1 | //======================================================================= |
2 | // Copyright (C) 2005-2009 Jongsoo Park <jongsoo.park -at- gmail.com> |
3 | // |
4 | // Distributed under the Boost Software License, Version 1.0. |
5 | // (See accompanying file LICENSE_1_0.txt or copy at |
6 | // http://www.boost.org/LICENSE_1_0.txt) |
7 | //======================================================================= |
8 | |
9 | #ifndef BOOST_GRAPH_DOMINATOR_HPP |
10 | #define BOOST_GRAPH_DOMINATOR_HPP |
11 | |
12 | #include <boost/config.hpp> |
13 | #include <deque> |
14 | #include <set> |
15 | #include <boost/graph/depth_first_search.hpp> |
16 | #include <boost/concept/assert.hpp> |
17 | |
18 | // Dominator tree computation |
19 | |
20 | namespace boost { |
21 | namespace detail { |
22 | /** |
23 | * An extended time_stamper which also records vertices for each dfs number |
24 | */ |
25 | template<class TimeMap, class VertexVector, class TimeT, class Tag> |
26 | class time_stamper_with_vertex_vector |
27 | : public base_visitor< |
28 | time_stamper_with_vertex_vector<TimeMap, VertexVector, TimeT, Tag> > |
29 | { |
30 | public : |
31 | typedef Tag event_filter; |
32 | time_stamper_with_vertex_vector(TimeMap timeMap, VertexVector& v, |
33 | TimeT& t) |
34 | : timeStamper_(timeMap, t), v_(v) { } |
35 | |
36 | template<class Graph> |
37 | void |
38 | operator()(const typename property_traits<TimeMap>::key_type& v, |
39 | const Graph& g) |
40 | { |
41 | timeStamper_(v, g); |
42 | v_[timeStamper_.m_time] = v; |
43 | } |
44 | |
45 | private : |
46 | time_stamper<TimeMap, TimeT, Tag> timeStamper_; |
47 | VertexVector& v_; |
48 | }; |
49 | |
50 | /** |
51 | * A convenient way to create a time_stamper_with_vertex_vector |
52 | */ |
53 | template<class TimeMap, class VertexVector, class TimeT, class Tag> |
54 | time_stamper_with_vertex_vector<TimeMap, VertexVector, TimeT, Tag> |
55 | stamp_times_with_vertex_vector(TimeMap timeMap, VertexVector& v, TimeT& t, |
56 | Tag) |
57 | { |
58 | return time_stamper_with_vertex_vector<TimeMap, VertexVector, TimeT, |
59 | Tag>(timeMap, v, t); |
60 | } |
61 | |
62 | template<class Graph, class IndexMap, class TimeMap, class PredMap, |
63 | class DomTreePredMap> |
64 | class dominator_visitor |
65 | { |
66 | typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
67 | typedef typename graph_traits<Graph>::vertices_size_type VerticesSizeType; |
68 | |
69 | public : |
70 | /** |
71 | * @param g [in] the target graph of the dominator tree |
72 | * @param entry [in] the entry node of g |
73 | * @param domTreePredMap [out] the immediate dominator map |
74 | * (parent map in dominator tree) |
75 | */ |
76 | dominator_visitor(const Graph& g, const Vertex& entry, |
77 | DomTreePredMap domTreePredMap) |
78 | : semi_(num_vertices(g)), |
79 | ancestor_(num_vertices(g), graph_traits<Graph>::null_vertex()), |
80 | samedom_(ancestor_), |
81 | best_(semi_), |
82 | semiMap_(make_iterator_property_map(semi_.begin(), |
83 | get(vertex_index, g))), |
84 | ancestorMap_(make_iterator_property_map(ancestor_.begin(), |
85 | get(vertex_index, g))), |
86 | bestMap_(make_iterator_property_map(best_.begin(), |
87 | get(vertex_index, g))), |
88 | buckets_(num_vertices(g)), |
89 | bucketMap_(make_iterator_property_map(buckets_.begin(), |
90 | get(vertex_index, g))), |
91 | entry_(entry), |
92 | domTreePredMap_(domTreePredMap), |
93 | numOfVertices_(num_vertices(g)), |
94 | samedomMap(make_iterator_property_map(samedom_.begin(), |
95 | get(vertex_index, g))) |
96 | { |
97 | } |
98 | |
99 | void |
100 | operator()(const Vertex& n, const TimeMap& dfnumMap, |
