1 | // -*- c++ -*- |
---|
2 | #ifndef LEMON_MINCOSTFLOW_H |
---|
3 | #define LEMON_MINCOSTFLOW_H |
---|
4 | |
---|
5 | ///\ingroup galgs |
---|
6 | ///\file |
---|
7 | ///\brief An algorithm for finding the minimum cost flow of given value in an uncapacitated network |
---|
8 | |
---|
9 | #include <lemon/dijkstra.h> |
---|
10 | #include <lemon/graph_wrapper.h> |
---|
11 | #include <lemon/maps.h> |
---|
12 | #include <vector> |
---|
13 | #include <list> |
---|
14 | #include <values.h> |
---|
15 | #include <lemon/for_each_macros.h> |
---|
16 | #include <lemon/unionfind.h> |
---|
17 | #include <lemon/bin_heap.h> |
---|
18 | #include <bfs_dfs.h> |
---|
19 | |
---|
20 | namespace lemon { |
---|
21 | |
---|
22 | /// \addtogroup galgs |
---|
23 | /// @{ |
---|
24 | |
---|
25 | ///\brief Implementation of an algorithm for solving the minimum cost general |
---|
26 | /// flow problem in an uncapacitated network |
---|
27 | /// |
---|
28 | /// |
---|
29 | /// The class \ref lemon::MinCostFlow "MinCostFlow" implements |
---|
30 | /// an algorithm for solving the following general minimum cost flow problem> |
---|
31 | /// |
---|
32 | /// |
---|
33 | /// |
---|
34 | /// \warning It is assumed here that the problem has a feasible solution |
---|
35 | /// |
---|
36 | /// The range of the cost (weight) function is nonnegative reals but |
---|
37 | /// the range of capacity function is the set of nonnegative integers. |
---|
38 | /// It is not a polinomial time algorithm for counting the minimum cost |
---|
39 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
---|
40 | /// where \c M is the value of the maximal flow. |
---|
41 | /// |
---|
42 | ///\author Attila Bernath |
---|
43 | template <typename Graph, typename CostMap, typename SupplyDemandMap> |
---|
44 | class MinCostFlow { |
---|
45 | |
---|
46 | typedef typename CostMap::ValueType Cost; |
---|
47 | |
---|
48 | |
---|
49 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
---|
50 | |
---|
51 | typedef typename Graph::Node Node; |
---|
52 | typedef typename Graph::NodeIt NodeIt; |
---|
53 | typedef typename Graph::Edge Edge; |
---|
54 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
55 | typedef typename Graph::template EdgeMap<SupplyDemand> FlowMap; |
---|
56 | typedef ConstMap<Edge,SupplyDemand> ConstEdgeMap; |
---|
57 | |
---|
58 | // typedef ConstMap<Edge,int> ConstMap; |
---|
59 | |
---|
60 | typedef ResGraphWrapper<const Graph,int,ConstEdgeMap,FlowMap> ResGraph; |
---|
61 | typedef typename ResGraph::Edge ResGraphEdge; |
---|
62 | |
---|
63 | class ModCostMap { |
---|
64 | //typedef typename ResGraph::template NodeMap<Cost> NodeMap; |
---|
65 | typedef typename Graph::template NodeMap<Cost> NodeMap; |
---|
66 | const ResGraph& res_graph; |
---|
67 | // const EdgeIntMap& rev; |
---|
68 | const CostMap &ol; |
---|
69 | const NodeMap &pot; |
---|
70 | public : |
---|
71 | typedef typename CostMap::KeyType KeyType; |
---|
72 | typedef typename CostMap::ValueType ValueType; |
---|
73 | |
---|
74 | ValueType operator[](typename ResGraph::Edge e) const { |
---|
75 | if (res_graph.forward(e)) |
---|
76 | return ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]); |
---|
