[ceph.git] / ceph / src / boost / boost / graph / king_ordering.hpp

//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Copyright 2004, 2005 Trustees of Indiana University
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek,
//          Doug Gregor, D. Kevin McGrath
//
// 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_KING_HPP
#define BOOST_GRAPH_KING_HPP

#include <deque>
#include <vector>
#include <algorithm>
#include <boost/config.hpp>
#include <boost/bind/bind.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/graph/detail/sparse_ordering.hpp>
#include <boost/graph/graph_utility.hpp>

/*
  King Algorithm for matrix reordering
*/

namespace boost
{
namespace detail
{
    template < typename OutputIterator, typename Buffer, typename Compare,
        typename PseudoDegreeMap, typename VecMap, typename VertexIndexMap >
    class bfs_king_visitor : public default_bfs_visitor
    {
    public:
        bfs_king_visitor(OutputIterator* iter, Buffer* b, Compare compare,
            PseudoDegreeMap deg, std::vector< int > loc, VecMap color,
            VertexIndexMap vertices)
        : permutation(iter)
        , Qptr(b)
        , degree(deg)
        , comp(compare)
        , Qlocation(loc)
        , colors(color)
        , vertex_map(vertices)
        {
        }

        template < typename Vertex, typename Graph >
        void finish_vertex(Vertex, Graph& g)
        {
            using namespace boost::placeholders;

            typename graph_traits< Graph >::out_edge_iterator ei, ei_end;
            Vertex v, w;

            typedef typename std::deque< Vertex >::reverse_iterator
                reverse_iterator;

            reverse_iterator rend = Qptr->rend() - index_begin;
            reverse_iterator rbegin = Qptr->rbegin();

            // heap the vertices already there
            std::make_heap(rbegin, rend, boost::bind< bool >(comp, _2, _1));

            unsigned i = 0;

            for (i = index_begin; i != Qptr->size(); ++i)
            {
                colors[get(vertex_map, (*Qptr)[i])] = 1;
                Qlocation[get(vertex_map, (*Qptr)[i])] = i;
            }

            i = 0;

            for (; rbegin != rend; rend--)
            {
                percolate_down< Vertex >(i);
                w = (*Qptr)[index_begin + i];
                for (boost::tie(ei, ei_end) = out_edges(w, g); ei != ei_end;
                     ++ei)
                {
                    v = target(*ei, g);
                    put(degree, v, get(degree, v) - 1);

                    if (colors[get(vertex_map, v)] == 1)
                    {
                        percolate_up< Vertex >(get(vertex_map, v), i);
                    }
                }

                colors[get(vertex_map, w)] = 0;
                i++;
            }
        }

        template < typename Vertex, typename Graph >
        void examine_vertex(Vertex u, const Graph&)
        {

            *(*permutation)++ = u;
            index_begin = Qptr->size();
        }

    protected:
        // this function replaces pop_heap, and tracks state information
        template < typename Vertex > void percolate_down(int offset)
        {
            int heap_last = index_begin + offset;
            int heap_first = Qptr->size() - 1;

            // pop_heap functionality:
            // swap first, last
            std::swap((*Qptr)[heap_last], (*Qptr)[heap_first]);

            // swap in the location queue
            std::swap(Qlocation[heap_first], Qlocation[heap_last]);

            // set drifter, children
            int drifter = heap_first;
            int drifter_heap = Qptr->size() - drifter;

            int right_child_heap = drifter_heap * 2 + 1;
            int right_child = Qptr->size() - right_child_heap;

            int left_child_heap = drifter_heap * 2;
            int left_child = Qptr->size() - left_child_heap;

            // check that we are staying in the heap
            bool valid = (right_child < heap_last) ? false : true;

            // pick smallest child of drifter, and keep in mind there might only
            // be left child
            int smallest_child = (valid
                                     && get(degree, (*Qptr)[left_child])
                                         > get(degree, (*Qptr)[right_child]))
                ? right_child
                : left_child;

            while (valid && smallest_child < heap_last
                && comp((*Qptr)[drifter], (*Qptr)[smallest_child]))
            {

                // if smallest child smaller than drifter, swap them
                std::swap((*Qptr)[smallest_child], (*Qptr)[drifter]);
                std::swap(Qlocation[drifter], Qlocation[smallest_child]);

