallocation happens in the push()/pop() methods
    // so this is faster than using std::stack's.
    //
    template < class SignedInteger > class Stacks
    {
        typedef SignedInteger value_type;
        typedef typename std::vector< value_type >::size_type size_type;

public:
        Stacks(size_type n) : data(n) {}

//: stack
        class stack
        {
            typedef typename std::vector< value_type >::iterator Iterator;

public:
            stack(Iterator _data, const value_type& head)
            : data(_data), current(head)
            {
            }

// did not use default argument here to avoid internal compiler
            // error in g++.
            stack(Iterator _data)
            : data(_data), current(-(std::numeric_limits< value_type >::max)())
            {
            }

void pop()
            {
                BOOST_ASSERT(!empty());
                current = data[current];
            }
            void push(value_type v)
            {
                data[v] = current;
                current = v;
            }
            bool empty()
            {
                return current == -(std::numeric_limits< value_type >::max)();
            }
            value_type& top() { return current; }

private:
            Iterator data;
            value_type current;
        };

// To return a stack object
        stack make_stack() { return stack(data.begin()); }

protected:
        std::vector< value_type > data;
    };

// marker class, a generalization of coloring.
    //
    // This class is to provide a generalization of coloring which has
    // complexity of amortized constant time to set all vertices' color
    // back to be untagged. It implemented by increasing a tag.
    //
    // The colors are:
    //   not tagged
    //   tagged
    //   multiple_tagged
    //   done
    //
    template < class SignedInteger, class Vertex, class VertexIndexMap >
    class Marker
    {
        typedef SignedInteger value_type;
        typedef typename std::vector< value_type >::size_type size_type;

static value_type done()
        {
            return (std::numeric_limits< value_type >::max)() / 2;
        }

public:
        Marker(size_type _num, VertexIndexMap index_map)
        : tag(1 - (std::numeric_limits< value_type >::max)())
        , data(_num, -(std::numeric_limits< value_type >::max)())
        , id(index_map)
        {
        }

void mark_done(Vertex node) { data[get(id, node)] = done(); }

bool is_done(Vertex node) { return data[get(id, node)] == done(); }

void mark_tagged(Vertex node) { data[get(id, node)] = tag; }

void mark_multiple_tagged(Vertex node)
        {
            data[get(id, node)] = multiple_tag;
        }

bool is_tagged(Vertex node) const { return data[get(id, node)] >= tag; }

bool is_not_tagged(Vertex node) const
        {
            return data[get(id, node)] < tag;
        }

bool is_multiple_tagged(Vertex node) const
        {
            return data[get(id, node)] >= multiple_tag;
        }

void increment_tag()
        {
            const size_type num = data.size();
            ++tag;
            if (tag >= done())
            {
                tag = 1 - (std::numeric_limits< value_type >::max)();
                for (size_type i = 0; i < num; ++i)
                    if (data[i] < done())
                        data[i] = -(std::numeric_limits< value_type >::max)();
            }
        }

void set_multiple_tag(value_type mdeg0)
        {
            const size_type num = data.size();
            multiple_tag = tag + mdeg0;

if (multiple_tag >= done())
            {
                tag = 1 - (std::numeric_limits< value_type >::max)();

for (size_type i = 0; i < num; i++)
                    if (data[i] < done())
                        data[i] = -(std::numeric_limits< value_type >::max)();

multiple_tag = tag + mdeg0;
            }
        }

void set_tag_as_multiple_tag() { tag = multiple_tag; }

protected:
        value_type tag;
        value_type multiple_tag;
        std::vector< value_type > data;
        VertexIndexMap id;
    };

template < class Iterator, class SignedInteger, class Vertex,
        class VertexIndexMap, int offset = 1 >
    class Numbering
    {
        typedef SignedInteger number_type;
        number_type num; // start from 1 instead of zero
        Iterator data;
        number_type max_num;
        VertexIndexMap id;

public:
        Numbering(Iterator _data, number_type _max_num, VertexIndexMap id)
        : num(1), data(_data), max_num(_max_num), id(id)
        {
        }
        void operator()(Vertex node) { data[get(id, node)] = -num; }
        bool all_done(number_type i = 0) const { return num + i > max_num; }
        void increment(number_type i = 1) { num += i; }
        bool is_numbered(Vertex node) const { return data[get(id, node)] < 0; }
        void indistinguishable(Vertex i, Vertex j)
        {
            data[get(id, i)] = -(get(id, j) + offset);
        }
    };

