gravatar
kpeter (Peter Kovacs)
kpeter@inf.elte.hu
Faster computation of the dual solution in CostScaling (#417)
0 1 0
default
1 file changed with 54 insertions and 26 deletions:
↑ Collapse diff ↑
Ignore white space 32 line context
... ...
@@ -224,33 +224,32 @@
224 224
      const Value& operator[](const Key& key) const {
225 225
        return _v[StaticDigraph::id(key)];
226 226
      }
227 227

	
228 228
      Value& operator[](const Key& key) {
229 229
        return _v[StaticDigraph::id(key)];
230 230
      }
231 231

	
232 232
      void set(const Key& key, const Value& val) {
233 233
        _v[StaticDigraph::id(key)] = val;
234 234
      }
235 235

	
236 236
    private:
237 237
      std::vector<Value>& _v;
238 238
    };
239 239

	
240
    typedef StaticVectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;
241 240
    typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
242 241

	
243 242
  private:
244 243

	
245 244
    // Data related to the underlying digraph
246 245
    const GR &_graph;
247 246
    int _node_num;
248 247
    int _arc_num;
249 248
    int _res_node_num;
250 249
    int _res_arc_num;
251 250
    int _root;
252 251

	
253 252
    // Parameters of the problem
254 253
    bool _have_lower;
255 254
    Value _sum_supply;
256 255
    int _sup_node_num;
... ...
@@ -275,40 +274,32 @@
275 274
    LargeCostVector _cost;
276 275
    LargeCostVector _pi;
277 276
    ValueVector _excess;
278 277
    IntVector _next_out;
279 278
    std::deque<int> _active_nodes;
280 279

	
281 280
    // Data for scaling
282 281
    LargeCost _epsilon;
283 282
    int _alpha;
284 283

	
285 284
    IntVector _buckets;
286 285
    IntVector _bucket_next;
287 286
    IntVector _bucket_prev;
288 287
    IntVector _rank;
289 288
    int _max_rank;
290 289

	
291
    // Data for a StaticDigraph structure
292
    typedef std::pair<int, int> IntPair;
293
    StaticDigraph _sgr;
294
    std::vector<IntPair> _arc_vec;
295
    std::vector<LargeCost> _cost_vec;
296
    LargeCostArcMap _cost_map;
297
    LargeCostNodeMap _pi_map;
298

	
299 290
  public:
300 291

	
301 292
    /// \brief Constant for infinite upper bounds (capacities).
302 293
    ///
303 294
    /// Constant for infinite upper bounds (capacities).
304 295
    /// It is \c std::numeric_limits<Value>::infinity() if available,
305 296
    /// \c std::numeric_limits<Value>::max() otherwise.
306 297
    const Value INF;
307 298

	
308 299
  public:
309 300

	
310 301
    /// \name Named Template Parameters
311 302
    /// @{
312 303

	
313 304
    template <typename T>
314 305
    struct SetLargeCostTraits : public Traits {
... ...
@@ -329,33 +320,32 @@
329 320

	
330 321
    /// @}
331 322

	
332 323
  protected:
333 324

	
334 325
    CostScaling() {}
335 326

	
336 327
  public:
337 328

	
338 329
    /// \brief Constructor.
339 330
    ///
340 331
    /// The constructor of the class.
341 332
    ///
342 333
    /// \param graph The digraph the algorithm runs on.
343 334
    CostScaling(const GR& graph) :
344 335
      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
345
      _cost_map(_cost_vec), _pi_map(_pi),
346 336
      INF(std::numeric_limits<Value>::has_infinity ?
347 337
          std::numeric_limits<Value>::infinity() :
348 338
          std::numeric_limits<Value>::max())
349 339
    {
350 340
      // Check the number types
351 341
      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
352 342
        "The flow type of CostScaling must be signed");
353 343
      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
354 344
        "The cost type of CostScaling must be signed");
355 345

	
356 346
      // Reset data structures
357 347
      reset();
358 348
    }
359 349

	
360 350
    /// \name Parameters
361 351
    /// The parameters of the algorithm can be specified using these
... ...
@@ -606,35 +596,32 @@
606 596
      _forward.resize(_res_arc_num);
607 597
      _source.resize(_res_arc_num);
608 598
      _target.resize(_res_arc_num);
609 599
      _reverse.resize(_res_arc_num);
610 600

	
611 601
      _lower.resize(_res_arc_num);
612 602
      _upper.resize(_res_arc_num);
613 603
      _scost.resize(_res_arc_num);
614 604
      _supply.resize(_res_node_num);
615 605