101 | const PredMap& parentMap, const Graph& g) |
102 | { |
103 | if (n == entry_) return; |
104 | |
105 | const Vertex p(get(parentMap, n)); |
106 | Vertex s(p); |
107 | |
108 | // 1. Calculate the semidominator of n, |
109 | // based on the semidominator thm. |
110 | // * Semidominator thm. : To find the semidominator of a node n, |
111 | // consider all predecessors v of n in the CFG (Control Flow Graph). |
112 | // - If v is a proper ancestor of n in the spanning tree |
113 | // (so dfnum(v) < dfnum(n)), then v is a candidate for semi(n) |
114 | // - If v is a non-ancestor of n (so dfnum(v) > dfnum(n)) |
115 | // then for each u that is an ancestor of v (or u = v), |
116 | // Let semi(u) be a candidate for semi(n) |
117 | // of all these candidates, the one with lowest dfnum is |
118 | // the semidominator of n. |
119 | |
120 | // For each predecessor of n |
121 | typename graph_traits<Graph>::in_edge_iterator inItr, inEnd; |
122 | for (boost::tie(inItr, inEnd) = in_edges(n, g); inItr != inEnd; ++inItr) |
123 | { |
124 | const Vertex v = source(*inItr, g); |
125 | // To deal with unreachable nodes |
126 | if (get(dfnumMap, v) < 0 || get(dfnumMap, v) >= numOfVertices_) |
127 | continue; |
128 | |
129 | Vertex s2; |
130 | if (get(dfnumMap, v) <= get(dfnumMap, n)) |
131 | s2 = v; |
132 | else |
133 | s2 = get(semiMap_, ancestor_with_lowest_semi_(v, dfnumMap)); |
134 | |
135 | if (get(dfnumMap, s2) < get(dfnumMap, s)) |
136 | s = s2; |
137 | } |
138 | put(semiMap_, n, s); |
139 | |
140 | // 2. Calculation of n's dominator is deferred until |
141 | // the path from s to n has been linked into the forest |
142 | get(bucketMap_, s).push_back(n); |
143 | get(ancestorMap_, n) = p; |
144 | get(bestMap_, n) = n; |
145 | |
146 | // 3. Now that the path from p to v has been linked into |
147 | // the spanning forest, these lines calculate the dominator of v, |
148 | // based on the dominator thm., or else defer the calculation |
149 | // until y's dominator is known |
150 | // * Dominator thm. : On the spanning-tree path below semi(n) and |
151 | // above or including n, let y be the node |
152 | // with the smallest-numbered semidominator. Then, |
153 | // |
154 | // idom(n) = semi(n) if semi(y)=semi(n) or |
155 | // idom(y) if semi(y) != semi(n) |
156 | typename std::deque<Vertex>::iterator buckItr; |
157 | for (buckItr = get(bucketMap_, p).begin(); |
158 | buckItr != get(bucketMap_, p).end(); |
159 | ++buckItr) |
160 | { |
161 | const Vertex v(*buckItr); |
162 | const Vertex y(ancestor_with_lowest_semi_(v, dfnumMap)); |
163 | if (get(semiMap_, y) == get(semiMap_, v)) |
164 | put(domTreePredMap_, v, p); |
165 | else |
166 | put(samedomMap, v, y); |
167 | } |
168 | |
169 | get(bucketMap_, p).clear(); |
170 | } |
171 | |
172 | protected : |
173 | |
174 | /** |
175 | * Evaluate function in Tarjan's path compression |
176 | */ |
177 | const Vertex |
178 | ancestor_with_lowest_semi_(const Vertex& v, const TimeMap& dfnumMap) |
179 | { |
180 | const Vertex a(get(ancestorMap_, v)); |
181 | |
182 | if (get(ancestorMap_, a) != graph_traits<Graph>::null_vertex()) |
183 | { |
184 | const Vertex b(ancestor_with_lowest_semi_(v: a, dfnumMap)); |
185 | |
186 | put(ancestorMap_, v, get(ancestorMap_, a)); |
187 | |
188 | if (get(dfnumMap, get(semiMap_, b)) < |
189 | get(dfnumMap, get(semiMap_, get(bestMap_, v)))) |
190 | put(bestMap_, v, b); |
191 | } |
192 | |
193 | return get(bestMap_, v); |
194 | } |
195 | |
196 | std::vector<Vertex> semi_, ancestor_, samedom_, best_; |
197 | PredMap semiMap_, ancestorMap_, bestMap_; |
198 | std::vector< std::deque<Vertex> > buckets_; |