77 | else |
---|
78 | return -ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]); |
---|
79 | } |
---|
80 | |
---|
81 | ModCostMap(const ResGraph& _res_graph, |
---|
82 | const CostMap &o, const NodeMap &p) : |
---|
83 | res_graph(_res_graph), /*rev(_rev),*/ ol(o), pot(p){}; |
---|
84 | };//ModCostMap |
---|
85 | |
---|
86 | |
---|
87 | protected: |
---|
88 | |
---|
89 | //Input |
---|
90 | const Graph& graph; |
---|
91 | const CostMap& cost; |
---|
92 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
---|
93 | |
---|
94 | |
---|
95 | //auxiliary variables |
---|
96 | |
---|
97 | //To store the flow |
---|
98 | FlowMap flow; |
---|
99 | //To store the potential (dual variables) |
---|
100 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
---|
101 | PotentialMap potential; |
---|
102 | |
---|
103 | |
---|
104 | Cost total_cost; |
---|
105 | |
---|
106 | |
---|
107 | public : |
---|
108 | |
---|
109 | |
---|
110 | MinCostFlow(Graph& _graph, CostMap& _cost, SupplyDemandMap& _supply_demand): |
---|
111 | graph(_graph), |
---|
112 | cost(_cost), |
---|
113 | supply_demand(_supply_demand), |
---|
114 | flow(_graph), |
---|
115 | potential(_graph){ } |
---|
116 | |
---|
117 | |
---|
118 | ///Runs the algorithm. |
---|
119 | |
---|
120 | ///Runs the algorithm. |
---|
121 | |
---|
122 | ///\todo May be it does make sense to be able to start with a nonzero |
---|
123 | /// feasible primal-dual solution pair as well. |
---|
124 | void run() { |
---|
125 | |
---|
126 | //To store excess-deficit values |
---|
127 | SupplyDemandMap excess_deficit(graph); |
---|
128 | |
---|
129 | //Resetting variables from previous runs |
---|
130 | //total_cost = 0; |
---|
131 | |
---|
132 | |
---|
133 | typedef typename Graph::template NodeMap<int> HeapMap; |
---|
134 | typedef BinHeap< Node, SupplyDemand, typename Graph::template NodeMap<int>, |
---|
135 | std::greater<SupplyDemand> > HeapType; |
---|
136 | |
---|
137 | //A heap for the excess nodes |
---|
138 | HeapMap excess_nodes_map(graph,-1); |
---|
139 | HeapType excess_nodes(excess_nodes_map); |
---|
140 | |
---|
141 | //A heap for the deficit nodes |
---|
142 | HeapMap deficit_nodes_map(graph,-1); |
---|
143 | HeapType deficit_nodes(deficit_nodes_map); |
---|
144 | |
---|
145 | //A container to store nonabundant arcs |
---|
146 | std::list<Edge> nonabundant_arcs; |
---|
147 | |
---|
148 | |
---|
149 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
---|
150 | flow.set(e,0); |
---|
151 | nonabundant_arcs.push_back(e); |
---|
152 | } |
---|
153 | |
---|
154 | //Initial value for delta |
---|
155 | SupplyDemand delta = 0; |
---|
156 | |
---|
157 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
---|
158 | |
---|
159 | //A union-find structure to store the abundant components |
---|
160 | typename UFE::MapType abund_comp_map(graph); |
---|
161 | UFE abundant_components(abund_comp_map); |
---|
162 | |
---|
163 | |
---|
164 | |
---|
165 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
---|
166 | excess_deficit.set(n,supply_demand[n]); |
---|
167 | //A supply node |
---|
168 | if (excess_deficit[n] > 0){ |
---|
169 | excess_nodes.push(n,excess_deficit[n]); |
---|
170 | } |
