Reference documentation for deal.II version 9.2.0
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graph_coloring.h
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16 
17 #ifndef dealii_graph_coloring_h
18 # define dealii_graph_coloring_h
19 
20 
21 # include <deal.II/base/config.h>
22 
24 
26 
27 # include <functional>
28 # include <set>
29 # include <unordered_map>
30 # include <unordered_set>
31 # include <vector>
32 
33 
35 
39 namespace GraphColoring
40 {
41  namespace internal
42  {
52  inline bool
54  const std::vector<types::global_dof_index> &indices1,
55  const std::vector<types::global_dof_index> &indices2)
56  {
57  // we assume that both arrays are sorted, so we can walk
58  // them in lockstep and see if we encounter an index that's
59  // in both arrays. once we reach the end of either array,
60  // we know that there is no intersection
61  std::vector<types::global_dof_index>::const_iterator p = indices1.begin(),
62  q = indices2.begin();
63  while ((p != indices1.end()) && (q != indices2.end()))
64  {
65  if (*p < *q)
66  ++p;
67  else if (*p > *q)
68  ++q;
69  else
70  // conflict found!
71  return true;
72  }
73 
74  // no conflict found!
75  return false;
76  }
77 
78 
109  template <typename Iterator>
110  std::vector<std::vector<Iterator>>
112  const Iterator & begin,
113  const typename identity<Iterator>::type &end,
114  const std::function<std::vector<types::global_dof_index>(
115  const Iterator &)> & get_conflict_indices)
116  {
117  // Number of iterators.
118  unsigned int n_iterators = 0;
119 
120  // Create a map from conflict indices to iterators
121  std::unordered_map<types::global_dof_index, std::vector<Iterator>>
122  indices_to_iterators;
123  for (Iterator it = begin; it != end; ++it)
124  {
125  const std::vector<types::global_dof_index> conflict_indices =
126  get_conflict_indices(it);
127  const unsigned int n_conflict_indices = conflict_indices.size();
128  for (unsigned int i = 0; i < n_conflict_indices; ++i)
129  indices_to_iterators[conflict_indices[i]].push_back(it);
130  ++n_iterators;
131  }
132 
133  // create the very first zone which contains only the first
134  // iterator. then create the other zones. keep track of all the
135  // iterators that have already been assigned to a zone
136  std::vector<std::vector<Iterator>> zones(1,
137  std::vector<Iterator>(1, begin));
138  std::set<Iterator> used_it;
139  used_it.insert(begin);
140  while (used_it.size() != n_iterators)
141  {
142  // loop over the elements of the previous zone. for each element of
143  // the previous zone, get the conflict indices and from there get
144  // those iterators that are conflicting with the current element
145  typename std::vector<Iterator>::iterator previous_zone_it(
146  zones.back().begin());
147  typename std::vector<Iterator>::iterator previous_zone_end(
148  zones.back().end());
149  std::vector<Iterator> new_zone;
150  for (; previous_zone_it != previous_zone_end; ++previous_zone_it)
151  {
152  const std::vector<types::global_dof_index> conflict_indices =
153  get_conflict_indices(*previous_zone_it);
154 
155  const unsigned int n_conflict_indices(conflict_indices.size());
156  for (unsigned int i = 0; i < n_conflict_indices; ++i)
157  {
158  const std::vector<Iterator> &conflicting_elements =
159  indices_to_iterators[conflict_indices[i]];
160  for (unsigned int j = 0; j < conflicting_elements.size(); ++j)
161  {
162  // check that the iterator conflicting with the current
163  // one is not associated to a zone yet and if so, assign
164  // it to the current zone. mark it as used
165  //
166  // we can shortcut this test if the conflicting iterator
167  // is the current iterator
168  if ((conflicting_elements[j] != *previous_zone_it) &&
169  (used_it.count(conflicting_elements[j]) == 0))
170  {
171  new_zone.push_back(conflicting_elements[j]);
172  used_it.insert(conflicting_elements[j]);
173  }
174  }
175  }
176  }
177 
178  // If there are iterators in the new zone, then the zone is added to
179  // the partition. Otherwise, the graph is disconnected and we need to
180  // find an iterator on the other part of the graph. start the whole
181  // process again with the first iterator that hasn't been assigned to
182  // a zone yet
183  if (new_zone.size() != 0)
184  zones.push_back(new_zone);
185  else
186  for (Iterator it = begin; it != end; ++it)
187  if (used_it.count(it) == 0)
188  {
189  zones.push_back(std::vector<Iterator>(1, it));
190  used_it.insert(it);
191  break;
192  }
193  }
194 
195  return zones;
196  }
197 
198 
199 
222  template <typename Iterator>
223  void
225  std::vector<Iterator> & partition,
226  const std::function<std::vector<types::global_dof_index>(
227  const Iterator &)> & get_conflict_indices,
228  std::vector<std::vector<Iterator>> &partition_coloring)
229  {
230  partition_coloring.clear();
231 
232  // Number of zones composing the partitioning.