199 | |
200 | iterator_property_map<typename std::vector<std::deque<Vertex> >::iterator, |
201 | IndexMap> bucketMap_; |
202 | |
203 | const Vertex& entry_; |
204 | DomTreePredMap domTreePredMap_; |
205 | const VerticesSizeType numOfVertices_; |
206 | |
207 | public : |
208 | |
209 | PredMap samedomMap; |
210 | }; |
211 | |
212 | } // namespace detail |
213 | |
214 | /** |
215 | * @brief Build dominator tree using Lengauer-Tarjan algorithm. |
216 | * It takes O((V+E)log(V+E)) time. |
217 | * |
218 | * @pre dfnumMap, parentMap and verticesByDFNum have dfs results corresponding |
219 | * indexMap. |
220 | * If dfs has already run before, |
221 | * this function would be good for saving computations. |
222 | * @pre Unreachable nodes must be masked as |
223 | * graph_traits<Graph>::null_vertex in parentMap. |
224 | * @pre Unreachable nodes must be masked as |
225 | * (std::numeric_limits<VerticesSizeType>::max)() in dfnumMap. |
226 | * |
227 | * @param domTreePredMap [out] : immediate dominator map (parent map |
228 | * in dom. tree) |
229 | * |
230 | * @note reference Appel. p. 452~453. algorithm 19.9, 19.10. |
231 | * |
232 | * @todo : Optimization in Finding Dominators in Practice, Loukas Georgiadis |
233 | */ |
234 | template<class Graph, class IndexMap, class TimeMap, class PredMap, |
235 | class VertexVector, class DomTreePredMap> |
236 | void |
237 | lengauer_tarjan_dominator_tree_without_dfs |
238 | (const Graph& g, |
239 | const typename graph_traits<Graph>::vertex_descriptor& entry, |
240 | const IndexMap& /*indexMap*/, |
241 | TimeMap dfnumMap, PredMap parentMap, VertexVector& verticesByDFNum, |
242 | DomTreePredMap domTreePredMap) |
243 | { |
244 | // Typedefs and concept check |
245 | typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
246 | typedef typename graph_traits<Graph>::vertices_size_type VerticesSizeType; |
247 | |
248 | BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph> )); |
249 | |
250 | const VerticesSizeType numOfVertices = num_vertices(g); |
251 | if (numOfVertices == 0) return; |
252 | |
253 | // 1. Visit each vertex in reverse post order and calculate sdom. |
254 | detail::dominator_visitor<Graph, IndexMap, TimeMap, PredMap, DomTreePredMap> |
255 | visitor(g, entry, domTreePredMap); |
256 | |
257 | VerticesSizeType i; |
258 | for (i = 0; i < numOfVertices; ++i) |
259 | { |
260 | const Vertex u(verticesByDFNum[numOfVertices - 1 - i]); |
261 | if (u != graph_traits<Graph>::null_vertex()) |
262 | visitor(u, dfnumMap, parentMap, g); |
263 | } |
264 | |
265 | // 2. Now all the deferred dominator calculations, |
266 | // based on the second clause of the dominator thm., are performed |
267 | for (i = 0; i < numOfVertices; ++i) |
268 | { |
269 | const Vertex n(verticesByDFNum[i]); |
270 | |
271 | if (n == entry || n == graph_traits<Graph>::null_vertex()) |
272 | continue; |
273 | |
274 | Vertex u = get(visitor.samedomMap, n); |
275 | if (u != graph_traits<Graph>::null_vertex()) |
276 | { |
277 | put(domTreePredMap, n, get(domTreePredMap, u)); |
278 | } |
279 | } |
280 | } |
281 | |
282 | /** |
283 | * Unlike lengauer_tarjan_dominator_tree_without_dfs, |
284 | * dfs is run in this function and |
285 | * the result is written to dfnumMap, parentMap, vertices. |
286 | * |
287 | * If the result of dfs required after this algorithm, |
288 | * this function can eliminate the need of rerunning dfs. |
289 | */ |
290 | template<class Graph, class IndexMap, class TimeMap, class PredMap, |
291 | class VertexVector, class DomTreePredMap> |
292 | void |
293 | lengauer_tarjan_dominator_tree |
294 | (const Graph& g, |
