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1 // Copyright (C) 2004-2006 The Trustees of Indiana University.
2
3 // Use, modification and distribution is subject to the Boost Software
4 // License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
5 // http://www.boost.org/LICENSE_1_0.txt)
6
7 // Authors: Brian Barrett
8 // Douglas Gregor
9 // Andrew Lumsdaine
10 #ifndef BOOST_GRAPH_PARALLEL_CC_PS_HPP
11 #define BOOST_GRAPH_PARALLEL_CC_PS_HPP
12
13 #ifndef BOOST_GRAPH_USE_MPI
14 #error "Parallel BGL files should not be included unless <boost/graph/use_mpi.hpp> has been included"
15 #endif
16
17 #include <boost/assert.hpp>
18 #include <boost/property_map/property_map.hpp>
19 #include <boost/graph/parallel/algorithm.hpp>
20 #include <boost/pending/indirect_cmp.hpp>
21 #include <boost/graph/graph_traits.hpp>
22 #include <boost/graph/overloading.hpp>
23 #include <boost/graph/distributed/concepts.hpp>
24 #include <boost/graph/parallel/properties.hpp>
25 #include <boost/graph/parallel/process_group.hpp>
26 #include <boost/optional.hpp>
27 #include <algorithm>
28 #include <vector>
29 #include <queue>
30 #include <limits>
31 #include <map>
32 #include <boost/graph/parallel/container_traits.hpp>
33 #include <boost/graph/iteration_macros.hpp>
34
35
36 // Connected components algorithm based on a parallel search.
37 //
38 // Every N nodes starts a parallel search from the first vertex in
39 // their local vertex list during the first superstep (the other nodes
40 // remain idle during the first superstep to reduce the number of
41 // conflicts in numbering the components). At each superstep, all new
42 // component mappings from remote nodes are handled. If there is no
43 // work from remote updates, a new vertex is removed from the local
44 // list and added to the work queue.
45 //
46 // Components are allocated from the component_value_allocator object,
47 // which ensures that a given component number is unique in the
48 // system, currently by using the rank and number of processes to
49 // stride allocations.
50 //
51 // When two components are discovered to actually be the same
52 // component, a mapping is created in the collisions object. The
53 // lower component number is prefered in the resolution, so component
54 // numbering resolution is consistent. After the search has exhausted
55 // all vertices in the graph, the mapping is shared with all
56 // processes, and they independently resolve the comonent mapping (so
57 // O((N * NP) + (V * NP)) work, in O(N + V) time, where N is the
58 // number of mappings and V is the number of local vertices). This
59 // phase can likely be significantly sped up if a clever algorithm for
60 // the reduction can be found.
61 namespace boost { namespace graph { namespace distributed {
62 namespace cc_ps_detail {
63 // Local object for allocating component numbers. There are two
64 // places this happens in the code, and I was getting sick of them
65 // getting out of sync. Components are not tightly packed in
66 // numbering, but are numbered to ensure each rank has its own
67 // independent sets of numberings.
68 template<typename component_value_type>
69 class component_value_allocator {
70 public:
71 component_value_allocator(int num, int size) :
72 last(0), num(num), size(size)
73 {
74 }
75
76 component_value_type allocate(void)
77 {
78 component_value_type ret = num + (last * size);
79 last++;
80 return ret;
81 }
82
83 private:
84 component_value_type last;
85 int num;
86 int size;
87 };
88
89
90 // Map of the "collisions" between component names in the global
91 // component mapping. TO make cleanup easier, component numbers
92 // are added, pointing to themselves, when a new component is
93 // found. In order to make the results deterministic, the lower
94 // component number is always taken. The resolver will drill
95 // through the map until it finds a component entry that points to
96 // itself as the next value, allowing some cleanup to happen at
97 // update() time. Attempts are also made to update the mapping
98 // when new entries are created.
99 //
100 // Note that there's an assumption that the entire mapping is
101 // shared during the end of the algorithm, but before component
102 // name resolution.
103 template<typename component_value_type>
104 class collision_map {
105 public:
106 collision_map() : num_unique(0)
107 {
108 }
109
110 // add new component mapping first time component is used. Own
111 // function only so that we can sanity check there isn't already
112 // a mapping for that component number (which would be bad)
113 void add(const component_value_type &a)
114 {
115 BOOST_ASSERT(collisions.count(a) == 0);
116 collisions[a] = a;
117 }
118
119 // add a mapping between component values saying they're the
120 // same component
121 void add(const component_value_type &a, const component_value_type &b)
122 {
123 component_value_type high, low, tmp;
124 if (a > b) {
125 high = a;
126 low = b;
127 } else {
128 high = b;
129 low = a;
130 }
131
132 if (collisions.count(high) != 0 && collisions[high] != low) {
133 tmp = collisions[high];
134 if (tmp > low) {
135 collisions[tmp] = low;
136 collisions[high] = low;
137 } else {
138 collisions[low] = tmp;
139 collisions[high] = tmp;
140 }
141 } else {
142 collisions[high] = low;
143 }
144
145 }
146
147 // get the "real" component number for the given component.