233  const unsigned int partition_size(partition.size());
234  std::vector<unsigned int> sorted_vertices(partition_size);
235  std::vector<int> degrees(partition_size);
236  std::vector<std::vector<types::global_dof_index>> conflict_indices(
237  partition_size);
238  std::vector<std::vector<unsigned int>> graph(partition_size);
239 
240  // Get the conflict indices associated to each iterator. The
241  // conflict_indices have to be sorted so we can more easily find conflicts
242  // later on
243  for (unsigned int i = 0; i < partition_size; ++i)
244  {
245  conflict_indices[i] = get_conflict_indices(partition[i]);
246  std::sort(conflict_indices[i].begin(), conflict_indices[i].end());
247  }
248 
249  // Compute the degree of each vertex of the graph using the
250  // intersection of the conflict indices.
251  for (unsigned int i = 0; i < partition_size; ++i)
252  for (unsigned int j = i + 1; j < partition_size; ++j)
253  // If the two iterators share indices then we increase the degree of
254  // the vertices and create an ''edge'' in the graph.
255  if (have_nonempty_intersection(conflict_indices[i],
256  conflict_indices[j]))
257  {
258  ++degrees[i];
259  ++degrees[j];
260  graph[i].push_back(j);
261  graph[j].push_back(i);
262  }
263 
264  // Sort the vertices by decreasing degree.
265  std::vector<int>::iterator degrees_it;
266  for (unsigned int i = 0; i < partition_size; ++i)
267  {
268  // Find the largest element.
269  degrees_it = std::max_element(degrees.begin(), degrees.end());
270  sorted_vertices[i] = degrees_it - degrees.begin();
271  // Put the largest element to -1 so it cannot be chosen again.
272  *degrees_it = -1;
273  }
274 
275  // Color the graph.
276  std::vector<std::unordered_set<unsigned int>> colors_used;
277  for (unsigned int i = 0; i < partition_size; ++i)
278  {
279  const unsigned int current_vertex(sorted_vertices[i]);
280  bool new_color(true);
281  // Try to use an existing color, i.e., try to find a color which is
282  // not associated to one of the vertices linked to current_vertex.
283  // Loop over the color.
284  for (unsigned int j = 0; j < partition_coloring.size(); ++j)
285  {
286  // Loop on the vertices linked to current_vertex. If one vertex
287  // linked to current_vertex is already using the color j, this
288  // color cannot be used anymore.
289  bool unused_color(true);
290  for (const auto adjacent_vertex : graph[current_vertex])
291  if (colors_used[j].count(adjacent_vertex) == 1)
292  {
293  unused_color = false;
294  break;
295  }
296  if (unused_color)
297  {
298  partition_coloring[j].push_back(partition[current_vertex]);
299  colors_used[j].insert(current_vertex);
300  new_color = false;
301  break;
302  }
303  }
304  // Add a new color.
305  if (new_color)
306  {
307  partition_coloring.push_back(
308  std::vector<Iterator>(1, partition[current_vertex]));
309  std::unordered_set<unsigned int> tmp;
310  tmp.insert(current_vertex);
311  colors_used.push_back(tmp);
312  }
313  }
314  }
315 
316 
317 
327  template <typename Iterator>
328  std::vector<std::vector<Iterator>>
330  const std::vector<std::vector<std::vector<Iterator>>> &partition_coloring)
331  {
332  std::vector<std::vector<Iterator>> coloring;
333 
334  // Count the number of iterators in each color.
