1 | // -*- c++ -*- |
---|
2 | #ifndef HUGO_MINCOSTFLOW_H |
---|
3 | #define HUGO_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 <hugo/dijkstra.h> |
---|
10 | #include <hugo/graph_wrapper.h> |
---|
11 | #include <hugo/maps.h> |
---|
12 | #include <vector> |
---|
13 | #include <list> |
---|
14 | #include <for_each_macros.h> |
---|
15 | #include <hugo/union_find.h> |
---|
16 | |
---|
17 | namespace hugo { |
---|
18 | |
---|
19 | /// \addtogroup galgs |
---|
20 | /// @{ |
---|
21 | |
---|
22 | ///\brief Implementation of an algorithm for finding the minimum cost flow |
---|
23 | /// of given value in an uncapacitated network |
---|
24 | /// |
---|
25 | /// |
---|
26 | /// The class \ref hugo::MinCostFlow "MinCostFlow" implements |
---|
27 | /// an algorithm for solving the following general minimum cost flow problem> |
---|
28 | /// |
---|
29 | /// |
---|
30 | /// |
---|
31 | /// \warning It is assumed here that the problem has a feasible solution |
---|
32 | /// |
---|
33 | /// The range of the length (weight) function is nonnegative reals but |
---|
34 | /// the range of capacity function is the set of nonnegative integers. |
---|
35 | /// It is not a polinomial time algorithm for counting the minimum cost |
---|
36 | /// maximal flow, since it counts the minimum cost flow for every value 0..M |
---|
37 | /// where \c M is the value of the maximal flow. |
---|
38 | /// |
---|
39 | ///\author Attila Bernath |
---|
40 | template <typename Graph, typename LengthMap, typename SupplyDemandMap> |
---|
41 | class MinCostFlow { |
---|
42 | |
---|
43 | typedef typename LengthMap::ValueType Length; |
---|
44 | |
---|
45 | |
---|
46 | typedef typename SupplyDemandMap::ValueType SupplyDemand; |
---|
47 | |
---|
48 | typedef typename Graph::Node Node; |
---|
49 | typedef typename Graph::NodeIt NodeIt; |
---|
50 | typedef typename Graph::Edge Edge; |
---|
51 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
52 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
---|
53 | |
---|
54 | // typedef ConstMap<Edge,int> ConstMap; |
---|
55 | |
---|
56 | typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType; |
---|
57 | typedef typename ResGraphType::Edge ResGraphEdge; |
---|
58 | |
---|
59 | class ModLengthMap { |
---|
60 | //typedef typename ResGraphType::template NodeMap<Length> NodeMap; |
---|
61 | typedef typename Graph::template NodeMap<Length> NodeMap; |
---|
62 | const ResGraphType& G; |
---|
63 | // const EdgeIntMap& rev; |
---|
64 | const LengthMap &ol; |
---|
65 | const NodeMap &pot; |
---|
66 | public : |
---|
67 | typedef typename LengthMap::KeyType KeyType; |
---|
68 | typedef typename LengthMap::ValueType ValueType; |
---|
69 | |
---|
70 | ValueType operator[](typename ResGraphType::Edge e) const { |
---|
71 | if (G.forward(e)) |
---|
72 | return ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
---|
73 | else |
---|
74 | return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
---|
75 | } |
---|
76 | |
---|
77 | ModLengthMap(const ResGraphType& _G, |
---|
78 | const LengthMap &o, const NodeMap &p) : |
---|
79 | G(_G), /*rev(_rev),*/ ol(o), pot(p){}; |
---|
80 | };//ModLengthMap |
---|
81 | |
---|
82 | |
---|
83 | protected: |
---|
84 | |
---|
85 | //Input |
---|
86 | const Graph& G; |
---|
87 | const LengthMap& length; |
---|
88 | const SupplyDemandMap& supply_demand;//supply or demand of nodes |
---|
89 | |
---|
90 | |
---|
91 | //auxiliary variables |
---|
92 | |
---|
93 | //To store the flow |
---|
94 | EdgeIntMap flow; |
---|
95 | //To store the potentila (dual variables) |
---|
96 | typename Graph::template NodeMap<Length> potential; |
---|
97 | //To store excess-deficit values |
---|
98 | SupplyDemandMap excess_deficit; |
---|
99 | |
---|
100 | |
---|
101 | Length total_length; |
---|
102 | |
---|
103 | |
---|
104 | public : |
---|
105 | |
---|
106 | |
---|
107 | MinCostFlow(Graph& _G, LengthMap& _length, SupplyDemandMap& _supply_demand) : G(_G), |
---|
108 | length(_length), supply_demand(_supply_demand), flow(_G), potential(_G){ } |
---|
109 | |
---|
110 | |
---|
111 | ///Runs the algorithm. |
---|
112 | |
---|
113 | ///Runs the algorithm. |
---|
114 | |
---|
