[478] | 1 | // -*- C++ -*- |
---|
[480] | 2 | #ifndef HUGO_MAX_FLOW_H |
---|
| 3 | #define HUGO_MAX_FLOW_H |
---|
[478] | 4 | |
---|
| 5 | #include <vector> |
---|
| 6 | #include <queue> |
---|
| 7 | #include <stack> |
---|
| 8 | |
---|
[557] | 9 | #include <hugo/graph_wrapper.h> |
---|
[602] | 10 | #include <bfs_dfs.h> |
---|
[555] | 11 | #include <hugo/invalid.h> |
---|
| 12 | #include <hugo/maps.h> |
---|
[640] | 13 | #include <hugo/for_each_macros.h> |
---|
[478] | 14 | |
---|
[488] | 15 | /// \file |
---|
[631] | 16 | /// \brief Maximum flow algorithms. |
---|
[615] | 17 | /// \ingroup galgs |
---|
[478] | 18 | |
---|
| 19 | namespace hugo { |
---|
| 20 | |
---|
[631] | 21 | /// \addtogroup galgs |
---|
| 22 | /// @{ |
---|
| 23 | ///Maximum flow algorithms class. |
---|
[488] | 24 | |
---|
[631] | 25 | ///This class provides various algorithms for finding a flow of |
---|
| 26 | ///maximum value in a directed graph. The \e source node, the \e |
---|
| 27 | ///target node, the \e capacity of the edges and the \e starting \e |
---|
| 28 | ///flow value of the edges can be passed to the algorithm through the |
---|
| 29 | ///constructor. It is possible to change these quantities using the |
---|
| 30 | ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
---|
| 31 | ///\ref resetFlow. Before any subsequent runs of any algorithm of |
---|
| 32 | ///the class \ref resetFlow should be called, otherwise it will |
---|
| 33 | ///start from a maximum flow. |
---|
| 34 | ///After running an algorithm of the class, the maximum value of a |
---|
| 35 | ///value can be obtained by calling \ref flowValue(). The minimum |
---|
| 36 | ///value cut can be written into a \c node map of \c bools by |
---|
| 37 | ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
---|
| 38 | ///the inclusionwise minimum and maximum of the minimum value |
---|
| 39 | ///cuts, resp.) |
---|
[632] | 40 | ///\param Graph The directed graph type the algorithm runs on. |
---|
[631] | 41 | ///\param Num The number type of the capacities and the flow values. |
---|
| 42 | ///\param CapMap The type of the capacity map. |
---|
| 43 | ///\param FlowMap The type of the flow map. |
---|
| 44 | ///\author Marton Makai, Jacint Szabo |
---|
[615] | 45 | template <typename Graph, typename Num, |
---|
| 46 | typename CapMap=typename Graph::template EdgeMap<Num>, |
---|
[478] | 47 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
---|
| 48 | class MaxFlow { |
---|
[615] | 49 | protected: |
---|
[478] | 50 | typedef typename Graph::Node Node; |
---|
| 51 | typedef typename Graph::NodeIt NodeIt; |
---|
[631] | 52 | typedef typename Graph::EdgeIt EdgeIt; |
---|
[478] | 53 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
| 54 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
| 55 | |
---|
| 56 | typedef typename std::vector<std::stack<Node> > VecStack; |
---|
| 57 | typedef typename Graph::template NodeMap<Node> NNMap; |
---|
| 58 | typedef typename std::vector<Node> VecNode; |
---|
| 59 | |
---|
| 60 | const Graph* g; |
---|
| 61 | Node s; |
---|
| 62 | Node t; |
---|
[615] | 63 | const CapMap* capacity; |
---|
[478] | 64 | FlowMap* flow; |
---|
| 65 | int n; //the number of nodes of G |
---|
| 66 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
---|
| 67 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
---|
| 68 | typedef typename ResGW::Edge ResGWEdge; |
---|
| 69 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
---|
| 70 | typedef typename Graph::template NodeMap<int> ReachedMap; |
---|
[631] | 71 | |
---|
| 72 | |
---|
