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2
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... | ... |
@@ -116,100 +116,82 @@ |
116 | 116 |
int prev, next; |
117 | 117 |
int visited; |
118 | 118 |
typename Graph::Arc first; |
119 | 119 |
bool inverted; |
120 | 120 |
}; |
121 | 121 |
|
122 | 122 |
template <typename Graph> |
123 | 123 |
struct NodeDataNode<Graph, false> { |
124 | 124 |
int prev, next; |
125 | 125 |
int visited; |
126 | 126 |
}; |
127 | 127 |
|
128 | 128 |
template <typename Graph> |
129 | 129 |
struct ChildListNode { |
130 | 130 |
typedef typename Graph::Node Node; |
131 | 131 |
Node first; |
132 | 132 |
Node prev, next; |
133 | 133 |
}; |
134 | 134 |
|
135 | 135 |
template <typename Graph> |
136 | 136 |
struct ArcListNode { |
137 | 137 |
typename Graph::Arc prev, next; |
138 | 138 |
}; |
139 | 139 |
|
140 |
} |
|
141 |
|
|
142 |
/// \ingroup planar |
|
143 |
/// |
|
144 |
/// \brief Planarity checking of an undirected simple graph |
|
145 |
/// |
|
146 |
/// This class implements the Boyer-Myrvold algorithm for planarity |
|
147 |
/// checking of an undirected graph. This class is a simplified |
|
148 |
/// version of the PlanarEmbedding algorithm class because neither |
|
149 |
/// the embedding nor the kuratowski subdivisons are not computed. |
|
150 | 140 |
template <typename Graph> |
151 | 141 |
class PlanarityChecking { |
152 | 142 |
private: |
153 | 143 |
|
154 | 144 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
155 | 145 |
|
156 | 146 |
const Graph& _graph; |
157 | 147 |
|
158 | 148 |
private: |
159 | 149 |
|
160 | 150 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
161 | 151 |
|
162 | 152 |
typedef typename Graph::template EdgeMap<bool> TreeMap; |
163 | 153 |
|
164 | 154 |
typedef typename Graph::template NodeMap<int> OrderMap; |
165 | 155 |
typedef std::vector<Node> OrderList; |
166 | 156 |
|
167 | 157 |
typedef typename Graph::template NodeMap<int> LowMap; |
168 | 158 |
typedef typename Graph::template NodeMap<int> AncestorMap; |
169 | 159 |
|
170 | 160 |
typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
171 | 161 |
typedef std::vector<NodeDataNode> NodeData; |
172 | 162 |
|
173 | 163 |
typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
174 | 164 |
typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
175 | 165 |
|
176 | 166 |
typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
177 | 167 |
|
178 | 168 |
typedef typename Graph::template NodeMap<bool> EmbedArc; |
179 | 169 |
|
180 | 170 |
public: |
181 | 171 |
|
182 |
/// \brief Constructor |
|
183 |
/// |
|
184 |
/// \note The graph should be simple, i.e. parallel and loop arc |
|
185 |
/// free. |
|
186 | 172 |
PlanarityChecking(const Graph& graph) : _graph(graph) {} |
187 | 173 |
|
188 |
/// \brief Runs the algorithm. |
|
189 |
/// |
|
190 |
/// Runs the algorithm. |
|
191 |
/// \return %True when the graph is planar. |
|
192 | 174 |
bool run() { |
193 | 175 |
typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
194 | 176 |
|
195 | 177 |
PredMap pred_map(_graph, INVALID); |
196 | 178 |
TreeMap tree_map(_graph, false); |
197 | 179 |
|
198 | 180 |
OrderMap order_map(_graph, -1); |
199 | 181 |
OrderList order_list; |
200 | 182 |
|
201 | 183 |
AncestorMap ancestor_map(_graph, -1); |
202 | 184 |
LowMap low_map(_graph, -1); |
203 | 185 |
|
204 | 186 |
Visitor visitor(_graph, pred_map, tree_map, |
205 | 187 |
order_map, order_list, ancestor_map, low_map); |