                // update the values, run again, as necessary
                drifter = smallest_child;
                drifter_heap = Qptr->size() - drifter;

                right_child_heap = drifter_heap * 2 + 1;
                right_child = Qptr->size() - right_child_heap;

                left_child_heap = drifter_heap * 2;
                left_child = Qptr->size() - left_child_heap;

                valid = (right_child < heap_last) ? false : true;

                smallest_child = (valid
                                     && get(degree, (*Qptr)[left_child])
                                         > get(degree, (*Qptr)[right_child]))
                    ? right_child
                    : left_child;
            }
        }

        // this is like percolate down, but we always compare against the
        // parent, as there is only a single choice
        template < typename Vertex > void percolate_up(int vertex, int offset)
        {

            int child_location = Qlocation[vertex];
            int heap_child_location = Qptr->size() - child_location;
            int heap_parent_location = (int)(heap_child_location / 2);
            unsigned parent_location = Qptr->size() - heap_parent_location;

            bool valid = (heap_parent_location != 0
                && child_location > index_begin + offset
                && parent_location < Qptr->size());

            while (valid
                && comp((*Qptr)[child_location], (*Qptr)[parent_location]))
            {

                // swap in the heap
                std::swap((*Qptr)[child_location], (*Qptr)[parent_location]);

                // swap in the location queue
                std::swap(
                    Qlocation[child_location], Qlocation[parent_location]);

                child_location = parent_location;
                heap_child_location = heap_parent_location;
                heap_parent_location = (int)(heap_child_location / 2);
                parent_location = Qptr->size() - heap_parent_location;
                valid = (heap_parent_location != 0
                    && child_location > index_begin + offset);
            }
        }

        OutputIterator* permutation;
        int index_begin;
        Buffer* Qptr;
        PseudoDegreeMap degree;
        Compare comp;
        std::vector< int > Qlocation;
        VecMap colors;
        VertexIndexMap vertex_map;
    };

} // namespace detail

template < class Graph, class OutputIterator, class ColorMap, class DegreeMap,
    typename VertexIndexMap >
OutputIterator king_ordering(const Graph& g,
    std::deque< typename graph_traits< Graph >::vertex_descriptor >
        vertex_queue,
    OutputIterator permutation, ColorMap color, DegreeMap degree,
    VertexIndexMap index_map)
{
    typedef typename property_traits< DegreeMap >::value_type ds_type;
    typedef typename property_traits< ColorMap >::value_type ColorValue;
    typedef color_traits< ColorValue > Color;
    typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
    typedef iterator_property_map< typename std::vector< ds_type >::iterator,
        VertexIndexMap, ds_type, ds_type& >
        PseudoDegreeMap;
    typedef indirect_cmp< PseudoDegreeMap, std::less< ds_type > > Compare;
    typedef typename boost::sparse::sparse_ordering_queue< Vertex > queue;
    typedef typename detail::bfs_king_visitor< OutputIterator, queue, Compare,
        PseudoDegreeMap, std::vector< int >, VertexIndexMap >
        Visitor;
    typedef
        typename graph_traits< Graph >::vertices_size_type vertices_size_type;
    std::vector< ds_type > pseudo_degree_vec(num_vertices(g));
    PseudoDegreeMap pseudo_degree(pseudo_degree_vec.begin(), index_map);

    typename graph_traits< Graph >::vertex_iterator ui, ui_end;
    queue Q;
    // Copy degree to pseudo_degree
    // initialize the color map
    for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui)
    {
        put(pseudo_degree, *ui, get(degree, *ui));
        put(color, *ui, Color::white());
    }

    Compare comp(pseudo_degree);
    std::vector< int > colors(num_vertices(g));

    for (vertices_size_type i = 0; i < num_vertices(g); i++)
        colors[i] = 0;

    std::vector< int > loc(num_vertices(g));

    // create the visitor
    Visitor vis(&permutation, &Q, comp, pseudo_degree, loc, colors, index_map);

    while (!vertex_queue.empty())
    {
        Vertex s = vertex_queue.front();
        vertex_queue.pop_front();