| 73 | //level works as a bool map in augmenting path algorithms and is |
---|
| 74 | //used by bfs for storing reached information. In preflow, it |
---|
| 75 | //shows the levels of nodes. |
---|
[478] | 76 | ReachedMap level; |
---|
[631] | 77 | |
---|
| 78 | //excess is needed only in preflow |
---|
[615] | 79 | typename Graph::template NodeMap<Num> excess; |
---|
[631] | 80 | |
---|
| 81 | //fixme |
---|
| 82 | // protected: |
---|
[602] | 83 | // MaxFlow() { } |
---|
[615] | 84 | // void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
---|
| 85 | // FlowMap& _flow) |
---|
[602] | 86 | // { |
---|
[615] | 87 | // g=&_G; |
---|
| 88 | // s=_s; |
---|
| 89 | // t=_t; |
---|
[602] | 90 | // capacity=&_capacity; |
---|
| 91 | // flow=&_flow; |
---|
| 92 | // n=_G.nodeNum; |
---|
[615] | 93 | // level.set (_G); //kellene vmi ilyesmi fv |
---|
[602] | 94 | // excess(_G,0); //itt is |
---|
| 95 | // } |
---|
[478] | 96 | |
---|
[615] | 97 | // constants used for heuristics |
---|
| 98 | static const int H0=20; |
---|
| 99 | static const int H1=1; |
---|
| 100 | |
---|
[478] | 101 | public: |
---|
[615] | 102 | |
---|
[631] | 103 | ///Indicates the property of the starting flow. |
---|
| 104 | |
---|
| 105 | ///Indicates the property of the starting flow. The meanings are as follows: |
---|
| 106 | ///- \c ZERO_FLOW: constant zero flow |
---|
| 107 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
---|
| 108 | ///the sum of the out-flows in every node except the \e source and |
---|
| 109 | ///the \e target. |
---|
| 110 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
---|
| 111 | ///least the sum of the out-flows in every node except the \e source. |
---|
| 112 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
---|
| 113 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
---|
[478] | 114 | enum flowEnum{ |
---|
[615] | 115 | ZERO_FLOW, |
---|
| 116 | GEN_FLOW, |
---|
| 117 | PRE_FLOW, |
---|
| 118 | NO_FLOW |
---|
[478] | 119 | }; |
---|
| 120 | |
---|
[615] | 121 | MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
---|
[478] | 122 | FlowMap& _flow) : |
---|
[615] | 123 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
---|
[478] | 124 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
---|
| 125 | |
---|
[631] | 126 | ///Runs a maximum flow algorithm. |
---|
| 127 | |
---|
| 128 | ///Runs a preflow algorithm, which is the fastest maximum flow |
---|
| 129 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
---|
| 130 | ///\pre The starting flow must be |
---|
| 131 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
---|
| 132 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
---|
| 133 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
---|
| 134 | /// - any map if \c fe is NO_FLOW. |
---|
[615] | 135 | void run(flowEnum fe=ZERO_FLOW) { |
---|
| 136 | preflow(fe); |
---|
[478] | 137 | } |
---|
[615] | 138 | |
---|
[631] | 139 | |
---|
| 140 | ///Runs a preflow algorithm. |
---|
| 141 | |
---|
| 142 | ///Runs a preflow algorithm. The preflow algorithms provide the |
---|
| 143 | ///fastest way to compute a maximum flow in a directed graph. |
---|
| 144 | ///\pre The starting flow must be |
---|
| 145 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
---|
| 146 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
---|
| 147 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
---|
| 148 | /// - any map if \c fe is NO_FLOW. |
---|
[488] | 149 | void preflow(flowEnum fe) { |
---|
[631] | 150 | preflowPhase1(fe); |
---|
| 151 | preflowPhase2(); |
---|
[478] | 152 | } |
---|