---|
171 | //A demand node |
---|
172 | if (excess_deficit[n] < 0){ |
---|
173 | deficit_nodes.push(n, - excess_deficit[n]); |
---|
174 | } |
---|
175 | //Finding out starting value of delta |
---|
176 | if (delta < abs(excess_deficit[n])){ |
---|
177 | delta = abs(excess_deficit[n]); |
---|
178 | } |
---|
179 | //Initialize the copy of the Dijkstra potential to zero |
---|
180 | potential.set(n,0); |
---|
181 | //Every single point is an abundant component initially |
---|
182 | abundant_components.insert(n); |
---|
183 | } |
---|
184 | |
---|
185 | //It'll be allright as an initial value, though this value |
---|
186 | //can be the maximum deficit here |
---|
187 | SupplyDemand max_excess = delta; |
---|
188 | |
---|
189 | ///\bug This is a serious cheat here, before we have an uncapacitated ResGraph |
---|
190 | ConstEdgeMap const_inf_map(MAXINT); |
---|
191 | |
---|
192 | //We need a residual graph which is uncapacitated |
---|
193 | ResGraph res_graph(graph, const_inf_map, flow); |
---|
194 | |
---|
195 | //An EdgeMap to tell which arcs are abundant |
---|
196 | typename Graph::template EdgeMap<bool> abundant_arcs(graph); |
---|
197 | |
---|
198 | //Let's construct the sugraph consisting only of the abundant edges |
---|
199 | typedef ConstMap< typename Graph::Node, bool > ConstNodeMap; |
---|
200 | |
---|
201 | ConstNodeMap const_true_map(true); |
---|
202 | typedef SubGraphWrapper< const Graph, ConstNodeMap, |
---|
203 | typename Graph::template EdgeMap<bool> > |
---|
204 | AbundantGraph; |
---|
205 | AbundantGraph abundant_graph(graph, const_true_map, abundant_arcs ); |
---|
206 | |
---|
207 | //Let's construct the residual graph for the abundant graph |
---|
208 | typedef ResGraphWrapper<const AbundantGraph,int,ConstEdgeMap,FlowMap> |
---|
209 | ResAbGraph; |
---|
210 | //Again uncapacitated |
---|
211 | ResAbGraph res_ab_graph(abundant_graph, const_inf_map, flow); |
---|
212 | |
---|
213 | //We need things for the bfs |
---|
214 | typename ResAbGraph::template NodeMap<bool> bfs_reached(res_ab_graph); |
---|
215 | typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge> |
---|
216 | bfs_pred(res_ab_graph); |
---|
217 | NullMap<typename ResAbGraph::Node, int> bfs_dist_dummy; |
---|
218 | //Teszt celbol: |
---|
219 | //BfsIterator<ResAbGraph, typename ResAbGraph::template NodeMap<bool> > |
---|
220 | //izebize(res_ab_graph, bfs_reached); |
---|
221 | //We want to run bfs-es (more) on this graph 'res_ab_graph' |
---|
222 | Bfs < const ResAbGraph , |
---|
223 | typename ResAbGraph::template NodeMap<bool>, |
---|
224 | typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge>, |
---|
225 | NullMap<typename ResAbGraph::Node, int> > |
---|
226 | bfs(res_ab_graph, bfs_reached, bfs_pred, bfs_dist_dummy); |
---|
227 | /*This is what Marci wants for a bfs |
---|
228 | template <typename Graph, |
---|
229 | typename ReachedMap=typename Graph::template NodeMap<bool>, |
---|
230 | typename PredMap |
---|
231 | =typename Graph::template NodeMap<typename Graph::Edge>, |
---|
232 | typename DistMap=typename Graph::template NodeMap<int> > |
---|
233 | class Bfs : public BfsIterator<Graph, ReachedMap> { |
---|
234 | |
---|
