1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
|
//=======================================================================
// Copyright (c) Aaron Windsor 2007
//
// 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 __PLANAR_CANONICAL_ORDERING_HPP__
#define __PLANAR_CANONICAL_ORDERING_HPP__
#include <vector>
#include <list>
#include <boost/config.hpp>
#include <boost/utility.hpp> //for next and prior
#include <boost/graph/graph_traits.hpp>
#include <boost/property_map/property_map.hpp>
namespace boost
{
namespace detail {
enum planar_canonical_ordering_state
{PCO_PROCESSED,
PCO_UNPROCESSED,
PCO_ONE_NEIGHBOR_PROCESSED,
PCO_READY_TO_BE_PROCESSED};
}
template<typename Graph,
typename PlanarEmbedding,
typename OutputIterator,
typename VertexIndexMap>
void planar_canonical_ordering(const Graph& g,
PlanarEmbedding embedding,
OutputIterator ordering,
VertexIndexMap vm)
{
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
typedef typename graph_traits<Graph>::edge_descriptor edge_t;
typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator_t;
typedef typename graph_traits<Graph>::adjacency_iterator
adjacency_iterator_t;
typedef typename std::pair<vertex_t, vertex_t> vertex_pair_t;
typedef typename property_traits<PlanarEmbedding>::value_type
embedding_value_t;
typedef typename embedding_value_t::const_iterator embedding_iterator_t;
typedef iterator_property_map
<typename std::vector<vertex_t>::iterator, VertexIndexMap>
vertex_to_vertex_map_t;
typedef iterator_property_map
<typename std::vector<std::size_t>::iterator, VertexIndexMap>
vertex_to_size_t_map_t;
std::vector<vertex_t> processed_neighbor_vector(num_vertices(g));
vertex_to_vertex_map_t processed_neighbor
(processed_neighbor_vector.begin(), vm);
std::vector<std::size_t> status_vector(num_vertices(g), detail::PCO_UNPROCESSED);
vertex_to_size_t_map_t status(status_vector.begin(), vm);
std::list<vertex_t> ready_to_be_processed;
vertex_t first_vertex = *vertices(g).first;
vertex_t second_vertex;
adjacency_iterator_t ai, ai_end;
for(boost::tie(ai,ai_end) = adjacent_vertices(first_vertex,g); ai != ai_end; ++ai)
{
if (*ai == first_vertex)
continue;
second_vertex = *ai;
break;
}
ready_to_be_processed.push_back(first_vertex);
status[first_vertex] = detail::PCO_READY_TO_BE_PROCESSED;
ready_to_be_processed.push_back(second_vertex);
status[second_vertex] = detail::PCO_READY_TO_BE_PROCESSED;
while(!ready_to_be_processed.empty())
{
vertex_t u = ready_to_be_processed.front();
ready_to_be_processed.pop_front();
if (status[u] != detail::PCO_READY_TO_BE_PROCESSED && u != second_vertex)
continue;
embedding_iterator_t ei, ei_start, ei_end;
embedding_iterator_t next_edge_itr, prior_edge_itr;
ei_start = embedding[u].begin();
ei_end = embedding[u].end();
prior_edge_itr = prior(ei_end);
while(source(*prior_edge_itr, g) == target(*prior_edge_itr,g))
prior_edge_itr = prior(prior_edge_itr);
for(ei = ei_start; ei != ei_end; ++ei)
{
edge_t e(*ei); // e = (u,v)
next_edge_itr = boost::next(ei) == ei_end ? ei_start : boost::next(ei);
vertex_t v = source(e,g) == u ? target(e,g) : source(e,g);
vertex_t prior_vertex = source(*prior_edge_itr, g) == u ?
target(*prior_edge_itr, g) : source(*prior_edge_itr, g);
vertex_t next_vertex = source(*next_edge_itr, g) == u ?
target(*next_edge_itr, g) : source(*next_edge_itr, g);
// Need prior_vertex, u, v, and next_vertex to all be
// distinct. This is possible, since the input graph is
// triangulated. It'll be true all the time in a simple
// graph, but loops and parallel edges cause some complications.
if (prior_vertex == v || prior_vertex == u)
{
prior_edge_itr = ei;
continue;
}
//Skip any self-loops
if (u == v)
continue;
// Move next_edge_itr (and next_vertex) forwards
// past any loops or parallel edges
while (next_vertex == v || next_vertex == u)
{
next_edge_itr = boost::next(next_edge_itr) == ei_end ?
ei_start : boost::next(next_edge_itr);
next_vertex = source(*next_edge_itr, g) == u ?
target(*next_edge_itr, g) : source(*next_edge_itr, g);
}
if (status[v] == detail::PCO_UNPROCESSED)
{
status[v] = detail::PCO_ONE_NEIGHBOR_PROCESSED;
processed_neighbor[v] = u;
}
else if (status[v] == detail::PCO_ONE_NEIGHBOR_PROCESSED)
{
vertex_t x = processed_neighbor[v];
//are edges (v,u) and (v,x) adjacent in the planar
//embedding? if so, set status[v] = 1. otherwise, set
//status[v] = 2.
if ((next_vertex == x &&
!(first_vertex == u && second_vertex == x)
)
||
(prior_vertex == x &&
!(first_vertex == x && second_vertex == u)
)
)
{
status[v] = detail::PCO_READY_TO_BE_PROCESSED;
}
else
{
status[v] = detail::PCO_READY_TO_BE_PROCESSED + 1;
}
}
else if (status[v] > detail::PCO_ONE_NEIGHBOR_PROCESSED)
{
//check the two edges before and after (v,u) in the planar
//embedding, and update status[v] accordingly
bool processed_before = false;
if (status[prior_vertex] == detail::PCO_PROCESSED)
processed_before = true;
bool processed_after = false;
if (status[next_vertex] == detail::PCO_PROCESSED)
processed_after = true;
if (!processed_before && !processed_after)
++status[v];
else if (processed_before && processed_after)
--status[v];
}
if (status[v] == detail::PCO_READY_TO_BE_PROCESSED)
ready_to_be_processed.push_back(v);
prior_edge_itr = ei;
}
status[u] = detail::PCO_PROCESSED;
*ordering = u;
++ordering;
}
}
template<typename Graph, typename PlanarEmbedding, typename OutputIterator>
void planar_canonical_ordering(const Graph& g,
PlanarEmbedding embedding,
OutputIterator ordering
)
{
planar_canonical_ordering(g, embedding, ordering, get(vertex_index,g));
}
} //namespace boost
#endif //__PLANAR_CANONICAL_ORDERING_HPP__
|