335  const unsigned int partition_size(partition_coloring.size());
336  std::vector<std::vector<unsigned int>> colors_counter(partition_size);
337  for (unsigned int i = 0; i < partition_size; ++i)
338  {
339  const unsigned int n_colors(partition_coloring[i].size());
340  colors_counter[i].resize(n_colors);
341  for (unsigned int j = 0; j < n_colors; ++j)
342  colors_counter[i][j] = partition_coloring[i][j].size();
343  }
344 
345  // Find the partition with the largest number of colors for the even
346  // partition.
347  unsigned int i_color(0);
348  unsigned int max_even_n_colors(0);
349  const unsigned int colors_size(colors_counter.size());
350  for (unsigned int i = 0; i < colors_size; i += 2)
351  {
352  if (max_even_n_colors < colors_counter[i].size())
353  {
354  max_even_n_colors = colors_counter[i].size();
355  i_color = i;
356  }
357  }
358  coloring.resize(max_even_n_colors);
359  for (unsigned int j = 0; j < colors_counter[i_color].size(); ++j)
360  coloring[j] = partition_coloring[i_color][j];
361 
362  for (unsigned int i = 0; i < partition_size; i += 2)
363  {
364  if (i != i_color)
365  {
366  std::unordered_set<unsigned int> used_k;
367  for (unsigned int j = 0; j < colors_counter[i].size(); ++j)
368  {
369  // Find the color in the current partition with the largest
370  // number of iterators.
371  std::vector<unsigned int>::iterator it;
372  it = std::max_element(colors_counter[i].begin(),
373  colors_counter[i].end());
374  unsigned int min_iterators(static_cast<unsigned int>(-1));
375  unsigned int pos(0);
376  // Find the color of coloring with the least number of colors
377  // among the colors that have not been used yet.
378  for (unsigned int k = 0; k < max_even_n_colors; ++k)
379  if (used_k.count(k) == 0)
380  if (colors_counter[i_color][k] < min_iterators)
381  {
382  min_iterators = colors_counter[i_color][k];
383  pos = k;
384  }
385  colors_counter[i_color][pos] += *it;
386  // Concatenate the current color with the existing coloring.
387  coloring[pos].insert(
388  coloring[pos].end(),
389  partition_coloring[i][it - colors_counter[i].begin()]
390  .begin(),
391  partition_coloring[i][it - colors_counter[i].begin()]
392  .end());
393  used_k.insert(pos);
394  // Put the number of iterators to the current color to zero.
395  *it = 0;
396  }
397  }
398  }
399 
400  // If there is more than one partition, do the same thing that we did for
401  // the even partitions to the odd partitions
402  if (partition_size > 1)
403  {
404  unsigned int max_odd_n_colors(0);
405  for (unsigned int i = 1; i < partition_size; i += 2)
406  {
407  if (max_odd_n_colors < colors_counter[i].size())
408  {
409  max_odd_n_colors = colors_counter[i].size();
410  i_color = i;
411  }
412  }
413  coloring.resize(max_even_n_colors + max_odd_n_colors);
414  for (unsigned int j = 0; j < colors_counter[i_color].size(); ++j)
415  coloring[max_even_n_colors + j] = partition_coloring[i_color][j];
416 
417  for (unsigned int i = 1; i < partition_size; i += 2)
418  {
419  if (i != i_color)
420  {
421  std::unordered_set<unsigned int> used_k;
422  for (unsigned int j = 0; j < colors_counter[i].size(); ++j)
423  {
424  // Find the color in the current partition with the
425  // largest number of iterators.
426  std::vector<unsigned int>::iterator it;
427  it = std::max_element(colors_counter[i].begin(),
428  colors_counter[i].end());
429  unsigned int min_iterators(static_cast<unsigned int>(-1));
430  unsigned int pos(0);
431  // Find the color of coloring with the least number of
432  // colors among the colors that have not been used yet.