295 | const typename graph_traits<Graph>::vertex_descriptor& entry, |
296 | const IndexMap& indexMap, |
297 | TimeMap dfnumMap, PredMap parentMap, VertexVector& verticesByDFNum, |
298 | DomTreePredMap domTreePredMap) |
299 | { |
300 | // Typedefs and concept check |
301 | typedef typename graph_traits<Graph>::vertices_size_type VerticesSizeType; |
302 | |
303 | BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph> )); |
304 | |
305 | // 1. Depth first visit |
306 | const VerticesSizeType numOfVertices = num_vertices(g); |
307 | if (numOfVertices == 0) return; |
308 | |
309 | VerticesSizeType time = |
310 | (std::numeric_limits<VerticesSizeType>::max)(); |
311 | std::vector<default_color_type> |
312 | colors(numOfVertices, color_traits<default_color_type>::white()); |
313 | depth_first_visit |
314 | (g, entry, |
315 | make_dfs_visitor |
316 | (make_pair(record_predecessors(parentMap, on_tree_edge()), |
317 | detail::stamp_times_with_vertex_vector |
318 | (dfnumMap, verticesByDFNum, time, on_discover_vertex()))), |
319 | make_iterator_property_map(colors.begin(), indexMap)); |
320 | |
321 | // 2. Run main algorithm. |
322 | lengauer_tarjan_dominator_tree_without_dfs(g, entry, indexMap, dfnumMap, |
323 | parentMap, verticesByDFNum, |
324 | domTreePredMap); |
325 | } |
326 | |
327 | /** |
328 | * Use vertex_index as IndexMap and make dfnumMap, parentMap, verticesByDFNum |
329 | * internally. |
330 | * If we don't need the result of dfs (dfnumMap, parentMap, verticesByDFNum), |
331 | * this function would be more convenient one. |
332 | */ |
333 | template<class Graph, class DomTreePredMap> |
334 | void |
335 | lengauer_tarjan_dominator_tree |
336 | (const Graph& g, |
337 | const typename graph_traits<Graph>::vertex_descriptor& entry, |
338 | DomTreePredMap domTreePredMap) |
339 | { |
340 | // typedefs |
341 | typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
342 | typedef typename graph_traits<Graph>::vertices_size_type VerticesSizeType; |
343 | typedef typename property_map<Graph, vertex_index_t>::const_type IndexMap; |
344 | typedef |
345 | iterator_property_map<typename std::vector<VerticesSizeType>::iterator, |
346 | IndexMap> TimeMap; |
347 | typedef |
348 | iterator_property_map<typename std::vector<Vertex>::iterator, IndexMap> |
349 | PredMap; |
350 | |
351 | // Make property maps |
352 | const VerticesSizeType numOfVertices = num_vertices(g); |
353 | if (numOfVertices == 0) return; |
354 | |
355 | const IndexMap indexMap = get(vertex_index, g); |
356 | |
357 | std::vector<VerticesSizeType> dfnum(numOfVertices, 0); |
358 | TimeMap dfnumMap(make_iterator_property_map(dfnum.begin(), indexMap)); |
359 | |
360 | std::vector<Vertex> parent(numOfVertices, |
361 | graph_traits<Graph>::null_vertex()); |
362 | PredMap parentMap(make_iterator_property_map(parent.begin(), indexMap)); |
363 | |
364 | std::vector<Vertex> verticesByDFNum(parent); |
365 | |
366 | // Run main algorithm |
367 | lengauer_tarjan_dominator_tree(g, entry, |
368 | indexMap, dfnumMap, parentMap, |
369 | verticesByDFNum, domTreePredMap); |
370 | } |
371 | |
372 | /** |
373 | * Muchnick. p. 182, 184 |
374 | * |
375 | * using iterative bit vector analysis |
376 | */ |
377 | template<class Graph, class IndexMap, class DomTreePredMap> |
378 | void |
379 | iterative_bit_vector_dominator_tree |
380 | (const Graph& g, |
381 | const typename graph_traits<Graph>::vertex_descriptor& entry, |
382 | const IndexMap& indexMap, |
383 | DomTreePredMap domTreePredMap) |
384 | { |
385 | typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
