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