206 | 188 |
DfsVisit<Graph, Visitor> visit(_graph, visitor); |
207 | 189 |
visit.run(); |
208 | 190 |
|
209 | 191 |
ChildLists child_lists(_graph); |
210 | 192 |
createChildLists(tree_map, order_map, low_map, child_lists); |
211 | 193 |
|
212 | 194 |
NodeData node_data(2 * order_list.size()); |
213 | 195 |
|
214 | 196 |
EmbedArc embed_arc(_graph, false); |
215 | 197 |
|
... | ... |
@@ -218,49 +200,50 @@ |
218 | 200 |
for (int i = order_list.size() - 1; i >= 0; --i) { |
219 | 201 |
|
220 | 202 |
Node node = order_list[i]; |
221 | 203 |
|
222 | 204 |
Node source = node; |
223 | 205 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
224 | 206 |
Node target = _graph.target(e); |
225 | 207 |
|
226 | 208 |
if (order_map[source] < order_map[target] && tree_map[e]) { |
227 | 209 |
initFace(target, node_data, order_map, order_list); |
228 | 210 |
} |
229 | 211 |
} |
230 | 212 |
|
231 | 213 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
232 | 214 |
Node target = _graph.target(e); |
233 | 215 |
|
234 | 216 |
if (order_map[source] < order_map[target] && !tree_map[e]) { |
235 | 217 |
embed_arc[target] = true; |
236 | 218 |
walkUp(target, source, i, pred_map, low_map, |
237 | 219 |
order_map, order_list, node_data, merge_roots); |
238 | 220 |
} |
239 | 221 |
} |
240 | 222 |
|
241 | 223 |
for (typename MergeRoots::Value::iterator it = |
242 |
merge_roots[node].begin(); |
|
224 |
merge_roots[node].begin(); |
|
225 |
it != merge_roots[node].end(); ++it) { |
|
243 | 226 |
int rn = *it; |
244 | 227 |
walkDown(rn, i, node_data, order_list, child_lists, |
245 | 228 |
ancestor_map, low_map, embed_arc, merge_roots); |
246 | 229 |
} |
247 | 230 |
merge_roots[node].clear(); |
248 | 231 |
|
249 | 232 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) { |
250 | 233 |
Node target = _graph.target(e); |
251 | 234 |
|
252 | 235 |
if (order_map[source] < order_map[target] && !tree_map[e]) { |
253 | 236 |
if (embed_arc[target]) { |
254 | 237 |
return false; |
255 | 238 |
} |
256 | 239 |
} |
257 | 240 |
} |
258 | 241 |
} |
259 | 242 |
|
260 | 243 |
return true; |
261 | 244 |
} |
262 | 245 |
|
263 | 246 |
private: |
264 | 247 |
|
265 | 248 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
266 | 249 |
const LowMap& low_map, ChildLists& child_lists) { |
... | ... |
@@ -428,49 +411,50 @@ |
428 | 411 |
|
429 | 412 |
// Embedding arc into external face |
430 | 413 |
if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
431 | 414 |
if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
432 | 415 |
pn = rn; |
433 | 416 |
|
434 | 417 |
embed_arc[order_list[n]] = false; |
435 | 418 |
} |
436 | 419 |
|
437 | 420 |
if (!merge_roots[node].empty()) { |
438 | 421 |
|
439 | 422 |
bool d = pn == node_data[n].prev; |
440 | 423 |
|
441 | 424 |
merge_stack.push_back(std::make_pair(n, d)); |
442 | 425 |
|
443 | 426 |
int rn = merge_roots[node].front(); |
444 | 427 |
|
445 | 428 |
int xn = node_data[rn].next; |
446 | 429 |
Node xnode = order_list[xn]; |
447 | 430 |
|
448 | 431 |
int yn = node_data[rn].prev; |
449 | 432 |
Node ynode = order_list[yn]; |
450 | 433 |
|
451 | 434 |
bool rd; |
452 |
if (!external(xnode, rorder, child_lists, |
|
435 |
if (!external(xnode, rorder, child_lists, |
|
436 |
ancestor_map, low_map)) { |
|
453 | 437 |
rd = true; |
454 | 438 |
} else if (!external(ynode, rorder, child_lists, |
455 | 439 |
ancestor_map, low_map)) { |
456 | 440 |
rd = false; |
457 | 441 |
} else if (pertinent(xnode, embed_arc, merge_roots)) { |
