Chris@16: //=======================================================================
Chris@16: // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
Chris@16: // Copyright 2004, 2005 Trustees of Indiana University
Chris@16: // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek,
Chris@16: //          Doug Gregor, D. Kevin McGrath
Chris@16: //
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //=======================================================================//
Chris@16: #ifndef BOOST_GRAPH_KING_HPP
Chris@16: #define BOOST_GRAPH_KING_HPP
Chris@16: 
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/graph/detail/sparse_ordering.hpp>
Chris@16: #include <boost/graph/graph_utility.hpp>
Chris@16: 
Chris@16: /*
Chris@16:   King Algorithm for matrix reordering
Chris@16: */
Chris@16: 
Chris@16: namespace boost {
Chris@16:   namespace detail {
Chris@16:     template<typename OutputIterator, typename Buffer, typename Compare, 
Chris@16:              typename PseudoDegreeMap, typename VecMap, typename VertexIndexMap>
Chris@16:     class bfs_king_visitor:public default_bfs_visitor
Chris@16:     {
Chris@16:     public:
Chris@16:       bfs_king_visitor(OutputIterator *iter, Buffer *b, Compare compare, 
Chris@16:                        PseudoDegreeMap deg, std::vector<int> loc, VecMap color, 
Chris@16:                        VertexIndexMap vertices): 
Chris@16:         permutation(iter), Qptr(b), degree(deg), comp(compare), 
Chris@16:         Qlocation(loc), colors(color), vertex_map(vertices) { }
Chris@16:       
Chris@16:       template <typename Vertex, typename Graph>
Chris@16:       void finish_vertex(Vertex, Graph& g) {
Chris@16:         typename graph_traits<Graph>::out_edge_iterator ei, ei_end;
Chris@16:         Vertex v, w;
Chris@16: 
Chris@16:         typedef typename std::deque<Vertex>::reverse_iterator reverse_iterator;
Chris@16: 
Chris@16:         reverse_iterator rend = Qptr->rend()-index_begin;
Chris@16:         reverse_iterator rbegin = Qptr->rbegin();
Chris@16: 
Chris@16: 
Chris@16:         //heap the vertices already there
Chris@16:         std::make_heap(rbegin, rend, boost::bind<bool>(comp, _2, _1));
Chris@16: 
Chris@16:         unsigned i = 0;
Chris@16:         
Chris@16:         for(i = index_begin; i != Qptr->size(); ++i){
Chris@16:           colors[get(vertex_map, (*Qptr)[i])] = 1;
Chris@16:           Qlocation[get(vertex_map, (*Qptr)[i])] = i;
Chris@16:         }
Chris@16: 
Chris@16:         i = 0;
Chris@16: 
Chris@16:         for( ; rbegin != rend; rend--){
Chris@16:           percolate_down<Vertex>(i);
Chris@16:           w = (*Qptr)[index_begin+i];
Chris@16:           for (boost::tie(ei, ei_end) = out_edges(w, g); ei != ei_end; ++ei) {
Chris@16:             v = target(*ei, g);
Chris@16:             put(degree, v, get(degree, v) - 1);
Chris@16:     
Chris@16:             if (colors[get(vertex_map, v)] == 1) {
Chris@16:               percolate_up<Vertex>(get(vertex_map, v), i);            
Chris@16:             }
Chris@16:           }
Chris@16:           
Chris@16:           colors[get(vertex_map, w)] = 0;
Chris@16:           i++;
Chris@16:         }
Chris@16:       }
Chris@16:     
Chris@16:       template <typename Vertex, typename Graph>
Chris@16:       void examine_vertex(Vertex u, const Graph&) {
Chris@16:         
Chris@16:         *(*permutation)++ = u;
Chris@16:         index_begin = Qptr->size();
Chris@16:         
Chris@16:       }
Chris@16:     protected:
Chris@16: 
Chris@16: 
Chris@16:       //this function replaces pop_heap, and tracks state information
Chris@16:       template <typename Vertex>