[631] | 153 | // Heuristics: |
---|
| 154 | // 2 phase |
---|
| 155 | // gap |
---|
| 156 | // list 'level_list' on the nodes on level i implemented by hand |
---|
| 157 | // stack 'active' on the active nodes on level i |
---|
| 158 | // runs heuristic 'highest label' for H1*n relabels |
---|
| 159 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
---|
| 160 | // Parameters H0 and H1 are initialized to 20 and 1. |
---|
[478] | 161 | |
---|
[631] | 162 | ///Runs the first phase of the preflow algorithm. |
---|
[478] | 163 | |
---|
[631] | 164 | ///The preflow algorithm consists of two phases, this method runs the |
---|
| 165 | ///first phase. After the first phase the maximum flow value and a |
---|
| 166 | ///minimum value cut can already be computed, though a maximum flow |
---|
| 167 | ///is net yet obtained. So after calling this method \ref flowValue |
---|
| 168 | ///and \ref actMinCut gives proper results. |
---|
| 169 | ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
---|
| 170 | ///give minimum value cuts unless calling \ref preflowPhase2. |
---|
| 171 | ///\pre The starting flow must be |
---|
| 172 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
---|
| 173 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
---|
| 174 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
---|
| 175 | /// - any map if \c fe is NO_FLOW. |
---|
| 176 | void preflowPhase1( flowEnum fe ); |
---|
| 177 | |
---|
| 178 | ///Runs the second phase of the preflow algorithm. |
---|
| 179 | |
---|
| 180 | ///The preflow algorithm consists of two phases, this method runs |
---|
| 181 | ///the second phase. After calling \ref preflowPhase1 and then |
---|
| 182 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
---|
| 183 | ///\ref minMinCut and \ref maxMinCut give proper results. |
---|
| 184 | ///\pre \ref preflowPhase1 must be called before. |
---|
| 185 | void preflowPhase2(); |
---|
[478] | 186 | |
---|
[615] | 187 | /// Starting from a flow, this method searches for an augmenting path |
---|
| 188 | /// according to the Edmonds-Karp algorithm |
---|
| 189 | /// and augments the flow on if any. |
---|
[487] | 190 | /// The return value shows if the augmentation was succesful. |
---|
[478] | 191 | bool augmentOnShortestPath(); |
---|
| 192 | |
---|
[615] | 193 | /// Starting from a flow, this method searches for an augmenting blocking |
---|
| 194 | /// flow according to Dinits' algorithm and augments the flow on if any. |
---|
| 195 | /// The blocking flow is computed in a physically constructed |
---|
[485] | 196 | /// residual graph of type \c Mutablegraph. |
---|
[487] | 197 | /// The return value show sif the augmentation was succesful. |
---|
[478] | 198 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
---|
| 199 | |
---|
[615] | 200 | /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
---|
[485] | 201 | /// residual graph is not constructed physically. |
---|
[487] | 202 | /// The return value shows if the augmentation was succesful. |
---|
[478] | 203 | bool augmentOnBlockingFlow2(); |
---|
| 204 | |
---|
[631] | 205 | /// Returns the maximum value of a flow. |
---|
| 206 | |
---|
| 207 | /// Returns the maximum value of a flow, by counting the |
---|
| 208 | /// over-flow of the target node \ref t. |
---|
| 209 | /// It can be called already after running \ref preflowPhase1. |
---|
[615] | 210 | Num flowValue() { |
---|
[478] | 211 | Num a=0; |
---|
[615] | 212 | FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e]; |
---|
| 213 | FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e]; |