458 | 442 |
rd = true; |
459 | 443 |
} else { |
460 | 444 |
rd = false; |
461 | 445 |
} |
462 | 446 |
|
463 | 447 |
merge_stack.push_back(std::make_pair(rn, rd)); |
464 | 448 |
|
465 | 449 |
pn = rn; |
466 | 450 |
n = rd ? xn : yn; |
467 | 451 |
|
468 | 452 |
} else if (!external(node, rorder, child_lists, |
469 | 453 |
ancestor_map, low_map)) { |
470 | 454 |
int nn = (node_data[n].next != pn ? |
471 | 455 |
node_data[n].next : node_data[n].prev); |
472 | 456 |
|
473 | 457 |
bool nd = n == node_data[nn].prev; |
474 | 458 |
|
475 | 459 |
if (nd) node_data[nn].prev = pn; |
476 | 460 |
else node_data[nn].next = pn; |
... | ... |
@@ -506,48 +490,64 @@ |
506 | 490 |
|
507 | 491 |
} |
508 | 492 |
|
509 | 493 |
bool external(const Node& node, int rorder, |
510 | 494 |
ChildLists& child_lists, AncestorMap& ancestor_map, |
511 | 495 |
LowMap& low_map) { |
512 | 496 |
Node child = child_lists[node].first; |
513 | 497 |
|
514 | 498 |
if (child != INVALID) { |
515 | 499 |
if (low_map[child] < rorder) return true; |
516 | 500 |
} |
517 | 501 |
|
518 | 502 |
if (ancestor_map[node] < rorder) return true; |
519 | 503 |
|
520 | 504 |
return false; |
521 | 505 |
} |
522 | 506 |
|
523 | 507 |
bool pertinent(const Node& node, const EmbedArc& embed_arc, |
524 | 508 |
const MergeRoots& merge_roots) { |
525 | 509 |
return !merge_roots[node].empty() || embed_arc[node]; |
526 | 510 |
} |
527 | 511 |
|
528 | 512 |
}; |
529 | 513 |
|
514 |
} |
|
515 |
|
|
516 |
/// \ingroup planar |
|
517 |
/// |
|
518 |
/// \brief Planarity checking of an undirected simple graph |
|
519 |
/// |
|
520 |
/// This function implements the Boyer-Myrvold algorithm for |
|
521 |
/// planarity checking of an undirected graph. It is a simplified |
|
522 |
/// version of the PlanarEmbedding algorithm class because neither |
|
523 |
/// the embedding nor the kuratowski subdivisons are not computed. |
|
524 |
template <typename GR> |
|
525 |
bool checkPlanarity(const GR& graph) { |
|
526 |
_planarity_bits::PlanarityChecking<GR> pc(graph); |
|
527 |
return pc.run(); |
|
528 |
} |
|
529 |
|
|
530 | 530 |
/// \ingroup planar |
531 | 531 |
/// |
532 | 532 |
/// \brief Planar embedding of an undirected simple graph |
533 | 533 |
/// |
534 | 534 |
/// This class implements the Boyer-Myrvold algorithm for planar |
535 | 535 |
/// embedding of an undirected graph. The planar embedding is an |
536 | 536 |
/// ordering of the outgoing edges of the nodes, which is a possible |
537 | 537 |
/// configuration to draw the graph in the plane. If there is not |
538 | 538 |
/// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
539 | 539 |
/// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on |
540 | 540 |
/// 3 ANode and 3 BNode) subdivision. |
541 | 541 |
/// |
542 | 542 |
/// The current implementation calculates either an embedding or a |
543 | 543 |
/// Kuratowski subdivision. The running time of the algorithm is |
544 | 544 |
/// \f$ O(n) \f$. |
545 | 545 |
template <typename Graph> |
546 | 546 |
class PlanarEmbedding { |
547 | 547 |
private: |
548 | 548 |
|
549 | 549 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
550 | 550 |
|
551 | 551 |
const Graph& _graph; |
552 | 552 |
typename Graph::template ArcMap<Arc> _embedding; |
553 | 553 |
|
... | ... |
@@ -691,49 +691,49 @@ |
691 | 691 |
for (int i = 0; i < int(order_list.size()); ++i) { |
692 | 692 |
|
693 | 693 |
mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