template < class SignedInteger, class Vertex, class VertexIndexMap >
    class degreelists_marker
    {
    public:
        typedef SignedInteger value_type;
        typedef typename std::vector< value_type >::size_type size_type;
        degreelists_marker(size_type n, VertexIndexMap id) : marks(n, 0), id(id)
        {
        }
        void mark_need_update(Vertex i) { marks[get(id, i)] = 1; }
        bool need_update(Vertex i) { return marks[get(id, i)] == 1; }
        bool outmatched_or_done(Vertex i) { return marks[get(id, i)] == -1; }
        void mark(Vertex i) { marks[get(id, i)] = -1; }
        void unmark(Vertex i) { marks[get(id, i)] = 0; }

private:
        std::vector< value_type > marks;
        VertexIndexMap id;
    };

// Helper function object for edge removal
    template < class Graph, class MarkerP, class NumberD, class Stack,
        class VertexIndexMap >
    class predicateRemoveEdge1
    {
        typedef typename graph_traits< Graph >::vertex_descriptor vertex_t;
        typedef typename graph_traits< Graph >::edge_descriptor edge_t;

public:
        predicateRemoveEdge1(Graph& _g, MarkerP& _marker, NumberD _numbering,
            Stack& n_e, VertexIndexMap id)
        : g(&_g)
        , marker(&_marker)
        , numbering(_numbering)
        , neighbor_elements(&n_e)
        , id(id)
        {
        }

bool operator()(edge_t e)
        {
            vertex_t dist = target(e, *g);
            if (marker->is_tagged(dist))
                return true;
            marker->mark_tagged(dist);
            if (numbering.is_numbered(dist))
            {
                neighbor_elements->push(get(id, dist));
                return true;
            }
            return false;
        }

private:
        Graph* g;
        MarkerP* marker;
        NumberD numbering;
        Stack* neighbor_elements;
        VertexIndexMap id;
    };

// Helper function object for edge removal
    template < class Graph, class MarkerP > class predicate_remove_tagged_edges
    {
        typedef typename graph_traits< Graph >::vertex_descriptor vertex_t;
        typedef typename graph_traits< Graph >::edge_descriptor edge_t;

public:
        predicate_remove_tagged_edges(Graph& _g, MarkerP& _marker)
        : g(&_g), marker(&_marker)
        {
        }

bool operator()(edge_t e)
        {
            vertex_t dist = target(e, *g);
            if (marker->is_tagged(dist))
                return true;
            return false;
        }

private:
        Graph* g;
        MarkerP* marker;
    };

template < class Graph, class DegreeMap, class InversePermutationMap,
        class PermutationMap, class SuperNodeMap, class VertexIndexMap >
    class mmd_impl
    {
        // Typedefs
        typedef graph_traits< Graph > Traits;
        typedef typename Traits::vertices_size_type size_type;
        typedef typename detail::integer_traits< size_type >::difference_type
            diff_t;
        typedef typename Traits::vertex_descriptor vertex_t;
        typedef typename Traits::adjacency_iterator adj_iter;
        typedef iterator_property_map< vertex_t*, identity_property_map,
            vertex_t, vertex_t& >
            IndexVertexMap;
        typedef detail::Stacks< diff_t > Workspace;
        typedef bucket_sorter< size_type, vertex_t, DegreeMap, VertexIndexMap >
            DegreeLists;
        typedef Numbering< InversePermutationMap, diff_t, vertex_t,
            VertexIndexMap >
            NumberingD;
        typedef degreelists_marker< diff_t, vertex_t, VertexIndexMap >
            DegreeListsMarker;
        typedef Marker< diff_t, vertex_t, VertexIndexMap > MarkerP;

// Data Members
        bool has_no_edges;

// input parameters
        Graph& G;
        int delta;
        DegreeMap degree;
        InversePermutationMap inverse_perm;
        PermutationMap perm;
        SuperNodeMap supernode_size;
        VertexIndexMap vertex_index_map;