---|
[478] | 214 | return a; |
---|
[631] | 215 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
---|
[478] | 216 | } |
---|
| 217 | |
---|
[631] | 218 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
---|
| 219 | |
---|
| 220 | ///After the first phase of the preflow algorithm the maximum flow |
---|
| 221 | ///value and a minimum value cut can already be computed. This |
---|
| 222 | ///method can be called after running \ref preflowPhase1 for |
---|
| 223 | ///obtaining a minimum value cut. |
---|
| 224 | /// \warning Gives proper result only right after calling \ref |
---|
| 225 | /// preflowPhase1. |
---|
[615] | 226 | /// \todo We have to make some status variable which shows the |
---|
| 227 | /// actual state |
---|
| 228 | /// of the class. This enables us to determine which methods are valid |
---|
[485] | 229 | /// for MinCut computation |
---|
[478] | 230 | template<typename _CutMap> |
---|
| 231 | void actMinCut(_CutMap& M) { |
---|
| 232 | NodeIt v; |
---|
[485] | 233 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
| 234 | if ( level[v] < n ) { |
---|
| 235 | M.set(v,false); |
---|
| 236 | } else { |
---|
| 237 | M.set(v,true); |
---|
| 238 | } |
---|
[478] | 239 | } |
---|
| 240 | } |
---|
| 241 | |
---|
[631] | 242 | ///Returns the inclusionwise minimum of the minimum value cuts. |
---|
| 243 | |
---|
| 244 | ///Sets \c M to the characteristic vector of the minimum value cut |
---|
| 245 | ///which is inclusionwise minimum. It is computed by processing |
---|
| 246 | ///a bfs from the source node \c s in the residual graph. |
---|
| 247 | ///\pre M should be a node map of bools initialized to false. |
---|
| 248 | ///\pre \c flow must be a maximum flow. |
---|
[478] | 249 | template<typename _CutMap> |
---|
| 250 | void minMinCut(_CutMap& M) { |
---|
[615] | 251 | |
---|
[478] | 252 | std::queue<Node> queue; |
---|
[615] | 253 | |
---|
| 254 | M.set(s,true); |
---|
[478] | 255 | queue.push(s); |
---|
| 256 | |
---|
| 257 | while (!queue.empty()) { |
---|
| 258 | Node w=queue.front(); |
---|
| 259 | queue.pop(); |
---|
| 260 | |
---|
| 261 | OutEdgeIt e; |
---|
| 262 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
---|
| 263 | Node v=g->head(e); |
---|
| 264 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
---|
| 265 | queue.push(v); |
---|
| 266 | M.set(v, true); |
---|
| 267 | } |
---|
[615] | 268 | } |
---|
[478] | 269 | |
---|
| 270 | InEdgeIt f; |
---|
| 271 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
---|
| 272 | Node v=g->tail(f); |
---|
| 273 | if (!M[v] && (*flow)[f] > 0 ) { |
---|
| 274 | queue.push(v); |
---|
| 275 | M.set(v, true); |
---|
| 276 | } |
---|
[615] | 277 | } |
---|
[478] | 278 | } |
---|
| 279 | } |
---|
| 280 | |
---|
[631] | 281 | ///Returns the inclusionwise maximum of the minimum value cuts. |
---|
[478] | 282 | |
---|
[631] | 283 | ///Sets \c M to the characteristic vector of the minimum value cut |
---|
| 284 | ///which is inclusionwise maximum. It is computed by processing a |
---|
| 285 | ///backward bfs from the target node \c t in the residual graph. |
---|
| 286 | ///\pre M should be a node map of bools initialized to false. |
---|
| 287 | ///\pre \c flow must be a maximum flow. |
---|
[478] | 288 | template<typename _CutMap> |
---|
| 289 | void maxMinCut(_CutMap& M) { |
---|
| 290 | |
---|
| 291 | NodeIt v; |
---|
| 292 | for(g->first(v) ; g->valid(v); g->next(v)) { |
---|
| 293 | M.set(v, true); |
---|
| 294 | } |
---|
| 295 | |
---|
| 296 | std::queue<Node> queue; |
---|
[615] | 297 | |
---|
| 298 | M.set(t,false); |
---|