148 // Used to resolve mapping at end of run.
149 component_value_type update(component_value_type a)
150 {
151 BOOST_ASSERT(num_unique > 0);
152 BOOST_ASSERT(collisions.count(a) != 0);
153 return collisions[a];
154 }
155
156 // collapse the collisions tree, so that update is a one lookup
157 // operation. Count unique components at the same time.
158 void uniqify(void)
159 {
160 typename std::map<component_value_type, component_value_type>::iterator i, end;
161
162 end = collisions.end();
163 for (i = collisions.begin() ; i != end ; ++i) {
164 if (i->first == i->second) {
165 num_unique++;
166 } else {
167 i->second = collisions[i->second];
168 }
169 }
170 }
171
172 // get the number of component entries that have an associated
173 // component number of themselves, which are the real components
174 // used in the final mapping. This is the number of unique
175 // components in the graph.
176 int unique(void)
177 {
178 BOOST_ASSERT(num_unique > 0);
179 return num_unique;
180 }
181
182 // "serialize" into a vector for communication.
183 std::vector<component_value_type> serialize(void)
184 {
185 std::vector<component_value_type> ret;
186 typename std::map<component_value_type, component_value_type>::iterator i, end;
187
188 end = collisions.end();
189 for (i = collisions.begin() ; i != end ; ++i) {
190 ret.push_back(i->first);
191 ret.push_back(i->second);
192 }
193
194 return ret;
195 }
196
197 private:
198 std::map<component_value_type, component_value_type> collisions;
199 int num_unique;
200 };
201
202
203 // resolver to handle remote updates. The resolver will add
204 // entries into the collisions map if required, and if it is the
205 // first time the vertex has been touched, it will add the vertex
206 // to the remote queue. Note that local updates are handled
207 // differently, in the main loop (below).
208
209 // BWB - FIX ME - don't need graph anymore - can pull from key value of Component Map.
210 template<typename ComponentMap, typename work_queue>
211 struct update_reducer {
212 BOOST_STATIC_CONSTANT(bool, non_default_resolver = false);
213
214 typedef typename property_traits<ComponentMap>::value_type component_value_type;
215 typedef typename property_traits<ComponentMap>::key_type vertex_descriptor;
216
217 update_reducer(work_queue *q,
218 cc_ps_detail::collision_map<component_value_type> *collisions,
219 processor_id_type pg_id) :
220 q(q), collisions(collisions), pg_id(pg_id)
221 {
222 }
223
224 // ghost cell initialization routine. This should never be
225 // called in this imlementation.
226 template<typename K>
227 component_value_type operator()(const K&) const
228 {
229 return component_value_type(0);
230 }
231
232 // resolver for remote updates. I'm not entirely sure why, but
233 // I decided to not change the value of the vertex if it's
234 // already non-infinite. It doesn't matter in the end, as we'll
235 // touch every vertex in the cleanup phase anyway. If the
236 // component is currently infinite, set to the new component
237 // number and add the vertex to the work queue. If it's not
238 // infinite, we've touched it already so don't add it to the
239 // work queue. Do add a collision entry so that we know the two
240 // components are the same.
241 component_value_type operator()(const vertex_descriptor &v,
242 const component_value_type& current,
243 const component_value_type& update) const
244 {
245 const component_value_type max = (std::numeric_limits<component_value_type>::max)();
246 component_value_type ret = current;
247
248 if (max == current) {
249 q->push(v);
250 ret = update;
251 } else if (current != update) {
252 collisions->add(current, update);
253 }
254
255 return ret;
256 }
257
258 // So for whatever reason, the property map can in theory call
259 // the resolver with a local descriptor in addition to the
260 // standard global descriptor. As far as I can tell, this code
261 // path is never taken in this implementation, but I need to
262 // have this code here to make it compile. We just make a
263 // global descriptor and call the "real" operator().