235 | */ |
---|
236 | |
---|
237 | ModCostMap mod_cost(res_graph, cost, potential); |
---|
238 | |
---|
239 | Dijkstra<ResGraph, ModCostMap> dijkstra(res_graph, mod_cost); |
---|
240 | |
---|
241 | //We will use the number of the nodes of the graph often |
---|
242 | int number_of_nodes = graph.nodeNum(); |
---|
243 | |
---|
244 | while (max_excess > 0){ |
---|
245 | |
---|
246 | //Reset delta if still too big |
---|
247 | if (8*number_of_nodes*max_excess <= delta){ |
---|
248 | delta = max_excess; |
---|
249 | |
---|
250 | } |
---|
251 | |
---|
252 | /* |
---|
253 | * Beginning of the delta scaling phase |
---|
254 | */ |
---|
255 | //Merge and stuff |
---|
256 | { |
---|
257 | SupplyDemand buf=8*number_of_nodes*delta; |
---|
258 | typename std::list<Edge>::iterator i = nonabundant_arcs.begin(); |
---|
259 | while ( i != nonabundant_arcs.end() ){ |
---|
260 | if (flow[*i]>=buf){ |
---|
261 | Node a = abundant_components.find(res_graph.head(*i)); |
---|
262 | Node b = abundant_components.find(res_graph.tail(*i)); |
---|
263 | //Merge |
---|
264 | if (a != b){ |
---|
265 | abundant_components.join(a,b); |
---|
266 | //We want to push the smaller |
---|
267 | //Which has greater absolut value excess/deficit |
---|
268 | Node root=(abs(excess_deficit[a])>abs(excess_deficit[b]))?a:b; |
---|
269 | //Which is the other |
---|
270 | Node non_root = ( a == root ) ? b : a ; |
---|
271 | abundant_components.makeRep(root); |
---|
272 | SupplyDemand qty_to_augment = abs(excess_deficit[non_root]); |
---|
273 | //Push the positive value |
---|
274 | if (excess_deficit[non_root] < 0) |
---|
275 | swap(root, non_root); |
---|
276 | //If the non_root node has excess/deficit at all |
---|
277 | if (qty_to_augment>0){ |
---|
278 | //Find path and augment |
---|
279 | bfs.run(typename AbundantGraph::Node(non_root)); |
---|
280 | //root should be reached |
---|
281 | |
---|
282 | //Augmenting on the found path |
---|
283 | Node n=root; |
---|
284 | ResGraphEdge e; |
---|
285 | while (n!=non_root){ |
---|
286 | e = bfs_pred[n]; |
---|
287 | n = res_graph.tail(e); |
---|
288 | res_graph.augment(e,qty_to_augment); |
---|
289 | } |
---|
290 | |
---|
291 | //We know that non_root had positive excess |
---|
292 | excess_nodes.set(non_root, |
---|
293 | excess_nodes[non_root] - qty_to_augment); |
---|
294 | //But what about root node |
---|
295 | //It might have been positive and so became larger |
---|
296 | if (excess_deficit[root]>0){ |
---|
297 | excess_nodes.set(root, |
---|
298 | excess_nodes[root] + qty_to_augment); |
---|
299 | } |
---|
300 | else{ |
---|
301 | //Or negative but not turned into positive |
---|
302 | deficit_nodes.set(root, |
---|
303 | deficit_nodes[root] - qty_to_augment); |
---|
304 | } |
---|
305 | |
---|
306 | //Update the excess_deficit map |
---|
307 | excess_deficit[non_root] -= qty_to_augment; |
---|
308 | excess_deficit[root] += qty_to_augment; |
---|
309 | |
---|
310 | |
---|
311 | } |
---|
312 | } |
---|
313 | //What happens to i? |
---|
314 | //Marci and Zsolt says I shouldn't do such things |
---|
315 | nonabundant_arcs.erase(i++); |
---|
316 | abundant_arcs[*i] = true; |
---|
317 | } |
---|
318 | else |
---|
319 | ++i; |