[478] | 299 | queue.push(t); |
---|
| 300 | |
---|
| 301 | while (!queue.empty()) { |
---|
| 302 | Node w=queue.front(); |
---|
| 303 | queue.pop(); |
---|
| 304 | |
---|
| 305 | InEdgeIt e; |
---|
| 306 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
---|
| 307 | Node v=g->tail(e); |
---|
| 308 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
---|
| 309 | queue.push(v); |
---|
| 310 | M.set(v, false); |
---|
| 311 | } |
---|
| 312 | } |
---|
[615] | 313 | |
---|
[478] | 314 | OutEdgeIt f; |
---|
| 315 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
---|
| 316 | Node v=g->head(f); |
---|
| 317 | if (M[v] && (*flow)[f] > 0 ) { |
---|
| 318 | queue.push(v); |
---|
| 319 | M.set(v, false); |
---|
| 320 | } |
---|
| 321 | } |
---|
| 322 | } |
---|
| 323 | } |
---|
| 324 | |
---|
[631] | 325 | ///Returns a minimum value cut. |
---|
[478] | 326 | |
---|
[631] | 327 | ///Sets \c M to the characteristic vector of a minimum value cut. |
---|
| 328 | ///\pre M should be a node map of bools initialized to false. |
---|
| 329 | ///\pre \c flow must be a maximum flow. |
---|
[478] | 330 | template<typename CutMap> |
---|
[485] | 331 | void minCut(CutMap& M) { minMinCut(M); } |
---|
[478] | 332 | |
---|
[631] | 333 | ///Resets the source node to \c _s. |
---|
| 334 | |
---|
| 335 | ///Resets the source node to \c _s. |
---|
| 336 | /// |
---|
[487] | 337 | void resetSource(Node _s) { s=_s; } |
---|
[631] | 338 | |
---|
| 339 | ///Resets the target node to \c _t. |
---|
| 340 | |
---|
| 341 | ///Resets the target node to \c _t. |
---|
[487] | 342 | /// |
---|
| 343 | void resetTarget(Node _t) { t=_t; } |
---|
[615] | 344 | |
---|
[631] | 345 | /// Resets the edge map of the capacities to _cap. |
---|
| 346 | |
---|
| 347 | /// Resets the edge map of the capacities to _cap. |
---|
| 348 | /// |
---|
[485] | 349 | void resetCap(const CapMap& _cap) { capacity=&_cap; } |
---|
[615] | 350 | |
---|
[631] | 351 | /// Resets the edge map of the flows to _flow. |
---|
| 352 | |
---|
| 353 | /// Resets the edge map of the flows to _flow. |
---|
| 354 | /// |
---|
[485] | 355 | void resetFlow(FlowMap& _flow) { flow=&_flow; } |
---|
[478] | 356 | |
---|
| 357 | |
---|
| 358 | private: |
---|
| 359 | |
---|
| 360 | int push(Node w, VecStack& active) { |
---|
[615] | 361 | |
---|
[478] | 362 | int lev=level[w]; |
---|
| 363 | Num exc=excess[w]; |
---|
| 364 | int newlevel=n; //bound on the next level of w |
---|
[615] | 365 | |
---|
[478] | 366 | OutEdgeIt e; |
---|
| 367 | for(g->first(e,w); g->valid(e); g->next(e)) { |
---|
[615] | 368 | |
---|
| 369 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
---|
| 370 | Node v=g->head(e); |
---|
| 371 | |
---|
[478] | 372 | if( lev > level[v] ) { //Push is allowed now |
---|
[615] | 373 | |
---|
[478] | 374 | if ( excess[v]<=0 && v!=t && v!=s ) { |
---|
| 375 | int lev_v=level[v]; |
---|
| 376 | active[lev_v].push(v); |
---|
| 377 | } |
---|
[615] | 378 | |
---|
[478] | 379 | Num cap=(*capacity)[e]; |
---|
| 380 | Num flo=(*flow)[e]; |
---|
| 381 | Num remcap=cap-flo; |
---|
[615] | 382 | |
---|
[478] | 383 | if ( remcap >= exc ) { //A nonsaturating push. |
---|
[615] | 384 | |
---|
[478] | 385 | flow->set(e, flo+exc); |
---|
| 386 | excess.set(v, excess[v]+exc); |
---|
| 387 | exc=0; |
---|
[615] | 388 | break; |
---|
| 389 | |
---|
[478] | 390 | } else { //A saturating push. |
---|
| 391 | flow->set(e, cap); |
---|
| 392 | excess.set(v, excess[v]+remcap); |
---|
| 393 | exc-=remcap; |
---|
| 394 | } |
---|
| 395 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