264 template<typename K>
265 component_value_type operator()(const K& v,
266 const component_value_type& current,
267 const component_value_type& update) const
268 {
269 return (*this)(vertex_descriptor(pg_id, v), current, update);
270 }
271
272 private:
273 work_queue *q;
274 collision_map<component_value_type> *collisions;
275 boost::processor_id_type pg_id;
276 };
277
278 } // namespace cc_ps_detail
279
280
281 template<typename Graph, typename ComponentMap>
282 typename property_traits<ComponentMap>::value_type
283 connected_components_ps(const Graph& g, ComponentMap c)
284 {
285 using boost::graph::parallel::process_group;
286
287 typedef typename property_traits<ComponentMap>::value_type component_value_type;
288 typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator;
289 typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
290 typedef typename boost::graph::parallel::process_group_type<Graph>
291 ::type process_group_type;
292 typedef typename process_group_type::process_id_type process_id_type;
293 typedef std::queue<vertex_descriptor> work_queue;
294
295 static const component_value_type max_component =
296 (std::numeric_limits<component_value_type>::max)();
297 typename property_map<Graph, vertex_owner_t>::const_type
298 owner = get(vertex_owner, g);
299
300 // standard who am i? stuff
301 process_group_type pg = process_group(g);
302 process_id_type id = process_id(pg);
303
304 // Initialize every vertex to have infinite component number
305 BGL_FORALL_VERTICES_T(v, g, Graph) put(c, v, max_component);
306
307 vertex_iterator current, end;
308 boost::tie(current, end) = vertices(g);
309
310 cc_ps_detail::component_value_allocator<component_value_type> cva(process_id(pg), num_processes(pg));
311 cc_ps_detail::collision_map<component_value_type> collisions;
312 work_queue q; // this is intentionally a local data structure
313 c.set_reduce(cc_ps_detail::update_reducer<ComponentMap, work_queue>(&q, &collisions, id));
314
315 // add starting work
316 while (true) {
317 bool useful_found = false;
318 component_value_type val = cva.allocate();
319 put(c, *current, val);
320 collisions.add(val);
321 q.push(*current);
322 if (0 != out_degree(*current, g)) useful_found = true;
323 ++current;
324 if (useful_found) break;
325 }
326
327 // Run the loop until everyone in the system is done
328 bool global_done = false;
329 while (!global_done) {
330
331 // drain queue of work for this superstep
332 while (!q.empty()) {
333 vertex_descriptor v = q.front();
334 q.pop();
335 // iterate through outedges of the vertex currently being
336 // examined, setting their component to our component. There
337 // is no way to end up in the queue without having a component
338 // number already.
339
340 BGL_FORALL_ADJ_T(v, peer, g, Graph) {
341 component_value_type my_component = get(c, v);
342
343 // update other vertex with our component information.
344 // Resolver will handle remote collisions as well as whether
345 // to put the vertex on the work queue or not. We have to
346 // handle local collisions and work queue management
347 if (id == get(owner, peer)) {
348 if (max_component == get(c, peer)) {
349 put(c, peer, my_component);
350 q.push(peer);
351 } else if (my_component != get(c, peer)) {
352 collisions.add(my_component, get(c, peer));
353 }
354 } else {
355 put(c, peer, my_component);
356 }
357 }
358 }
359
360 // synchronize / start a new superstep.
361 synchronize(pg);
362 global_done = all_reduce(pg, (q.empty() && (current == end)), boost::parallel::minimum<bool>());
363
364 // If the queue is currently empty, add something to do to start
365 // the current superstep (supersteps start at the sync, not at
366 // the top of the while loop as one might expect). Down at the
367 // bottom of the while loop so that not everyone starts the
368 // algorithm with something to do, to try to reduce component
369 // name conflicts
370 if (q.empty()) {
371 bool useful_found = false;
372 for ( ; current != end && !useful_found ; ++current) {
373 if (max_component == get(c, *current)) {
374 component_value_type val = cva.allocate();
375 put(c, *current, val);
376 collisions.add(val);
377 q.push(*current);
378 if (0 != out_degree(*current, g)) useful_found = true;
379 }
380 }
381 }
382 }
383
384 // share component mappings
385 std::vector<component_value_type> global;
386 std::vector<component_value_type> mine = collisions.serialize();
387 all_gather(pg, mine.begin(), mine.end(), global);
388 for (size_t i = 0 ; i < global.size() ; i += 2) {
389 collisions.add(global[i], global[i + 1]);
390 }
391 collisions.uniqify();
392
393 // update the component mappings
394 BGL_FORALL_VERTICES_T(v, g, Graph) {
395 put(c, v, collisions.update(get(c, v)));
396 }
397
398 return collisions.unique();
399 }
400
401 } // end namespace distributed
402
403 } // end namespace graph
404
405 } // end namespace boost
406
407 #endif // BOOST_GRAPH_PARALLEL_CC_HPP