386 | typedef typename graph_traits<Graph>::vertex_iterator vertexItr; |
387 | typedef typename graph_traits<Graph>::vertices_size_type VerticesSizeType; |
388 | typedef |
389 | iterator_property_map<typename std::vector< std::set<Vertex> >::iterator, |
390 | IndexMap> vertexSetMap; |
391 | |
392 | BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph> )); |
393 | |
394 | // 1. Finding dominator |
395 | // 1.1. Initialize |
396 | const VerticesSizeType numOfVertices = num_vertices(g); |
397 | if (numOfVertices == 0) return; |
398 | |
399 | vertexItr vi, viend; |
400 | boost::tie(vi, viend) = vertices(g); |
401 | const std::set<Vertex> N(vi, viend); |
402 | |
403 | bool change = true; |
404 | |
405 | std::vector< std::set<Vertex> > dom(numOfVertices, N); |
406 | vertexSetMap domMap(make_iterator_property_map(dom.begin(), indexMap)); |
407 | get(domMap, entry).clear(); |
408 | get(domMap, entry).insert(entry); |
409 | |
410 | while (change) |
411 | { |
412 | change = false; |
413 | for (boost::tie(vi, viend) = vertices(g); vi != viend; ++vi) |
414 | { |
415 | if (*vi == entry) continue; |
416 | |
417 | std::set<Vertex> T(N); |
418 | |
419 | typename graph_traits<Graph>::in_edge_iterator inItr, inEnd; |
420 | for (boost::tie(inItr, inEnd) = in_edges(*vi, g); inItr != inEnd; ++inItr) |
421 | { |
422 | const Vertex p = source(*inItr, g); |
423 | |
424 | std::set<Vertex> tempSet; |
425 | std::set_intersection(T.begin(), T.end(), |
426 | get(domMap, p).begin(), |
427 | get(domMap, p).end(), |
428 | std::inserter(tempSet, tempSet.begin())); |
429 | T.swap(tempSet); |
430 | } |
431 | |
432 | T.insert(*vi); |
433 | if (T != get(domMap, *vi)) |
434 | { |
435 | change = true; |
436 | get(domMap, *vi).swap(T); |
437 | } |
438 | } // end of for (boost::tie(vi, viend) = vertices(g) |
439 | } // end of while(change) |
440 | |
441 | // 2. Build dominator tree |
442 | for (boost::tie(vi, viend) = vertices(g); vi != viend; ++vi) |
443 | get(domMap, *vi).erase(*vi); |
444 | |
445 | Graph domTree(numOfVertices); |
446 | |
447 | for (boost::tie(vi, viend) = vertices(g); vi != viend; ++vi) |
448 | { |
449 | if (*vi == entry) continue; |
450 | |
451 | // We have to iterate through copied dominator set |
452 | const std::set<Vertex> tempSet(get(domMap, *vi)); |
453 | typename std::set<Vertex>::const_iterator s; |
454 | for (s = tempSet.begin(); s != tempSet.end(); ++s) |
455 | { |
456 | typename std::set<Vertex>::iterator t; |
457 | for (t = get(domMap, *vi).begin(); t != get(domMap, *vi).end(); ) |
458 | { |
459 | typename std::set<Vertex>::iterator old_t = t; |
460 | ++t; // Done early because t may become invalid |
461 | if (*old_t == *s) continue; |
462 | if (get(domMap, *s).find(*old_t) != get(domMap, *s).end()) |
463 | get(domMap, *vi).erase(old_t); |
464 | } |
465 | } |
466 | } |
467 | |
468 | for (boost::tie(vi, viend) = vertices(g); vi != viend; ++vi) |
469 | { |
470 | if (*vi != entry && get(domMap, *vi).size() == 1) |
471 | { |
472 | Vertex temp = *get(domMap, *vi).begin(); |
473 | put(domTreePredMap, *vi, temp); |
474 | } |
475 | } |
476 | } |
477 | |
478 | template<class Graph, class DomTreePredMap> |
479 | void |
480 | iterative_bit_vector_dominator_tree |
481 | (const Graph& g, |
482 | const typename graph_traits<Graph>::vertex_descriptor& entry, |
483 | DomTreePredMap domTreePredMap) |
484 | { |
485 | typename property_map<Graph, vertex_index_t>::const_type |
486 | indexMap = get(vertex_index, g); |
487 | |
488 | iterative_bit_vector_dominator_tree(g, entry, indexMap, domTreePredMap); |
489 | } |
490 | } // namespace boost |
491 | |
492 | #endif // BOOST_GRAPH_DOMINATOR_HPP |
493 | |