694 | 694 |
child_lists, arc_lists); |
695 | 695 |
storeEmbedding(order_list[i], node_data, order_map, pred_map, |
696 | 696 |
arc_lists, flip_map); |
697 | 697 |
} |
698 | 698 |
|
699 | 699 |
return true; |
700 | 700 |
} |
701 | 701 |
|
702 | 702 |
/// \brief Gives back the successor of an arc |
703 | 703 |
/// |
704 | 704 |
/// Gives back the successor of an arc. This function makes |
705 | 705 |
/// possible to query the cyclic order of the outgoing arcs from |
706 | 706 |
/// a node. |
707 | 707 |
Arc next(const Arc& arc) const { |
708 | 708 |
return _embedding[arc]; |
709 | 709 |
} |
710 | 710 |
|
711 | 711 |
/// \brief Gives back the calculated embedding map |
712 | 712 |
/// |
713 | 713 |
/// The returned map contains the successor of each arc in the |
714 | 714 |
/// graph. |
715 |
const EmbeddingMap& |
|
715 |
const EmbeddingMap& embeddingMap() const { |
|
716 | 716 |
return _embedding; |
717 | 717 |
} |
718 | 718 |
|
719 | 719 |
/// \brief Gives back true if the undirected arc is in the |
720 | 720 |
/// kuratowski subdivision |
721 | 721 |
/// |
722 | 722 |
/// Gives back true if the undirected arc is in the kuratowski |
723 | 723 |
/// subdivision |
724 | 724 |
/// \note The \c run() had to be called with true value. |
725 | 725 |
bool kuratowski(const Edge& edge) { |
726 | 726 |
return _kuratowski[edge]; |
727 | 727 |
} |
728 | 728 |
|
729 | 729 |
private: |
730 | 730 |
|
731 | 731 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
732 | 732 |
const LowMap& low_map, ChildLists& child_lists) { |
733 | 733 |
|
734 | 734 |
for (NodeIt n(_graph); n != INVALID; ++n) { |
735 | 735 |
Node source = n; |
736 | 736 |
|
737 | 737 |
std::vector<Node> targets; |
738 | 738 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
739 | 739 |
Node target = _graph.target(e); |
... | ... |
@@ -218,42 +218,45 @@ |
218 | 218 |
} |
219 | 219 |
|
220 | 220 |
void checkColoring(const Graph& graph, PC& pc, int num) { |
221 | 221 |
for (NodeIt n(graph); n != INVALID; ++n) { |
222 | 222 |
check(pc.colorIndex(n) >= 0 && pc.colorIndex(n) < num, |
223 | 223 |
"Wrong coloring"); |
224 | 224 |
} |
225 | 225 |
for (EdgeIt e(graph); e != INVALID; ++e) { |
226 | 226 |
check(pc.colorIndex(graph.u(e)) != pc.colorIndex(graph.v(e)), |
227 | 227 |
"Wrong coloring"); |
228 | 228 |
} |
229 | 229 |
} |
230 | 230 |
|
231 | 231 |
int main() { |
232 | 232 |
|
233 | 233 |
for (int i = 0; i < lgfn; ++i) { |
234 | 234 |
std::istringstream lgfs(lgf[i]); |
235 | 235 |
|
236 | 236 |
SmartGraph graph; |
237 | 237 |
graphReader(graph, lgfs).run(); |
238 | 238 |
|
239 | 239 |
check(simpleGraph(graph), "Test graphs must be simple"); |
240 | 240 |
|
241 | 241 |
PE pe(graph); |
242 |
|
|
242 |
bool planar = pe.run(); |
|
243 |
check(checkPlanarity(graph) == planar, "Planarity checking failed"); |
|
244 |
|
|
245 |
if (planar) { |
|
243 | 246 |
checkEmbedding(graph, pe); |
244 | 247 |
|
245 | 248 |
PlanarDrawing<Graph> pd(graph); |
246 |
pd.run(pe. |
|
249 |
pd.run(pe.embeddingMap()); |
|
247 | 250 |
checkDrawing(graph, pd); |
248 | 251 |
|
249 | 252 |
PlanarColoring<Graph> pc(graph); |
250 |
pc.runFiveColoring(pe. |
|
253 |
pc.runFiveColoring(pe.embeddingMap()); |
|
251 | 254 |
checkColoring(graph, pc, 5); |
252 | 255 |
|
253 | 256 |
} else { |
254 | 257 |
checkKuratowski(graph, pe); |
255 | 258 |
} |
256 | 259 |
} |
257 | 260 |
|
258 | 261 |
return 0; |
259 | 262 |
} |
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