Chris@16:       void percolate_down(int offset){
Chris@16:         int heap_last = index_begin + offset;
Chris@16:         int heap_first = Qptr->size() - 1;
Chris@16:         
Chris@16:         //pop_heap functionality:
Chris@16:         //swap first, last
Chris@16:         std::swap((*Qptr)[heap_last], (*Qptr)[heap_first]);
Chris@16:         
Chris@16:         //swap in the location queue
Chris@16:         std::swap(Qlocation[heap_first], Qlocation[heap_last]);
Chris@16: 
Chris@16:         //set drifter, children
Chris@16:         int drifter = heap_first;
Chris@16:         int drifter_heap = Qptr->size() - drifter;
Chris@16: 
Chris@16:         int right_child_heap = drifter_heap * 2 + 1;
Chris@16:         int right_child = Qptr->size() - right_child_heap;
Chris@16: 
Chris@16:         int left_child_heap = drifter_heap * 2;
Chris@16:         int left_child = Qptr->size() - left_child_heap;
Chris@16: 
Chris@16:         //check that we are staying in the heap
Chris@16:         bool valid = (right_child < heap_last) ? false : true;
Chris@16:         
Chris@16:         //pick smallest child of drifter, and keep in mind there might only be left child
Chris@16:         int smallest_child = (valid && get(degree, (*Qptr)[left_child]) > get(degree,(*Qptr)[right_child])) ? 
Chris@16:           right_child : left_child;
Chris@16:         
Chris@16:         while(valid && smallest_child < heap_last && comp((*Qptr)[drifter], (*Qptr)[smallest_child])){
Chris@16:           
Chris@16:           //if smallest child smaller than drifter, swap them
Chris@16:           std::swap((*Qptr)[smallest_child], (*Qptr)[drifter]);
Chris@16:           std::swap(Qlocation[drifter], Qlocation[smallest_child]);
Chris@16: 
Chris@16:           //update the values, run again, as necessary
Chris@16:           drifter = smallest_child;
Chris@16:           drifter_heap = Qptr->size() - drifter;
Chris@16: 
Chris@16:           right_child_heap = drifter_heap * 2 + 1;
Chris@16:           right_child = Qptr->size() - right_child_heap;
Chris@16: 
Chris@16:           left_child_heap = drifter_heap * 2;
Chris@16:           left_child = Qptr->size() - left_child_heap;
Chris@16: 
Chris@16:           valid = (right_child < heap_last) ? false : true;
Chris@16: 
Chris@16:           smallest_child = (valid && get(degree, (*Qptr)[left_child]) > get(degree,(*Qptr)[right_child])) ? 
Chris@16:             right_child : left_child;
Chris@16:         }
Chris@16: 
Chris@16:       }
Chris@16: 
Chris@16: 
Chris@16:       
Chris@16:       // this is like percolate down, but we always compare against the
Chris@16:       // parent, as there is only a single choice
Chris@16:       template <typename Vertex>
Chris@16:       void percolate_up(int vertex, int offset){
Chris@16:         
Chris@16:         int child_location = Qlocation[vertex];
Chris@16:         int heap_child_location = Qptr->size() - child_location;
Chris@16:         int heap_parent_location = (int)(heap_child_location/2);
Chris@16:         unsigned parent_location = Qptr->size() - heap_parent_location; 
Chris@16: 
Chris@16:         bool valid = (heap_parent_location != 0 && child_location > index_begin + offset && 
Chris@16:                       parent_location < Qptr->size());
Chris@16: 
Chris@16:         while(valid && comp((*Qptr)[child_location], (*Qptr)[parent_location])){
Chris@16:           
Chris@16:           //swap in the heap
Chris@16:           std::swap((*Qptr)[child_location], (*Qptr)[parent_location]);
Chris@16:           
Chris@16:           //swap in the location queue
Chris@16:           std::swap(Qlocation[child_location], Qlocation[parent_location]);