// internal data-structures
        std::vector< vertex_t > index_vertex_vec;
        size_type n;
        IndexVertexMap index_vertex_map;
        DegreeLists degreelists;
        NumberingD numbering;
        DegreeListsMarker degree_lists_marker;
        MarkerP marker;
        Workspace work_space;

public:
        mmd_impl(Graph& g, size_type n_, int delta, DegreeMap degree,
            InversePermutationMap inverse_perm, PermutationMap perm,
            SuperNodeMap supernode_size, VertexIndexMap id)
        : has_no_edges(true)
        , G(g)
        , delta(delta)
        , degree(degree)
        , inverse_perm(inverse_perm)
        , perm(perm)
        , supernode_size(supernode_size)
        , vertex_index_map(id)
        , index_vertex_vec(n_)
        , n(n_)
        , degreelists(n_ + 1, n_, degree, id)
        , numbering(inverse_perm, n_, vertex_index_map)
        , degree_lists_marker(n_, vertex_index_map)
        , marker(n_, vertex_index_map)
        , work_space(n_)
        {
            typename graph_traits< Graph >::vertex_iterator v, vend;
            size_type vid = 0;
            for (boost::tie(v, vend) = vertices(G); v != vend; ++v, ++vid)
                index_vertex_vec[vid] = *v;
            index_vertex_map = IndexVertexMap(&index_vertex_vec[0]);

// Initialize degreelists.  Degreelists organizes the nodes
            // according to their degree.
            for (boost::tie(v, vend) = vertices(G); v != vend; ++v)
            {
                typename Traits::degree_size_type d = out_degree(*v, G);
                put(degree, *v, d);
                if (0 < d)
                    has_no_edges = false;
                degreelists.push(*v);
            }
        }

void do_mmd()
        {
            // Eliminate the isolated nodes -- these are simply the nodes
            // with no neighbors, which are accessible as a list (really, a
            // stack) at location 0.  Since these don't affect any other
            // nodes, we can eliminate them without doing degree updates.
            typename DegreeLists::stack list_isolated = degreelists[0];
            while (!list_isolated.empty())
            {
                vertex_t node = list_isolated.top();
                marker.mark_done(node);
                numbering(node);
                numbering.increment();
                list_isolated.pop();
            }

if (has_no_edges)
            {
                return;
            }

size_type min_degree = 1;
            typename DegreeLists::stack list_min_degree
                = degreelists[min_degree];

while (list_min_degree.empty())
            {
                ++min_degree;
                list_min_degree = degreelists[min_degree];
            }

// check if the whole eliminating process is done
            while (!numbering.all_done())
            {

size_type min_degree_limit = min_degree + delta; // WARNING
                typename Workspace::stack llist = work_space.make_stack();

// multiple elimination
                while (delta >= 0)
                {

// Find the next non-empty degree
                    for (list_min_degree = degreelists[min_degree];
                         list_min_degree.empty()
                         && min_degree <= min_degree_limit;
                         ++min_degree,
                        list_min_degree = degreelists[min_degree])
                        ;
                    if (min_degree > min_degree_limit)
                        break;

const vertex_t node = list_min_degree.top();
                    const size_type node_id = get(vertex_index_map, node);
                    list_min_degree.pop();
                    numbering(node);

// check if node is the last one
                    if (numbering.all_done(supernode_size[node]))
                    {
                        numbering.increment(supernode_size[node]);
                        break;
                    }
                    marker.increment_tag();
                    marker.mark_tagged(node);

this->eliminate(node);

numbering.increment(supernode_size[node]);
                    llist.push(node_id);
                } // multiple elimination

if (numbering.all_done())
                    break;

this->update(llist, min_degree);
            }

} // do_mmd()

void eliminate(vertex_t node)
        {
            typename Workspace::stack element_neighbor
                = work_space.make_stack();

// Create two function objects for edge removal
            typedef typename Workspace::stack WorkStack;
            predicateRemoveEdge1< Graph, MarkerP, NumberingD, WorkStack,
                VertexIndexMap >
                p(G, marker, numbering, element_neighbor, vertex_index_map);

predicate_remove_tagged_edges< Graph, MarkerP > p2(G, marker);

// Reconstruct the adjacent node list, push element neighbor in a
            // List.
            remove_out_edge_if(node, p, G);
            // during removal element neighbors are collected.