433  for (unsigned int k = 0; k < max_odd_n_colors; ++k)
434  if (used_k.count(k) == 0)
435  if (colors_counter[i_color][k] < min_iterators)
436  {
437  min_iterators = colors_counter[i_color][k];
438  pos = k;
439  }
440  colors_counter[i_color][pos] += *it;
441  // Concatenate the current color with the existing
442  // coloring.
443  coloring[max_even_n_colors + pos].insert(
444  coloring[max_even_n_colors + pos].end(),
445  partition_coloring[i][it - colors_counter[i].begin()]
446  .begin(),
447  partition_coloring[i][it - colors_counter[i].begin()]
448  .end());
449  used_k.insert(pos);
450  // Put the number of iterators to the current color to
451  // zero.
452  *it = 0;
453  }
454  }
455  }
456  }
457 
458  return coloring;
459  }
460  } // namespace internal
461 
462 
542  template <typename Iterator>
543  std::vector<std::vector<Iterator>>
545  const Iterator & begin,
546  const typename identity<Iterator>::type & end,
547  const std::function<std::vector<types::global_dof_index>(
548  const typename identity<Iterator>::type &)> &get_conflict_indices)
549  {
550  Assert(begin != end,
551  ExcMessage(
552  "GraphColoring is not prepared to deal with empty ranges!"));
553 
554  // Create the partitioning.
555  std::vector<std::vector<Iterator>> partitioning =
556  internal::create_partitioning(begin, end, get_conflict_indices);
557 
558  // Color the iterators within each partition.
559  // Run the coloring algorithm on each zone in parallel
560  const unsigned int partitioning_size(partitioning.size());
561  std::vector<std::vector<std::vector<Iterator>>> partition_coloring(
562  partitioning_size);
563 
564  Threads::TaskGroup<> tasks;
565  for (unsigned int i = 0; i < partitioning_size; ++i)
566  tasks += Threads::new_task(&internal::make_dsatur_coloring<Iterator>,
567  partitioning[i],
568  get_conflict_indices,
569  partition_coloring[i]);
570  tasks.join_all();
571 
572  // Gather the colors together.
573  return internal::gather_colors(partition_coloring);
574  }
575 
582  unsigned int
583  color_sparsity_pattern(const SparsityPattern & sparsity_pattern,
584  std::vector<unsigned int> &color_indices);
585 
586 } // namespace GraphColoring
587 
589 
590 
591 //---------------------------- graph_coloring.h ---------------------------
592 // end of #ifndef dealii_graph_coloring_h
593 #endif
594 //---------------------------- graph_coloring.h ---------------------------
std::vector< std::vector< Iterator > > create_partitioning(const Iterator &begin, const typename identity< Iterator >::type &end, const std::function< std::vector< types::global_dof_index >(const Iterator &)> &get_conflict_indices)
Task< RT > new_task(const std::function< RT()> &function)
std::vector< std::vector< Iterator > > make_graph_coloring(const Iterator &begin, const typename identity< Iterator >::type &end, const std::function< std::vector< types::global_dof_index >(const typename identity< Iterator >::type &)> &get_conflict_indices)
bool have_nonempty_intersection(const std::vector< types::global_dof_index > &indices1, const std::vector< types::global_dof_index > &indices2)
static ::ExceptionBase & ExcMessage(std::string arg1)
void partition(const SparsityPattern &sparsity_pattern, const unsigned int n_partitions, std::vector< unsigned int > &partition_indices, const Partitioner partitioner=Partitioner::metis)
#define Assert(cond, exc)
Definition: exceptions.h:1419
void make_dsatur_coloring(std::vector< Iterator > &partition, const std::function< std::vector< types::global_dof_index >(const Iterator &)> &get_conflict_indices, std::vector< std::vector< Iterator >> &partition_coloring)
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:359
VectorType::value_type * end(VectorType &V)
unsigned int color_sparsity_pattern(const SparsityPattern &sparsity_pattern, std::vector< unsigned int > &color_indices)
MatrixTableIterators::Iterator< TransposeTable< T >, Constness, MatrixTableIterators::Storage::column_major > Iterator
Definition: table.h:1913
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:358
VectorType::value_type * begin(VectorType &V)
std::vector< std::vector< Iterator > > gather_colors(const std::vector< std::vector< std::vector< Iterator >>> &partition_coloring)