115 | ///\todo May be it does make sense to be able to start with a nonzero |
---|
116 | /// feasible primal-dual solution pair as well. |
---|
117 | int run() { |
---|
118 | |
---|
119 | //Resetting variables from previous runs |
---|
120 | //total_length = 0; |
---|
121 | |
---|
122 | typedef typename Graph::template NodeMap<int> HeapMap; |
---|
123 | typedef Heap< Node, SupplyDemand, typename Graph::template NodeMap<int>, |
---|
124 | std::greater<SupplyDemand> > HeapType; |
---|
125 | |
---|
126 | //A heap for the excess nodes |
---|
127 | HeapMap excess_nodes_map(G,-1); |
---|
128 | HeapType excess_nodes(excess_nodes_map); |
---|
129 | |
---|
130 | //A heap for the deficit nodes |
---|
131 | HeapMap deficit_nodes_map(G,-1); |
---|
132 | HeapType deficit_nodes(deficit_nodes_map); |
---|
133 | |
---|
134 | //A container to store nonabundant arcs |
---|
135 | list<Edge> nonabundant_arcs; |
---|
136 | |
---|
137 | FOR_EACH_LOC(typename Graph::EdgeIt, e, G){ |
---|
138 | flow.set(e,0); |
---|
139 | nonabundant_arcs.push_back(e); |
---|
140 | } |
---|
141 | |
---|
142 | //Initial value for delta |
---|
143 | SupplyDemand delta = 0; |
---|
144 | |
---|
145 | typedef UnionFindEnum<Node, Graph::template NodeMap> UFE; |
---|
146 | |
---|
147 | //A union-find structure to store the abundant components |
---|
148 | UFE::MapType abund_comp_map(G); |
---|
149 | UFE abundant_components(abund_comp_map); |
---|
150 | |
---|
151 | |
---|
152 | |
---|
153 | FOR_EACH_LOC(typename Graph::NodeIt, n, G){ |
---|
154 | excess_deficit.set(n,supply_demand[n]); |
---|
155 | //A supply node |
---|
156 | if (excess_deficit[n] > 0){ |
---|
157 | excess_nodes.push(n,excess_deficit[n]); |
---|
158 | } |
---|
159 | //A demand node |
---|
160 | if (excess_deficit[n] < 0){ |
---|
161 | deficit_nodes.push(n, - excess_deficit[n]); |
---|
162 | } |
---|
163 | //Finding out starting value of delta |
---|
164 | if (delta < abs(excess_deficit[n])){ |
---|
165 | delta = abs(excess_deficit[n]); |
---|
166 | } |
---|
167 | //Initialize the copy of the Dijkstra potential to zero |
---|
168 | potential.set(n,0); |
---|
169 | //Every single point is an abundant component initially |
---|
170 | abundant_components.insert(n); |
---|
171 | } |
---|
172 | |
---|
173 | //It'll be allright as an initial value, though this value |
---|
174 | //can be the maximum deficit here |
---|
175 | SupplyDemand max_excess = delta; |
---|
176 | |
---|
177 | //We need a residual graph which is uncapacitated |
---|
178 | ResGraphType res_graph(G, flow); |
---|
179 | |
---|
180 | |
---|
181 | |
---|
182 | ModLengthMap mod_length(res_graph, length, potential); |
---|
183 | |
---|
184 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
---|
185 | |
---|
186 | |
---|
187 | while (max_excess > 0){ |
---|
188 | |
---|
189 | //Reset delta if still too big |
---|
190 | if (8*number_of_nodes*max_excess <= delta){ |
---|
191 | delta = max_excess; |
---|
192 | |
---|
193 | } |
---|
194 | |
---|
195 | /* |
---|
196 | * Beginning of the delta scaling phase |
---|
197 | */ |
---|
198 | //Merge and stuff |
---|
199 | { |
---|
200 | SupplyDemand buf=8*number_of_nodes*delta; |
---|
201 | list<Edge>::iterator i = nonabundant_arcs.begin(); |
---|
202 | while ( i != nonabundant_arcs.end() ){ |
---|
203 | if (flow[i]>=buf){ |
---|
204 | Node a = abundant_components.find(res_graph.head(i)); |
---|
205 | Node b = abundant_components.find(res_graph.tail(i)); |
---|
206 | //Merge |
---|
207 | if (a != b){ |
---|
208 | //Find path and augment |
---|
209 | //!!! |
---|
210 | //Find path and augment |
---|
211 | abundant_components.join(a,b); |
---|
212 | } |
---|
213 | //What happens to i? |
---|
214 | nonabundant_arcs.erase(i); |
---|
215 | } |
---|
216 | else |
---|
217 | ++i; |
---|
218 | } |
---|
219 | } |
---|
220 | |
---|
221 | |
---|
222 | Node s = excess_nodes.top(); |
---|
223 | SupplyDemand max_excess = excess_nodes[s]; |
---|
224 | Node t = deficit_nodes.top(); |
---|
225 | if (max_excess < dificit_nodes[t]){ |
---|
226 | max_excess = dificit_nodes[t]; |
---|
227 | } |
---|
228 | |
---|
229 | |
---|
230 | while(max_excess > 0){ |
---|
231 | |
---|
232 | |
---|
233 | //s es t valasztasa |
---|
234 | |
---|
235 | //Dijkstra part |
