1 //=======================================================================
2 // Copyright (c) Aaron Windsor 2007
4 // Distributed under the Boost Software License, Version 1.0. (See
5 // accompanying file LICENSE_1_0.txt or copy at
6 // http://www.boost.org/LICENSE_1_0.txt)
7 //=======================================================================
9 #ifndef __PLANAR_CANONICAL_ORDERING_HPP__
10 #define __PLANAR_CANONICAL_ORDERING_HPP__
14 #include <boost/config.hpp>
15 #include <boost/next_prior.hpp>
16 #include <boost/graph/graph_traits.hpp>
17 #include <boost/property_map/property_map.hpp>
25 enum planar_canonical_ordering_state
28 PCO_ONE_NEIGHBOR_PROCESSED,
29 PCO_READY_TO_BE_PROCESSED};
32 template<typename Graph,
33 typename PlanarEmbedding,
34 typename OutputIterator,
35 typename VertexIndexMap>
36 void planar_canonical_ordering(const Graph& g,
37 PlanarEmbedding embedding,
38 OutputIterator ordering,
42 typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
43 typedef typename graph_traits<Graph>::edge_descriptor edge_t;
44 typedef typename graph_traits<Graph>::adjacency_iterator
46 typedef typename property_traits<PlanarEmbedding>::value_type
48 typedef typename embedding_value_t::const_iterator embedding_iterator_t;
49 typedef iterator_property_map
50 <typename std::vector<vertex_t>::iterator, VertexIndexMap>
51 vertex_to_vertex_map_t;
52 typedef iterator_property_map
53 <typename std::vector<std::size_t>::iterator, VertexIndexMap>
54 vertex_to_size_t_map_t;
56 std::vector<vertex_t> processed_neighbor_vector(num_vertices(g));
57 vertex_to_vertex_map_t processed_neighbor
58 (processed_neighbor_vector.begin(), vm);
60 std::vector<std::size_t> status_vector(num_vertices(g), detail::PCO_UNPROCESSED);
61 vertex_to_size_t_map_t status(status_vector.begin(), vm);
63 std::list<vertex_t> ready_to_be_processed;
65 vertex_t first_vertex = *vertices(g).first;
66 vertex_t second_vertex = first_vertex;
67 adjacency_iterator_t ai, ai_end;
68 for(boost::tie(ai,ai_end) = adjacent_vertices(first_vertex,g); ai != ai_end; ++ai)
70 if (*ai == first_vertex)
76 ready_to_be_processed.push_back(first_vertex);
77 status[first_vertex] = detail::PCO_READY_TO_BE_PROCESSED;
78 ready_to_be_processed.push_back(second_vertex);
79 status[second_vertex] = detail::PCO_READY_TO_BE_PROCESSED;
81 while(!ready_to_be_processed.empty())
83 vertex_t u = ready_to_be_processed.front();
84 ready_to_be_processed.pop_front();
86 if (status[u] != detail::PCO_READY_TO_BE_PROCESSED && u != second_vertex)
89 embedding_iterator_t ei, ei_start, ei_end;
90 embedding_iterator_t next_edge_itr, prior_edge_itr;
92 ei_start = embedding[u].begin();
93 ei_end = embedding[u].end();
94 prior_edge_itr = prior(ei_end);
95 while(source(*prior_edge_itr, g) == target(*prior_edge_itr,g))
96 prior_edge_itr = prior(prior_edge_itr);
98 for(ei = ei_start; ei != ei_end; ++ei)
101 edge_t e(*ei); // e = (u,v)
102 next_edge_itr = boost::next(ei) == ei_end ? ei_start : boost::next(ei);
103 vertex_t v = source(e,g) == u ? target(e,g) : source(e,g);
105 vertex_t prior_vertex = source(*prior_edge_itr, g) == u ?
106 target(*prior_edge_itr, g) : source(*prior_edge_itr, g);
107 vertex_t next_vertex = source(*next_edge_itr, g) == u ?
108 target(*next_edge_itr, g) : source(*next_edge_itr, g);
110 // Need prior_vertex, u, v, and next_vertex to all be
111 // distinct. This is possible, since the input graph is
112 // triangulated. It'll be true all the time in a simple
113 // graph, but loops and parallel edges cause some complications.
114 if (prior_vertex == v || prior_vertex == u)
120 //Skip any self-loops
124 // Move next_edge_itr (and next_vertex) forwards
125 // past any loops or parallel edges
126 while (next_vertex == v || next_vertex == u)
128 next_edge_itr = boost::next(next_edge_itr) == ei_end ?
129 ei_start : boost::next(next_edge_itr);
130 next_vertex = source(*next_edge_itr, g) == u ?
131 target(*next_edge_itr, g) : source(*next_edge_itr, g);
135 if (status[v] == detail::PCO_UNPROCESSED)
137 status[v] = detail::PCO_ONE_NEIGHBOR_PROCESSED;
138 processed_neighbor[v] = u;
140 else if (status[v] == detail::PCO_ONE_NEIGHBOR_PROCESSED)
142 vertex_t x = processed_neighbor[v];
143 //are edges (v,u) and (v,x) adjacent in the planar
144 //embedding? if so, set status[v] = 1. otherwise, set
147 if ((next_vertex == x &&
148 !(first_vertex == u && second_vertex == x)
151 (prior_vertex == x &&
152 !(first_vertex == x && second_vertex == u)
156 status[v] = detail::PCO_READY_TO_BE_PROCESSED;
160 status[v] = detail::PCO_READY_TO_BE_PROCESSED + 1;
163 else if (status[v] > detail::PCO_ONE_NEIGHBOR_PROCESSED)
165 //check the two edges before and after (v,u) in the planar
166 //embedding, and update status[v] accordingly
168 bool processed_before = false;
169 if (status[prior_vertex] == detail::PCO_PROCESSED)
170 processed_before = true;
172 bool processed_after = false;
173 if (status[next_vertex] == detail::PCO_PROCESSED)
174 processed_after = true;
176 if (!processed_before && !processed_after)
179 else if (processed_before && processed_after)
184 if (status[v] == detail::PCO_READY_TO_BE_PROCESSED)
185 ready_to_be_processed.push_back(v);
191 status[u] = detail::PCO_PROCESSED;
200 template<typename Graph, typename PlanarEmbedding, typename OutputIterator>
201 void planar_canonical_ordering(const Graph& g,
202 PlanarEmbedding embedding,
203 OutputIterator ordering
206 planar_canonical_ordering(g, embedding, ordering, get(vertex_index,g));
212 #endif //__PLANAR_CANONICAL_ORDERING_HPP__