[615] | 396 | } //for out edges wv |
---|
| 397 | |
---|
| 398 | if ( exc > 0 ) { |
---|
[478] | 399 | InEdgeIt e; |
---|
| 400 | for(g->first(e,w); g->valid(e); g->next(e)) { |
---|
[615] | 401 | |
---|
| 402 | if( (*flow)[e] <= 0 ) continue; |
---|
| 403 | Node v=g->tail(e); |
---|
| 404 | |
---|
[478] | 405 | if( lev > level[v] ) { //Push is allowed now |
---|
[615] | 406 | |
---|
[478] | 407 | if ( excess[v]<=0 && v!=t && v!=s ) { |
---|
| 408 | int lev_v=level[v]; |
---|
| 409 | active[lev_v].push(v); |
---|
| 410 | } |
---|
[615] | 411 | |
---|
[478] | 412 | Num flo=(*flow)[e]; |
---|
[615] | 413 | |
---|
[478] | 414 | if ( flo >= exc ) { //A nonsaturating push. |
---|
[615] | 415 | |
---|
[478] | 416 | flow->set(e, flo-exc); |
---|
| 417 | excess.set(v, excess[v]+exc); |
---|
| 418 | exc=0; |
---|
[615] | 419 | break; |
---|
[478] | 420 | } else { //A saturating push. |
---|
[615] | 421 | |
---|
[478] | 422 | excess.set(v, excess[v]+flo); |
---|
| 423 | exc-=flo; |
---|
| 424 | flow->set(e,0); |
---|
[615] | 425 | } |
---|
[478] | 426 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 427 | } //for in edges vw |
---|
[615] | 428 | |
---|
[478] | 429 | } // if w still has excess after the out edge for cycle |
---|
[615] | 430 | |
---|
[478] | 431 | excess.set(w, exc); |
---|
[615] | 432 | |
---|
[478] | 433 | return newlevel; |
---|
[485] | 434 | } |
---|
[478] | 435 | |
---|
| 436 | |
---|
[615] | 437 | void preflowPreproc(flowEnum fe, VecStack& active, |
---|
| 438 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
[602] | 439 | { |
---|
[615] | 440 | std::queue<Node> bfs_queue; |
---|
[478] | 441 | |
---|
[615] | 442 | switch (fe) { |
---|
[631] | 443 | case NO_FLOW: //flow is already set to const zero in this case |
---|
[615] | 444 | case ZERO_FLOW: |
---|
[602] | 445 | { |
---|
| 446 | //Reverse_bfs from t, to find the starting level. |
---|
| 447 | level.set(t,0); |
---|
| 448 | bfs_queue.push(t); |
---|
[615] | 449 | |
---|
[602] | 450 | while (!bfs_queue.empty()) { |
---|
[615] | 451 | |
---|
| 452 | Node v=bfs_queue.front(); |
---|
[602] | 453 | bfs_queue.pop(); |
---|
| 454 | int l=level[v]+1; |
---|
[615] | 455 | |
---|
[602] | 456 | InEdgeIt e; |
---|
| 457 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 458 | Node w=g->tail(e); |
---|
| 459 | if ( level[w] == n && w != s ) { |
---|
| 460 | bfs_queue.push(w); |
---|
| 461 | Node first=level_list[l]; |
---|
| 462 | if ( g->valid(first) ) left.set(first,w); |
---|
| 463 | right.set(w,first); |
---|
| 464 | level_list[l]=w; |
---|
| 465 | level.set(w, l); |
---|
| 466 | } |
---|
| 467 | } |
---|
| 468 | } |
---|
[615] | 469 | |
---|
[602] | 470 | //the starting flow |
---|
| 471 | OutEdgeIt e; |
---|
[615] | 472 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
[602] | 473 | { |
---|
| 474 | Num c=(*capacity)[e]; |
---|
| 475 | if ( c <= 0 ) continue; |
---|
| 476 | Node w=g->head(e); |
---|
[615] | 477 | if ( level[w] < n ) { |
---|
[602] | 478 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
[615] | 479 | flow->set(e, c); |
---|
[602] | 480 | excess.set(w, excess[w]+c); |
---|
| 481 | } |
---|
| 482 | } |
---|
| 483 | break; |
---|
| 484 | } |
---|
[615] | 485 | |
---|
[602] | 486 | case GEN_FLOW: |
---|
[615] | 487 | case PRE_FLOW: |
---|
[602] | 488 | { |
---|
[615] | 489 | //Reverse_bfs from t in the residual graph, |
---|
[602] | 490 | //to find the starting level. |
---|
| 491 | level.set(t,0); |
---|
| 492 | bfs_queue.push(t); |
---|
[615] | 493 | |
---|
[602] | 494 | while (!bfs_queue.empty()) { |
---|
[615] | 495 | |
---|