---|
320 | } |
---|
321 | } |
---|
322 | |
---|
323 | |
---|
324 | Node s = excess_nodes.top(); |
---|
325 | max_excess = excess_nodes[s]; |
---|
326 | Node t = deficit_nodes.top(); |
---|
327 | if (max_excess < deficit_nodes[t]){ |
---|
328 | max_excess = deficit_nodes[t]; |
---|
329 | } |
---|
330 | |
---|
331 | |
---|
332 | while(max_excess > (number_of_nodes-1)*delta/number_of_nodes){ |
---|
333 | |
---|
334 | |
---|
335 | //s es t valasztasa |
---|
336 | |
---|
337 | //Dijkstra part |
---|
338 | dijkstra.run(s); |
---|
339 | |
---|
340 | /*We know from theory that t can be reached |
---|
341 | if (!dijkstra.reached(t)){ |
---|
342 | //There are no k paths from s to t |
---|
343 | break; |
---|
344 | }; |
---|
345 | */ |
---|
346 | |
---|
347 | //We have to change the potential |
---|
348 | FOR_EACH_LOC(typename ResGraph::NodeIt, n, res_graph){ |
---|
349 | potential[n] += dijkstra.distMap()[n]; |
---|
350 | } |
---|
351 | |
---|
352 | |
---|
353 | //Augmenting on the sortest path |
---|
354 | Node n=t; |
---|
355 | ResGraphEdge e; |
---|
356 | while (n!=s){ |
---|
357 | e = dijkstra.pred(n); |
---|
358 | n = dijkstra.predNode(n); |
---|
359 | res_graph.augment(e,delta); |
---|
360 | /* |
---|
361 | //Let's update the total cost |
---|
362 | if (res_graph.forward(e)) |
---|
363 | total_cost += cost[e]; |
---|
364 | else |
---|
365 | total_cost -= cost[e]; |
---|
366 | */ |
---|
367 | } |
---|
368 | |
---|
369 | //Update the excess_deficit map |
---|
370 | excess_deficit[s] -= delta; |
---|
371 | excess_deficit[t] += delta; |
---|
372 | |
---|
373 | |
---|
374 | //Update the excess_nodes heap |
---|
375 | if (delta > excess_nodes[s]){ |
---|
376 | if (delta > excess_nodes[s]) |
---|
377 | deficit_nodes.push(s,delta - excess_nodes[s]); |
---|
378 | excess_nodes.pop(); |
---|
379 | |
---|
380 | } |
---|
381 | else{ |
---|
382 | excess_nodes.set(s, excess_nodes[s] - delta); |
---|
383 | } |
---|
384 | //Update the deficit_nodes heap |
---|
385 | if (delta > deficit_nodes[t]){ |
---|
386 | if (delta > deficit_nodes[t]) |
---|
387 | excess_nodes.push(t,delta - deficit_nodes[t]); |
---|
388 | deficit_nodes.pop(); |
---|
389 | |
---|
390 | } |
---|
391 | else{ |
---|
392 | deficit_nodes.set(t, deficit_nodes[t] - delta); |
---|
393 | } |
---|
394 | //Dijkstra part ends here |
---|
395 | |
---|
396 | //Choose s and t again |
---|
397 | s = excess_nodes.top(); |
---|
398 | max_excess = excess_nodes[s]; |
---|
399 | t = deficit_nodes.top(); |
---|
400 | if (max_excess < deficit_nodes[t]){ |
---|
401 | max_excess = deficit_nodes[t]; |
---|
402 | } |
---|
403 | |
---|
404 | } |
---|
405 | |
---|
406 | /* |
---|
407 | * End of the delta scaling phase |
---|
408 | */ |
---|
409 | |
---|
410 | //Whatever this means |
---|
411 | delta = delta / 2; |
---|
412 | |
---|
413 | /*This is not necessary here |
---|
414 | //Update the max_excess |
---|
415 | max_excess = 0; |
---|
416 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
---|
417 | if (max_excess < excess_deficit[n]){ |
---|
418 | max_excess = excess_deficit[n]; |
---|
419 | } |
---|
420 | } |
---|
421 | */ |
---|
422 | |
---|
423 | |
---|
424 | }//while(max_excess > 0) |
