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//======================================================================= // Copyright 1997, 1998, 1999, 2000 University of Notre Dame. // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. 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) //======================================================================= // Revision History: // 17 March 2006: Fixed a bug: when updating the degree a vertex // could be moved to a wrong bucket. (Roman Dementiev) // #ifndef BOOST_SMALLEST_LAST_VERTEX_ORDERING_HPP #define BOOST_SMALLEST_LAST_VERTEX_ORDERING_HPP /* The smallest-last ordering is defined for the loopless graph G with vertices a(j), j = 1,2,...,n where a(j) is the j-th column of A and with edge (a(i),a(j)) if and only if columns i and j have a non-zero in the same row position. The smallest-last ordering is determined recursively by letting list(k), k = n,...,1 be a column with least degree in the subgraph spanned by the un-ordered columns. */ #include #include #include #include #include #include namespace boost { template < class VertexListGraph, class Order, class Degree, class Marker > void smallest_last_vertex_ordering( const VertexListGraph& G, Order order, Degree degree, Marker marker) { typedef typename boost::graph_traits< VertexListGraph > GraphTraits; typedef typename GraphTraits::vertex_descriptor Vertex; // typedef typename GraphTraits::size_type size_type; typedef std::size_t size_type; const size_type num = num_vertices(G); typedef typename boost::property_map< VertexListGraph, vertex_index_t >::type ID; typedef bucket_sorter< size_type, Vertex, Degree, ID > BucketSorter; BucketSorter degree_bucket_sorter(num, num, degree, get(vertex_index, G)); smallest_last_vertex_ordering( G, order, degree, marker, degree_bucket_sorter); } template < class VertexListGraph, class Order, class Degree, class Marker, class BucketSorter > void smallest_last_vertex_ordering(const VertexListGraph& G, Order order, Degree degree, Marker marker, BucketSorter& degree_buckets) { typedef typename boost::graph_traits< VertexListGraph > GraphTraits; typedef typename GraphTraits::vertex_descriptor Vertex; // typedef typename GraphTraits::size_type size_type; typedef std::size_t size_type; const size_type num = num_vertices(G); typename GraphTraits::vertex_iterator v, vend; for (boost::tie(v, vend) = vertices(G); v != vend; ++v) { put(marker, *v, num); put(degree, *v, out_degree(*v, G)); degree_buckets.push(*v); } size_type minimum_degree = 0; size_type current_order = num - 1; while (1) { typedef typename BucketSorter::stack MDStack; MDStack minimum_degree_stack = degree_buckets[minimum_degree]; while (minimum_degree_stack.empty()) minimum_degree_stack = degree_buckets[++minimum_degree]; Vertex node = minimum_degree_stack.top(); put(order, current_order, node); if (current_order == 0) // find all vertices break; minimum_degree_stack.pop(); put(marker, node, 0); // node has been ordered. typename GraphTraits::adjacency_iterator v, vend; for (boost::tie(v, vend) = adjacent_vertices(node, G); v != vend; ++v) if (get(marker, *v) > current_order) { //*v is unordered vertex put(marker, *v, current_order); // mark the columns adjacent to node // delete *v from the bucket sorter degree_buckets.remove(*v); // It is possible minimum degree goes down // Here we keep tracking it. put(degree, *v, get(degree, *v) - 1); BOOST_USING_STD_MIN(); minimum_degree = min BOOST_PREVENT_MACRO_SUBSTITUTION( minimum_degree, get(degree, *v)); // reinsert *v in the bucket sorter with the new degree degree_buckets.push(*v); } current_order--; } // at this point, order[i] = v_i; } template < class VertexListGraph, class Order > void smallest_last_vertex_ordering(const VertexListGraph& G, Order order) { typedef typename graph_traits< VertexListGraph >::vertex_descriptor vertex_descriptor; typedef typename graph_traits< VertexListGraph >::degree_size_type degree_size_type; smallest_last_vertex_ordering(G, order, make_shared_array_property_map( num_vertices(G), degree_size_type(0), get(vertex_index, G)), make_shared_array_property_map( num_vertices(G), (std::size_t)(0), get(vertex_index, G))); } template < class VertexListGraph > std::vector< typename graph_traits< VertexListGraph >::vertex_descriptor > smallest_last_vertex_ordering(const VertexListGraph& G) { std::vector< typename graph_traits< VertexListGraph >::vertex_descriptor > o(num_vertices(G)); smallest_last_vertex_ordering(G, make_iterator_property_map( o.begin(), typed_identity_property_map< std::size_t >())); return o; } } #endif