---|
236 | dijkstra.run(s); |
---|
237 | |
---|
238 | /*We know from theory that t can be reached |
---|
239 | if (!dijkstra.reached(t)){ |
---|
240 | //There are no k paths from s to t |
---|
241 | break; |
---|
242 | }; |
---|
243 | */ |
---|
244 | |
---|
245 | //We have to change the potential |
---|
246 | FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){ |
---|
247 | potential[n] += dijkstra.distMap()[n]; |
---|
248 | } |
---|
249 | |
---|
250 | |
---|
251 | //Augmenting on the sortest path |
---|
252 | Node n=t; |
---|
253 | ResGraphEdge e; |
---|
254 | while (n!=s){ |
---|
255 | e = dijkstra.pred(n); |
---|
256 | n = dijkstra.predNode(n); |
---|
257 | res_graph.augment(e,delta); |
---|
258 | /* |
---|
259 | //Let's update the total length |
---|
260 | if (res_graph.forward(e)) |
---|
261 | total_length += length[e]; |
---|
262 | else |
---|
263 | total_length -= length[e]; |
---|
264 | */ |
---|
265 | } |
---|
266 | |
---|
267 | //Update the excess_nodes heap |
---|
268 | if (delta >= excess_nodes[s]){ |
---|
269 | if (delta > excess_nodes[s]) |
---|
270 | deficit_nodes.push(s,delta - excess_nodes[s]); |
---|
271 | excess_nodes.pop(); |
---|
272 | |
---|
273 | } |
---|
274 | else{ |
---|
275 | excess_nodes[s] -= delta; |
---|
276 | } |
---|
277 | //Update the deficit_nodes heap |
---|
278 | if (delta >= deficit_nodes[t]){ |
---|
279 | if (delta > deficit_nodes[t]) |
---|
280 | excess_nodes.push(t,delta - deficit_nodes[t]); |
---|
281 | deficit_nodes.pop(); |
---|
282 | |
---|
283 | } |
---|
284 | else{ |
---|
285 | deficit_nodes[t] -= delta; |
---|
286 | } |
---|
287 | //Dijkstra part ends here |
---|
288 | } |
---|
289 | |
---|
290 | /* |
---|
291 | * End of the delta scaling phase |
---|
292 | */ |
---|
293 | |
---|
294 | //Whatever this means |
---|
295 | delta = delta / 2; |
---|
296 | |
---|
297 | /*This is not necessary here |
---|
298 | //Update the max_excess |
---|
299 | max_excess = 0; |
---|
300 | FOR_EACH_LOC(typename Graph::NodeIt, n, G){ |
---|
301 | if (max_excess < excess_deficit[n]){ |
---|
302 | max_excess = excess_deficit[n]; |
---|
303 | } |
---|
304 | } |
---|
305 | */ |
---|
306 | |
---|
307 | |
---|
308 | }//while(max_excess > 0) |
---|
309 | |
---|
310 | |
---|
311 | return i; |
---|
312 | } |
---|
313 | |
---|
314 | |
---|
315 | |
---|
316 | |
---|
317 | ///This function gives back the total length of the found paths. |
---|
318 | ///Assumes that \c run() has been run and nothing changed since then. |
---|
319 | Length totalLength(){ |
---|
320 | return total_length; |
---|
321 | } |
---|
322 | |
---|
323 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
---|
324 | ///be called before using this function. |
---|
325 | const EdgeIntMap &getFlow() const { return flow;} |
---|
326 | |
---|
327 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
---|
328 | /// \pre \ref run() must be called before using this function. |
---|
329 | const EdgeIntMap &getPotential() const { return potential;} |
---|
330 | |
---|
331 | ///This function checks, whether the given solution is optimal |
---|
332 | ///Running after a \c run() should return with true |
---|
333 | ///In this "state of the art" this only check optimality, doesn't bother with feasibility |
---|
334 | /// |
---|
335 | ///\todo Is this OK here? |
---|
336 | bool checkComplementarySlackness(){ |
---|
337 | Length mod_pot; |
---|
338 | Length fl_e; |
---|
339 | FOR_EACH_LOC(typename Graph::EdgeIt, e, G){ |
---|
340 | //C^{\Pi}_{i,j} |
---|
341 | mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)]; |
---|
342 | fl_e = flow[e]; |
---|
343 | // std::cout << fl_e << std::endl; |
---|
344 | if (0<fl_e && fl_e<capacity[e]){ |
---|
345 | if (mod_pot != 0) |
---|
346 | return false; |
---|
347 | } |
---|
348 | else{ |
---|
349 | if (mod_pot > 0 && fl_e != 0) |
---|
350 | return false; |
---|
351 | if (mod_pot < 0 && fl_e != capacity[e]) |
---|
352 | return false; |
---|
353 | } |
---|
354 | } |
---|
355 | return true; |
---|
356 | } |
---|
357 | |
---|
358 | |
---|
359 | }; //class MinCostFlow |
---|
360 | |
---|
361 | ///@} |
---|
362 | |
---|
363 | } //namespace hugo |
---|
364 | |
---|
365 | #endif //HUGO_MINCOSTFLOW_H |
---|