---|
425 | |
---|
426 | |
---|
427 | //return i; |
---|
428 | } |
---|
429 | |
---|
430 | |
---|
431 | |
---|
432 | |
---|
433 | ///This function gives back the total cost of the found paths. |
---|
434 | ///Assumes that \c run() has been run and nothing changed since then. |
---|
435 | Cost totalCost(){ |
---|
436 | return total_cost; |
---|
437 | } |
---|
438 | |
---|
439 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
---|
440 | ///be called before using this function. |
---|
441 | const FlowMap &getFlow() const { return flow;} |
---|
442 | |
---|
443 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
---|
444 | /// \pre \ref run() must be called before using this function. |
---|
445 | const PotentialMap &getPotential() const { return potential;} |
---|
446 | |
---|
447 | ///This function checks, whether the given solution is optimal |
---|
448 | ///Running after a \c run() should return with true |
---|
449 | ///In this "state of the art" this only checks optimality, doesn't bother with feasibility |
---|
450 | /// |
---|
451 | ///\todo Is this OK here? |
---|
452 | bool checkComplementarySlackness(){ |
---|
453 | Cost mod_pot; |
---|
454 | Cost fl_e; |
---|
455 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
---|
456 | //C^{\Pi}_{i,j} |
---|
457 | mod_pot = cost[e]-potential[graph.head(e)]+potential[graph.tail(e)]; |
---|
458 | fl_e = flow[e]; |
---|
459 | // std::cout << fl_e << std::endl; |
---|
460 | if (mod_pot > 0 && fl_e != 0) |
---|
461 | return false; |
---|
462 | |
---|
463 | } |
---|
464 | return true; |
---|
465 | } |
---|
466 | |
---|
467 | /* |
---|
468 | //For testing purposes only |
---|
469 | //Lists the node_properties |
---|
470 | void write_property_vector(const SupplyDemandMap& a, |
---|
471 | char* prop_name="property"){ |
---|
472 | FOR_EACH_LOC(typename Graph::NodeIt, i, graph){ |
---|
473 | cout<<"Node id.: "<<graph.id(i)<<", "<<prop_name<<" value: "<<a[i]<<endl; |
---|
474 | } |
---|
475 | cout<<endl; |
---|
476 | } |
---|
477 | */ |
---|
478 | bool checkFeasibility(){ |
---|
479 | SupplyDemandMap supdem(graph); |
---|
480 | FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){ |
---|
481 | |
---|
482 | if ( flow[e] < 0){ |
---|
483 | |
---|
484 | return false; |
---|
485 | } |
---|
486 | supdem[graph.tail(e)] += flow[e]; |
---|
487 | supdem[graph.head(e)] -= flow[e]; |
---|
488 | } |
---|
489 | //write_property_vector(supdem, "supdem"); |
---|
490 | //write_property_vector(supply_demand, "supply_demand"); |
---|
491 | |
---|
492 | FOR_EACH_LOC(typename Graph::NodeIt, n, graph){ |
---|
493 | |
---|
494 | if ( supdem[n] != supply_demand[n]){ |
---|
495 | //cout<<"Node id.: "<<graph.id(n)<<" : "<<supdem[n]<<", should be: "<<supply_demand[n]<<endl; |
---|
496 | return false; |
---|
497 | } |
---|
498 | } |
---|
499 | |
---|
500 | return true; |
---|
501 | } |
---|
502 | |
---|
503 | bool checkOptimality(){ |
---|
504 | return checkFeasibility() && checkComplementarySlackness(); |
---|
505 | } |
---|
506 | |
---|
507 | }; //class MinCostFlow |
---|
508 | |
---|
509 | ///@} |
---|
510 | |
---|
511 | } //namespace lemon |
---|
512 | |
---|
513 | #endif //LEMON_MINCOSTFLOW_H |
---|