Chris@16: 
Chris@16:           child_location = parent_location;
Chris@16:           heap_child_location = heap_parent_location;
Chris@16:           heap_parent_location = (int)(heap_child_location/2);
Chris@16:           parent_location = Qptr->size() - heap_parent_location; 
Chris@16:           valid = (heap_parent_location != 0 && child_location > index_begin + offset);
Chris@16:         }
Chris@16:       }
Chris@16:       
Chris@16:       OutputIterator *permutation;
Chris@16:       int index_begin;
Chris@16:       Buffer *Qptr;
Chris@16:       PseudoDegreeMap degree;
Chris@16:       Compare comp;
Chris@16:       std::vector<int> Qlocation;
Chris@16:       VecMap colors;
Chris@16:       VertexIndexMap vertex_map;
Chris@16:     };
Chris@16:   
Chris@16: 
Chris@16:   } // namespace detail  
Chris@16:   
Chris@16: 
Chris@16:   template<class Graph, class OutputIterator, class ColorMap, class DegreeMap,
Chris@16:            typename VertexIndexMap> 
Chris@16:   OutputIterator
Chris@16:   king_ordering(const Graph& g,
Chris@16:                 std::deque< typename graph_traits<Graph>::vertex_descriptor >
Chris@16:                   vertex_queue,
Chris@16:                 OutputIterator permutation, 
Chris@16:                 ColorMap color, DegreeMap degree,
Chris@16:                 VertexIndexMap index_map)
Chris@16:   {
Chris@16:     typedef typename property_traits<DegreeMap>::value_type ds_type;
Chris@16:     typedef typename property_traits<ColorMap>::value_type ColorValue;
Chris@16:     typedef color_traits<ColorValue> Color;
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:     typedef iterator_property_map<typename std::vector<ds_type>::iterator, VertexIndexMap, ds_type, ds_type&> PseudoDegreeMap;
Chris@16:     typedef indirect_cmp<PseudoDegreeMap, std::less<ds_type> > Compare;
Chris@16:     typedef typename boost::sparse::sparse_ordering_queue<Vertex> queue;
Chris@16:     typedef typename detail::bfs_king_visitor<OutputIterator, queue, Compare,             
Chris@16:       PseudoDegreeMap, std::vector<int>, VertexIndexMap > Visitor;
Chris@16:     typedef typename graph_traits<Graph>::vertices_size_type
Chris@16:       vertices_size_type;
Chris@16:     std::vector<ds_type> pseudo_degree_vec(num_vertices(g));
Chris@16:     PseudoDegreeMap pseudo_degree(pseudo_degree_vec.begin(), index_map);
Chris@16:     
Chris@16:     typename graph_traits<Graph>::vertex_iterator ui, ui_end;    
Chris@16:     queue Q;
Chris@16:     // Copy degree to pseudo_degree
Chris@16:     // initialize the color map
Chris@16:     for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui){
Chris@16:       put(pseudo_degree, *ui, get(degree, *ui));
Chris@16:       put(color, *ui, Color::white());
Chris@16:     }
Chris@16:     
Chris@16:     Compare comp(pseudo_degree);
Chris@16:     std::vector<int> colors(num_vertices(g));
Chris@16: 
Chris@16:     for(vertices_size_type i = 0; i < num_vertices(g); i++) 
Chris@16:       colors[i] = 0;
Chris@16: 
Chris@16:     std::vector<int> loc(num_vertices(g));
Chris@16: 
Chris@16:     //create the visitor
Chris@16:     Visitor vis(&permutation, &Q, comp, pseudo_degree, loc, colors, index_map);
Chris@16:     
Chris@16:     while( !vertex_queue.empty() ) {
Chris@16:       Vertex s = vertex_queue.front();
Chris@16:       vertex_queue.pop_front();
Chris@16:       
Chris@16:       //call BFS with visitor
Chris@16:       breadth_first_visit(g, s, Q, vis, color);
Chris@16:     }
Chris@16: 
Chris@16:     return permutation;
Chris@16:   }
Chris@16: 
Chris@16:   
Chris@16:   // This is the case where only a single starting vertex is supplied.