while (!element_neighbor.empty())
            {
                // element absorb
                size_type e_id = element_neighbor.top();
                vertex_t element = get(index_vertex_map, e_id);
                adj_iter i, i_end;
                for (boost::tie(i, i_end) = adjacent_vertices(element, G);
                     i != i_end; ++i)
                {
                    vertex_t i_node = *i;
                    if (!marker.is_tagged(i_node)
                        && !numbering.is_numbered(i_node))
                    {
                        marker.mark_tagged(i_node);
                        add_edge(node, i_node, G);
                    }
                }
                element_neighbor.pop();
            }
            adj_iter v, ve;
            for (boost::tie(v, ve) = adjacent_vertices(node, G); v != ve; ++v)
            {
                vertex_t v_node = *v;
                if (!degree_lists_marker.need_update(v_node)
                    && !degree_lists_marker.outmatched_or_done(v_node))
                {
                    degreelists.remove(v_node);
                }
                // update out edges of v_node
                remove_out_edge_if(v_node, p2, G);

if (out_degree(v_node, G) == 0)
                { // indistinguishable nodes
                    supernode_size[node] += supernode_size[v_node];
                    supernode_size[v_node] = 0;
                    numbering.indistinguishable(v_node, node);
                    marker.mark_done(v_node);
                    degree_lists_marker.mark(v_node);
                }
                else
                { // not indistinguishable nodes
                    add_edge(v_node, node, G);
                    degree_lists_marker.mark_need_update(v_node);
                }
            }
        } // eliminate()

template < class Stack > void update(Stack llist, size_type& min_degree)
        {
            size_type min_degree0 = min_degree + delta + 1;

while (!llist.empty())
            {
                size_type deg, deg0 = 0;

marker.set_multiple_tag(min_degree0);
                typename Workspace::stack q2list = work_space.make_stack();
                typename Workspace::stack qxlist = work_space.make_stack();

vertex_t current = get(index_vertex_map, llist.top());
                adj_iter i, ie;
                for (boost::tie(i, ie) = adjacent_vertices(current, G); i != ie;
                     ++i)
                {
                    vertex_t i_node = *i;
                    const size_type i_id = get(vertex_index_map, i_node);
                    if (supernode_size[i_node] != 0)
                    {
                        deg0 += supernode_size[i_node];
                        marker.mark_multiple_tagged(i_node);
                        if (degree_lists_marker.need_update(i_node))
                        {
                            if (out_degree(i_node, G) == 2)
                                q2list.push(i_id);
                            else
                                qxlist.push(i_id);
                        }
                    }
                }

while (!q2list.empty())
                {
                    const size_type u_id = q2list.top();
                    vertex_t u_node = get(index_vertex_map, u_id);
                    // if u_id is outmatched by others, no need to update degree
                    if (degree_lists_marker.outmatched_or_done(u_node))
                    {
                        q2list.pop();
                        continue;
                    }
                    marker.increment_tag();
                    deg = deg0;

adj_iter nu = adjacent_vertices(u_node, G).first;
                    vertex_t neighbor = *nu;
                    if (neighbor == u_node)
                    {
                        ++nu;
                        neighbor = *nu;
                    }
                    if (numbering.is_numbered(neighbor))
                    {
                        adj_iter i, ie;
                        for (boost::tie(i, ie) = adjacent_vertices(neighbor, G);
                             i != ie; ++i)
                        {
                            const vertex_t i_node = *i;
                            if (i_node == u_node || supernode_size[i_node] == 0)
                                continue;
                            if (marker.is_tagged(i_node))
                            {
                                if (degree_lists_marker.need_update(i_node))
                                {
                                    if (out_degree(i_node, G) == 2)
                                    { // is indistinguishable
                                        supernode_size[u_node]
                                            += supernode_size[i_node];
                                        supernode_size[i_node] = 0;
                                        numbering.indistinguishable(
                                            i_node, u_node);
                                        marker.mark_done(i_node);
                                        degree_lists_marker.mark(i_node);
                                    }
                                    else // is outmatched
                                        degree_lists_marker.mark(i_node);
                                }
                            }
                            else
                            {
                                marker.mark_tagged(i_node);
                                deg += supernode_size[i_node];
                            }
                        }
                    }
                    else
                        deg += supernode_size[neighbor];

deg -= supernode_size[u_node];
                    degree[u_node] = deg; // update degree
                    degreelists[deg].push(u_node);
                    // u_id has been pushed back into degreelists
                    degree_lists_marker.unmark(u_node);
                    if (min_degree > deg)
                        min_degree = deg;
                    q2list.pop();
                } // while (!q2list.empty())

while (!qxlist.empty())
                {
                    const size_type u_id = qxlist.top();
                    const vertex_t u_node = get(index_vertex_map, u_id);