        // call BFS with visitor
        breadth_first_visit(g, s, Q, vis, color);
    }

    return permutation;
}

// This is the case where only a single starting vertex is supplied.
template < class Graph, class OutputIterator, class ColorMap, class DegreeMap,
    typename VertexIndexMap >
OutputIterator king_ordering(const Graph& g,
    typename graph_traits< Graph >::vertex_descriptor s,
    OutputIterator permutation, ColorMap color, DegreeMap degree,
    VertexIndexMap index_map)
{

    std::deque< typename graph_traits< Graph >::vertex_descriptor >
        vertex_queue;
    vertex_queue.push_front(s);
    return king_ordering(
        g, vertex_queue, permutation, color, degree, index_map);
}

template < class Graph, class OutputIterator, class ColorMap, class DegreeMap,
    class VertexIndexMap >
OutputIterator king_ordering(const Graph& G, OutputIterator permutation,
    ColorMap color, DegreeMap degree, VertexIndexMap index_map)
{
    if (has_no_vertices(G))
        return permutation;

    typedef typename boost::graph_traits< Graph >::vertex_descriptor Vertex;
    typedef typename property_traits< ColorMap >::value_type ColorValue;
    typedef color_traits< ColorValue > Color;

    std::deque< Vertex > vertex_queue;

    // Mark everything white
    BGL_FORALL_VERTICES_T(v, G, Graph) put(color, v, Color::white());

    // Find one vertex from each connected component
    BGL_FORALL_VERTICES_T(v, G, Graph)
    {
        if (get(color, v) == Color::white())
        {
            depth_first_visit(G, v, dfs_visitor<>(), color);
            vertex_queue.push_back(v);
        }
    }

    // Find starting nodes for all vertices
    // TBD: How to do this with a directed graph?
    for (typename std::deque< Vertex >::iterator i = vertex_queue.begin();
         i != vertex_queue.end(); ++i)
        *i = find_starting_node(G, *i, color, degree);

    return king_ordering(
        G, vertex_queue, permutation, color, degree, index_map);
}

template < typename Graph, typename OutputIterator, typename VertexIndexMap >
OutputIterator king_ordering(
    const Graph& G, OutputIterator permutation, VertexIndexMap index_map)
{
    if (has_no_vertices(G))
        return permutation;

    std::vector< default_color_type > colors(num_vertices(G));
    return king_ordering(G, permutation,
        make_iterator_property_map(&colors[0], index_map, colors[0]),
        make_out_degree_map(G), index_map);
}

template < typename Graph, typename OutputIterator >
inline OutputIterator king_ordering(const Graph& G, OutputIterator permutation)
{
    return king_ordering(G, permutation, get(vertex_index, G));
}