Chris@16:   template <class Graph, class OutputIterator,
Chris@16:             class ColorMap, class DegreeMap, typename VertexIndexMap>
Chris@16:   OutputIterator
Chris@16:   king_ordering(const Graph& g,
Chris@16:                 typename graph_traits<Graph>::vertex_descriptor s,
Chris@16:                 OutputIterator permutation, 
Chris@16:                 ColorMap color, DegreeMap degree, VertexIndexMap index_map)
Chris@16:   {
Chris@16: 
Chris@16:     std::deque< typename graph_traits<Graph>::vertex_descriptor > vertex_queue;
Chris@16:     vertex_queue.push_front( s );
Chris@16:     return king_ordering(g, vertex_queue, permutation, color, degree,
Chris@16:                          index_map);
Chris@16:   }
Chris@16: 
Chris@16:   
Chris@16:   template < class Graph, class OutputIterator, 
Chris@16:              class ColorMap, class DegreeMap, class VertexIndexMap>
Chris@16:   OutputIterator 
Chris@16:   king_ordering(const Graph& G, OutputIterator permutation, 
Chris@16:                 ColorMap color, DegreeMap degree, VertexIndexMap index_map)
Chris@16:   {
Chris@16:     if (has_no_vertices(G))
Chris@16:       return permutation;
Chris@16: 
Chris@16:     typedef typename boost::graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:     typedef typename property_traits<ColorMap>::value_type ColorValue;
Chris@16:     typedef color_traits<ColorValue> Color;
Chris@16: 
Chris@16:     std::deque<Vertex>      vertex_queue;
Chris@16: 
Chris@16:     // Mark everything white
Chris@16:     BGL_FORALL_VERTICES_T(v, G, Graph) put(color, v, Color::white());
Chris@16: 
Chris@16:     // Find one vertex from each connected component 
Chris@16:     BGL_FORALL_VERTICES_T(v, G, Graph) {
Chris@16:       if (get(color, v) == Color::white()) {
Chris@16:         depth_first_visit(G, v, dfs_visitor<>(), color);
Chris@16:         vertex_queue.push_back(v);
Chris@16:       }
Chris@16:     }
Chris@16: 
Chris@16:     // Find starting nodes for all vertices
Chris@16:     // TBD: How to do this with a directed graph?
Chris@16:     for (typename std::deque<Vertex>::iterator i = vertex_queue.begin();
Chris@16:          i != vertex_queue.end(); ++i)
Chris@16:       *i = find_starting_node(G, *i, color, degree);
Chris@16:     
Chris@16:     return king_ordering(G, vertex_queue, permutation, color, degree,
Chris@16:                          index_map);
Chris@16:   }
Chris@16: 
Chris@16:   template<typename Graph, typename OutputIterator, typename VertexIndexMap>
Chris@16:   OutputIterator 
Chris@16:   king_ordering(const Graph& G, OutputIterator permutation, 
Chris@16:                 VertexIndexMap index_map)
Chris@16:   {
Chris@16:     if (has_no_vertices(G))
Chris@16:       return permutation;
Chris@16: 
Chris@16:     std::vector<default_color_type> colors(num_vertices(G));
Chris@16:     return king_ordering(G, permutation, 
Chris@16:                          make_iterator_property_map(&colors[0], index_map,
Chris@16:                                                     colors[0]),
Chris@16:                          make_out_degree_map(G), index_map);
Chris@16:   }
Chris@16: 
Chris@16:   template<typename Graph, typename OutputIterator>
Chris@16:   inline OutputIterator 
Chris@16:   king_ordering(const Graph& G, OutputIterator permutation)
Chris@16:   { return king_ordering(G, permutation, get(vertex_index, G)); }
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: 
Chris@16: #endif // BOOST_GRAPH_KING_HPP