	
616 606
      _res_cap.resize(_res_arc_num);
617 607
      _cost.resize(_res_arc_num);
618 608
      _pi.resize(_res_node_num);
619 609
      _excess.resize(_res_node_num);
620 610
      _next_out.resize(_res_node_num);
621 611

	
622
      _arc_vec.reserve(_res_arc_num);
623
      _cost_vec.reserve(_res_arc_num);
624

	
625 612
      // Copy the graph
626 613
      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
627 614
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
628 615
        _node_id[n] = i;
629 616
      }
630 617
      i = 0;
631 618
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
632 619
        _first_out[i] = j;
633 620
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
634 621
          _arc_idf[a] = j;
635 622
          _forward[j] = true;
636 623
          _source[j] = i;
637 624
          _target[j] = _node_id[_graph.runningNode(a)];
638 625
        }
639 626
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
640 627
          _arc_idb[a] = j;
... ...
@@ -910,48 +897,89 @@
910 897
    // Execute the algorithm and transform the results
911 898
    void start(Method method) {
912 899
      const int MAX_PARTIAL_PATH_LENGTH = 4;
913 900

	
914 901
      switch (method) {
915 902
        case PUSH:
916 903
          startPush();
917 904
          break;
918 905
        case AUGMENT:
919 906
          startAugment(_res_node_num - 1);
920 907
          break;
921 908
        case PARTIAL_AUGMENT:
922 909
          startAugment(MAX_PARTIAL_PATH_LENGTH);
923 910
          break;
924 911
      }
925 912

	
926
      // Compute node potentials for the original costs
927
      _arc_vec.clear();
928
      _cost_vec.clear();
929
      for (int j = 0; j != _res_arc_num; ++j) {
930
        if (_res_cap[j] > 0) {
931
          _arc_vec.push_back(IntPair(_source[j], _target[j]));
932
          _cost_vec.push_back(_scost[j]);
913
      // Compute node potentials (dual solution)
914
      for (int i = 0; i != _res_node_num; ++i) {
915
        _pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha));
916
      }
917
      bool optimal = true;
918
      for (int i = 0; optimal && i != _res_node_num; ++i) {
919
        LargeCost pi_i = _pi[i];
920
        int last_out = _first_out[i+1];
921
        for (int j = _first_out[i]; j != last_out; ++j) {
922
          if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) {
923
            optimal = false;
924
            break;
925
          }
933 926
        }
934 927
      }
935
      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
936 928

	
937
      typename BellmanFord<StaticDigraph, LargeCostArcMap>
938
        ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);
939
      bf.distMap(_pi_map);
940
      bf.init(0);
941
      bf.start();
929
      if (!optimal) {
930
        // Compute node potentials for the original costs with BellmanFord
931
        // (if it is necessary)
932
        typedef std::pair<int, int> IntPair;
933
        StaticDigraph sgr;
934
        std::vector<IntPair> arc_vec;
935
        std::vector<LargeCost> cost_vec;
936
        LargeCostArcMap cost_map(cost_vec);
937

	
938
        arc_vec.clear();
939
        cost_vec.clear();
940
        for (int j = 0; j != _res_arc_num; ++j) {
941
          if (_res_cap[j] > 0) {
942
            int u = _source[j], v = _target[j];
943
            arc_vec.push_back(IntPair(u, v));
944
            cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]);
945
          }
946
        }
947
        sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end());
948

	
949
        typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create
950
          bf(sgr, cost_map);
951
        bf.init(0);
952
        bf.start();
953

	
954
        for (int i = 0; i != _res_node_num; ++i) {
955
          _pi[i] += bf.dist(sgr.node(i));
956
        }
957
      }
958

	
959
      // Shift potentials to meet the requirements of the GEQ type
960
      // optimality conditions
961
      LargeCost max_pot = _pi[_root];
962
      for (int i = 0; i != _res_node_num; ++i) {
963
        if (_pi[i] > max_pot) max_pot = _pi[i];
964
      }
965
      if (max_pot != 0) {
966
        for (int i = 0; i != _res_node_num; ++i) {
967
          _pi[i] -= max_pot;
968
        }
969
      }
942 970

	
943 971
      // Handle non-zero lower bounds
944 972
      if (_have_lower) {
945 973
        int limit = _first_out[_root];
946 974
        for (int j = 0; j != limit; ++j) {
947 975
          if (!_forward[j]) _res_cap[j] += _lower[j];
948 976
        }
949 977
      }
950 978
    }
951 979

	
952 980
    // Initialize a cost scaling phase
953 981
    void initPhase() {
954 982
      // Saturate arcs not satisfying the optimality condition
955 983
      for (int u = 0; u != _res_node_num; ++u) {
956 984
        int last_out = _first_out[u+1];
957 985
        LargeCost pi_u = _pi[u];
0 comments (0 inline)