} // namespace boost

#endif // BOOST_GRAPH_KING_HPP
Commit	Line	Data
7c673cae FG	1	//=======================================================================
	2	// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
	3	// Copyright 2004, 2005 Trustees of Indiana University
	4	// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek,
	5	// Doug Gregor, D. Kevin McGrath
	6	//
	7	// Distributed under the Boost Software License, Version 1.0. (See
	8	// accompanying file LICENSE_1_0.txt or copy at
	9	// http://www.boost.org/LICENSE_1_0.txt)
	10	//=======================================================================//
	11	#ifndef BOOST_GRAPH_KING_HPP
	12	#define BOOST_GRAPH_KING_HPP
	13
1e59de90 TL	14	#include <deque>
	15	#include <vector>
	16	#include <algorithm>
7c673cae	17	#include <boost/config.hpp>
1e59de90 TL	18	#include <boost/bind/bind.hpp>
1e59de90 TL	19	#include <boost/tuple/tuple.hpp>
7c673cae FG	20	#include <boost/graph/detail/sparse_ordering.hpp>
	21	#include <boost/graph/graph_utility.hpp>
	22
	23	/*
	24	King Algorithm for matrix reordering
	25	*/
	26
f67539c2 TL	27	namespace boost
	28	{
	29	namespace detail
	30	{
	31	template < typename OutputIterator, typename Buffer, typename Compare,
	32	typename PseudoDegreeMap, typename VecMap, typename VertexIndexMap >
	33	class bfs_king_visitor : public default_bfs_visitor
7c673cae FG	34	{
7c673cae FG	35	public:
f67539c2 TL	36	bfs_king_visitor(OutputIterator* iter, Buffer* b, Compare compare,
	37	PseudoDegreeMap deg, std::vector< int > loc, VecMap color,
	38	VertexIndexMap vertices)
	39	: permutation(iter)
	40	, Qptr(b)
	41	, degree(deg)
	42	, comp(compare)
	43	, Qlocation(loc)
	44	, colors(color)
	45	, vertex_map(vertices)
	46	{
7c673cae FG	47	}
7c673cae FG	48
f67539c2 TL	49	template < typename Vertex, typename Graph >
	50	void finish_vertex(Vertex, Graph& g)
	51	{
1e59de90 TL	52	using namespace boost::placeholders;
1e59de90 TL	53
f67539c2 TL	54	typename graph_traits< Graph >::out_edge_iterator ei, ei_end;
	55	Vertex v, w;
	56
	57	typedef typename std::deque< Vertex >::reverse_iterator
	58	reverse_iterator;
	59
	60	reverse_iterator rend = Qptr->rend() - index_begin;
	61	reverse_iterator rbegin = Qptr->rbegin();
	62
	63	// heap the vertices already there
	64	std::make_heap(rbegin, rend, boost::bind< bool >(comp, _2, _1));
	65
	66	unsigned i = 0;
	67
	68	for (i = index_begin; i != Qptr->size(); ++i)
	69	{
	70	colors[get(vertex_map, (*Qptr)[i])] = 1;
	71	Qlocation[get(vertex_map, (*Qptr)[i])] = i;
7c673cae	72	}
f67539c2 TL	73
	74	i = 0;
	75
	76	for (; rbegin != rend; rend--)
	77	{
	78	percolate_down< Vertex >(i);
	79	w = (*Qptr)[index_begin + i];
	80	for (boost::tie(ei, ei_end) = out_edges(w, g); ei != ei_end;
	81	++ei)
	82	{
	83	v = target(*ei, g);
	84	put(degree, v, get(degree, v) - 1);
	85
	86	if (colors[get(vertex_map, v)] == 1)
	87	{
	88	percolate_up< Vertex >(get(vertex_map, v), i);
	89	}
	90	}
	91
	92	colors[get(vertex_map, w)] = 0;
	93	i++;
	94	}
	95	}
	96
	97	template < typename Vertex, typename Graph >
	98	void examine_vertex(Vertex u, const Graph&)
	99	{
	100
	101	(permutation)++ = u;
	102	index_begin = Qptr->size();
7c673cae	103	}
f67539c2	104
7c673cae	105	protected:
f67539c2 TL	106	// this function replaces pop_heap, and tracks state information
	107	template < typename Vertex > void percolate_down(int offset)
	108	{
	109	int heap_last = index_begin + offset;
	110	int heap_first = Qptr->size() - 1;
	111
	112	// pop_heap functionality:
	113	// swap first, last
	114	std::swap((Qptr)[heap_last], (Qptr)[heap_first]);
	115
	116	// swap in the location queue
	117	std::swap(Qlocation[heap_first], Qlocation[heap_last]);
	118
	119	// set drifter, children
	120	int drifter = heap_first;
	121	int drifter_heap = Qptr->size() - drifter;
	122
	123	int right_child_heap = drifter_heap * 2 + 1;
	124	int right_child = Qptr->size() - right_child_heap;
	125
	126	int left_child_heap = drifter_heap * 2;
	127	int left_child = Qptr->size() - left_child_heap;
	128
	129	// check that we are staying in the heap