// if u_id is outmatched by others, no need to update degree
                    if (degree_lists_marker.outmatched_or_done(u_node))
                    {
                        qxlist.pop();
                        continue;
                    }
                    marker.increment_tag();
                    deg = deg0;
                    adj_iter i, ie;
                    for (boost::tie(i, ie) = adjacent_vertices(u_node, G);
                         i != ie; ++i)
                    {
                        vertex_t i_node = *i;
                        if (marker.is_tagged(i_node))
                            continue;
                        marker.mark_tagged(i_node);

if (numbering.is_numbered(i_node))
                        {
                            adj_iter j, je;
                            for (boost::tie(j, je)
                                 = adjacent_vertices(i_node, G);
                                 j != je; ++j)
                            {
                                const vertex_t j_node = *j;
                                if (marker.is_not_tagged(j_node))
                                {
                                    marker.mark_tagged(j_node);
                                    deg += supernode_size[j_node];
                                }
                            }
                        }
                        else
                            deg += supernode_size[i_node];
                    } // for adjacent vertices of u_node
                    deg -= supernode_size[u_node];
                    degree[u_node] = deg;
                    degreelists[deg].push(u_node);
                    // u_id has been pushed back into degreelists
                    degree_lists_marker.unmark(u_node);
                    if (min_degree > deg)
                        min_degree = deg;
                    qxlist.pop();
                } // while (!qxlist.empty()) {

marker.set_tag_as_multiple_tag();
                llist.pop();
            } // while (! llist.empty())

} // update()

void build_permutation(InversePermutationMap next, PermutationMap prev)
        {
            // collect the permutation info
            size_type i;
            for (i = 0; i < n; ++i)
            {
                diff_t size = supernode_size[get(index_vertex_map, i)];
                if (size <= 0)
                {
                    prev[i] = next[i];
                    supernode_size[get(index_vertex_map, i)]
                        = next[i] + 1; // record the supernode info
                }
                else
                    prev[i] = -next[i];
            }
            for (i = 1; i < n + 1; ++i)
            {
                if (prev[i - 1] > 0)
                    continue;
                diff_t parent = i;
                while (prev[parent - 1] < 0)
                {
                    parent = -prev[parent - 1];
                }

diff_t root = parent;
                diff_t num = prev[root - 1] + 1;
                next[i - 1] = -num;
                prev[root - 1] = num;

parent = i;
                diff_t next_node = -prev[parent - 1];
                while (next_node > 0)
                {
                    prev[parent - 1] = -root;
                    parent = next_node;
                    next_node = -prev[parent - 1];
                }
            }
            for (i = 0; i < n; i++)
            {
                diff_t num = -next[i] - 1;
                next[i] = num;
                prev[num] = i;
            }
        } // build_permutation()
    };

} // namespace detail

// MMD algorithm
//
// The implementation presently includes the enhancements for mass
// elimination, incomplete degree update, multiple elimination, and
// external degree.
//
// Important Note: This implementation requires the BGL graph to be
// directed.  Therefore, nonzero entry (i, j) in a symmetrical matrix
// A coresponds to two directed edges (i->j and j->i).
//
// see Alan George and Joseph W. H. Liu, The Evolution of the Minimum
// Degree Ordering Algorithm, SIAM Review, 31, 1989, Page 1-19
template < class Graph, class DegreeMap, class InversePermutationMap,
    class PermutationMap, class SuperNodeMap, class VertexIndexMap >
void minimum_degree_ordering(Graph& G, DegreeMap degree,
    InversePermutationMap inverse_perm, PermutationMap perm,
    SuperNodeMap supernode_size, int delta, VertexIndexMap vertex_index_map)
{
    detail::mmd_impl< Graph, DegreeMap, InversePermutationMap, PermutationMap,
        SuperNodeMap, VertexIndexMap >
        impl(G, num_vertices(G), delta, degree, inverse_perm, perm,
            supernode_size, vertex_index_map);
    impl.do_mmd();
    impl.build_permutation(inverse_perm, perm);
}

} // namespace boost

#endif // BOOST_GRAPH_MINIMUM_DEGREE_ORDERING_HPP

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