	130	bool valid = (right_child < heap_last) ? false : true;
	131
	132	// pick smallest child of drifter, and keep in mind there might only
	133	// be left child
	134	int smallest_child = (valid
	135	&& get(degree, (*Qptr)[left_child])
	136	> get(degree, (*Qptr)[right_child]))
	137	? right_child
	138	: left_child;
	139
	140	while (valid && smallest_child < heap_last
	141	&& comp((Qptr)[drifter], (Qptr)[smallest_child]))
	142	{
7c673cae	143
f67539c2 TL	144	// if smallest child smaller than drifter, swap them
	145	std::swap((Qptr)[smallest_child], (Qptr)[drifter]);
	146	std::swap(Qlocation[drifter], Qlocation[smallest_child]);
7c673cae	147
f67539c2 TL	148	// update the values, run again, as necessary
	149	drifter = smallest_child;
	150	drifter_heap = Qptr->size() - drifter;
	151
	152	right_child_heap = drifter_heap * 2 + 1;
	153	right_child = Qptr->size() - right_child_heap;
	154
	155	left_child_heap = drifter_heap * 2;
	156	left_child = Qptr->size() - left_child_heap;
	157
	158	valid = (right_child < heap_last) ? false : true;
	159
	160	smallest_child = (valid
	161	&& get(degree, (*Qptr)[left_child])
	162	> get(degree, (*Qptr)[right_child]))
	163	? right_child
	164	: left_child;
	165	}
7c673cae FG	166	}
7c673cae FG	167
f67539c2 TL	168	// this is like percolate down, but we always compare against the
	169	// parent, as there is only a single choice
	170	template < typename Vertex > void percolate_up(int vertex, int offset)
	171	{
	172
	173	int child_location = Qlocation[vertex];
	174	int heap_child_location = Qptr->size() - child_location;
	175	int heap_parent_location = (int)(heap_child_location / 2);
	176	unsigned parent_location = Qptr->size() - heap_parent_location;
	177
	178	bool valid = (heap_parent_location != 0
	179	&& child_location > index_begin + offset
	180	&& parent_location < Qptr->size());
	181
	182	while (valid
	183	&& comp((Qptr)[child_location], (Qptr)[parent_location]))
	184	{
	185
	186	// swap in the heap
	187	std::swap((Qptr)[child_location], (Qptr)[parent_location]);
	188
	189	// swap in the location queue
	190	std::swap(
	191	Qlocation[child_location], Qlocation[parent_location]);
	192
	193	child_location = parent_location;
	194	heap_child_location = heap_parent_location;
	195	heap_parent_location = (int)(heap_child_location / 2);
	196	parent_location = Qptr->size() - heap_parent_location;
	197	valid = (heap_parent_location != 0
	198	&& child_location > index_begin + offset);
	199	}
7c673cae	200	}
f67539c2 TL	201
	202	OutputIterator* permutation;
	203	int index_begin;
	204	Buffer* Qptr;
	205	PseudoDegreeMap degree;
	206	Compare comp;
	207	std::vector< int > Qlocation;
	208	VecMap colors;
	209	VertexIndexMap vertex_map;
7c673cae	210	};
f67539c2 TL	211
	212	} // namespace detail
	213
	214	template < class Graph, class OutputIterator, class ColorMap, class DegreeMap,
	215	typename VertexIndexMap >
	216	OutputIterator king_ordering(const Graph& g,
	217	std::deque< typename graph_traits< Graph >::vertex_descriptor >
	218	vertex_queue,
	219	OutputIterator permutation, ColorMap color, DegreeMap degree,
	220	VertexIndexMap index_map)
	221	{
	222	typedef typename property_traits< DegreeMap >::value_type ds_type;
	223	typedef typename property_traits< ColorMap >::value_type ColorValue;
	224	typedef color_traits< ColorValue > Color;
	225	typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
	226	typedef iterator_property_map< typename std::vector< ds_type >::iterator,
	227	VertexIndexMap, ds_type, ds_type& >
	228	PseudoDegreeMap;
	229	typedef indirect_cmp< PseudoDegreeMap, std::less< ds_type > > Compare;
	230	typedef typename boost::sparse::sparse_ordering_queue< Vertex > queue;
	231	typedef typename detail::bfs_king_visitor< OutputIterator, queue, Compare,
	232	PseudoDegreeMap, std::vector< int >, VertexIndexMap >
	233	Visitor;
	234	typedef
	235	typename graph_traits< Graph >::vertices_size_type vertices_size_type;
	236	std::vector< ds_type > pseudo_degree_vec(num_vertices(g));
7c673cae	237	PseudoDegreeMap pseudo_degree(pseudo_degree_vec.begin(), index_map);
f67539c2 TL	238
f67539c2 TL	239	typename graph_traits< Graph >::vertex_iterator ui, ui_end;
7c673cae FG	240	queue Q;
	241	// Copy degree to pseudo_degree
	242	// initialize the color map
f67539c2 TL	243	for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui)
	244	{
	245	put(pseudo_degree, ui, get(degree, ui));
	246	put(color, *ui, Color::white());
7c673cae	247	}
f67539c2	248
7c673cae	249	Compare comp(pseudo_degree);
f67539c2	250	std::vector< int > colors(num_vertices(g));
7c673cae	251
f67539c2 TL	252	for (vertices_size_type i = 0; i < num_vertices(g); i++)
f67539c2 TL	253	colors[i] = 0;
7c673cae	254
f67539c2	255	std::vector< int > loc(num_vertices(g));
7c673cae	256
f67539c2	257	// create the visitor
7c673cae	258	Visitor vis(&permutation, &Q, comp, pseudo_degree, loc, colors, index_map);
f67539c2 TL	259
	260	while (!vertex_queue.empty())
	261	{
	262	Vertex s = vertex_queue.front();
	263	vertex_queue.pop_front();
	264
	265	// call BFS with visitor
	266	breadth_first_visit(g, s, Q, vis, color);
7c673cae FG	267	}
	268
	269	return permutation;
f67539c2 TL	270	}
	271
	272	// This is the case where only a single starting vertex is supplied.
	273	template < class Graph, class OutputIterator, class ColorMap, class DegreeMap,
	274	typename VertexIndexMap >
	275	OutputIterator king_ordering(const Graph& g,
	276	typename graph_traits< Graph >::vertex_descriptor s,
	277	OutputIterator permutation, ColorMap color, DegreeMap degree,
	278	VertexIndexMap index_map)
	279	{
	280
	281	std::deque< typename graph_traits< Graph >::vertex_descriptor >
	282	vertex_queue;
	283	vertex_queue.push_front(s);
	284	return king_ordering(
	285	g, vertex_queue, permutation, color, degree, index_map);
	286	}
	287
	288	template < class Graph, class OutputIterator, class ColorMap, class DegreeMap,
	289	class VertexIndexMap >
	290	OutputIterator king_ordering(const Graph& G, OutputIterator permutation,
	291	ColorMap color, DegreeMap degree, VertexIndexMap index_map)
	292	{
7c673cae	293	if (has_no_vertices(G))
f67539c2	294	return permutation;
7c673cae	295
f67539c2 TL	296	typedef typename boost::graph_traits< Graph >::vertex_descriptor Vertex;
	297	typedef typename property_traits< ColorMap >::value_type ColorValue;
	298	typedef color_traits< ColorValue > Color;
7c673cae	299
f67539c2	300	std::deque< Vertex > vertex_queue;
7c673cae FG	301
	302	// Mark everything white
	303	BGL_FORALL_VERTICES_T(v, G, Graph) put(color, v, Color::white());
	304
f67539c2 TL	305	// Find one vertex from each connected component
	306	BGL_FORALL_VERTICES_T(v, G, Graph)
	307	{
	308	if (get(color, v) == Color::white())
	309	{
	310	depth_first_visit(G, v, dfs_visitor<>(), color);
	311	vertex_queue.push_back(v);
	312	}
7c673cae FG	313	}
	314
	315	// Find starting nodes for all vertices
	316	// TBD: How to do this with a directed graph?
f67539c2	317	for (typename std::deque< Vertex >::iterator i = vertex_queue.begin();
7c673cae	318	i != vertex_queue.end(); ++i)
f67539c2 TL	319	i = find_starting_node(G, i, color, degree);
	320
	321	return king_ordering(
	322	G, vertex_queue, permutation, color, degree, index_map);
	323	}
	324
	325	template < typename Graph, typename OutputIterator, typename VertexIndexMap >
	326	OutputIterator king_ordering(
	327	const Graph& G, OutputIterator permutation, VertexIndexMap index_map)
	328	{
7c673cae	329	if (has_no_vertices(G))
f67539c2	330	return permutation;
7c673cae	331
f67539c2 TL	332	std::vector< default_color_type > colors(num_vertices(G));
	333	return king_ordering(G, permutation,
	334	make_iterator_property_map(&colors[0], index_map, colors[0]),
	335	make_out_degree_map(G), index_map);
	336	}
7c673cae	337
f67539c2 TL	338	template < typename Graph, typename OutputIterator >
	339	inline OutputIterator king_ordering(const Graph& G, OutputIterator permutation)
	340	{
	341	return king_ordering(G, permutation, get(vertex_index, G));
	342	}
7c673cae FG	343
	344	} // namespace boost
	345
7c673cae	346	#endif // BOOST_GRAPH_KING_HPP