| 496 | Node v=bfs_queue.front(); |
---|
[602] | 497 | bfs_queue.pop(); |
---|
| 498 | int l=level[v]+1; |
---|
[615] | 499 | |
---|
[602] | 500 | InEdgeIt e; |
---|
| 501 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 502 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 503 | Node w=g->tail(e); |
---|
| 504 | if ( level[w] == n && w != s ) { |
---|
| 505 | bfs_queue.push(w); |
---|
| 506 | Node first=level_list[l]; |
---|
| 507 | if ( g->valid(first) ) left.set(first,w); |
---|
| 508 | right.set(w,first); |
---|
| 509 | level_list[l]=w; |
---|
| 510 | level.set(w, l); |
---|
| 511 | } |
---|
| 512 | } |
---|
[615] | 513 | |
---|
[602] | 514 | OutEdgeIt f; |
---|
| 515 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 516 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 517 | Node w=g->head(f); |
---|
| 518 | if ( level[w] == n && w != s ) { |
---|
| 519 | bfs_queue.push(w); |
---|
| 520 | Node first=level_list[l]; |
---|
| 521 | if ( g->valid(first) ) left.set(first,w); |
---|
| 522 | right.set(w,first); |
---|
| 523 | level_list[l]=w; |
---|
| 524 | level.set(w, l); |
---|
| 525 | } |
---|
| 526 | } |
---|
| 527 | } |
---|
[615] | 528 | |
---|
| 529 | |
---|
[602] | 530 | //the starting flow |
---|
| 531 | OutEdgeIt e; |
---|
[615] | 532 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
[602] | 533 | { |
---|
| 534 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
| 535 | if ( rem <= 0 ) continue; |
---|
| 536 | Node w=g->head(e); |
---|
[615] | 537 | if ( level[w] < n ) { |
---|
[602] | 538 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
[615] | 539 | flow->set(e, (*capacity)[e]); |
---|
[602] | 540 | excess.set(w, excess[w]+rem); |
---|
| 541 | } |
---|
| 542 | } |
---|
[615] | 543 | |
---|
[602] | 544 | InEdgeIt f; |
---|
[615] | 545 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
[602] | 546 | { |
---|
| 547 | if ( (*flow)[f] <= 0 ) continue; |
---|
| 548 | Node w=g->tail(f); |
---|
[615] | 549 | if ( level[w] < n ) { |
---|
[602] | 550 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
| 551 | excess.set(w, excess[w]+(*flow)[f]); |
---|
[615] | 552 | flow->set(f, 0); |
---|
[602] | 553 | } |
---|
[615] | 554 | } |
---|
[602] | 555 | break; |
---|
[615] | 556 | } //case PRE_FLOW |
---|
[602] | 557 | } |
---|
| 558 | } //preflowPreproc |
---|
[478] | 559 | |
---|
| 560 | |
---|
| 561 | |
---|
[615] | 562 | void relabel(Node w, int newlevel, VecStack& active, |
---|
| 563 | VecNode& level_list, NNMap& left, |
---|
| 564 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
[478] | 565 | { |
---|
| 566 | |
---|
[615] | 567 | Num lev=level[w]; |
---|
| 568 | |
---|
[478] | 569 | Node right_n=right[w]; |
---|
| 570 | Node left_n=left[w]; |
---|
[615] | 571 | |
---|
[478] | 572 | //unlacing starts |
---|
| 573 | if ( g->valid(right_n) ) { |
---|
| 574 | if ( g->valid(left_n) ) { |
---|
| 575 | right.set(left_n, right_n); |
---|
| 576 | left.set(right_n, left_n); |
---|
| 577 | } else { |
---|
[615] | 578 | level_list[lev]=right_n; |
---|
[478] | 579 | left.set(right_n, INVALID); |
---|
[615] | 580 | } |
---|
[478] | 581 | } else { |
---|
| 582 | if ( g->valid(left_n) ) { |
---|
| 583 | right.set(left_n, INVALID); |
---|
[615] | 584 | } else { |
---|
| 585 | level_list[lev]=INVALID; |
---|
| 586 | } |
---|
| 587 | } |
---|
[478] | 588 | //unlacing ends |
---|
[615] | 589 | |
---|
[478] | 590 | if ( !g->valid(level_list[lev]) ) { |
---|
[615] | 591 | |
---|
[478] | 592 | //gapping starts |
---|
| 593 | for (int i=lev; i!=k ; ) { |
---|
| 594 | Node v=level_list[++i]; |
---|
| 595 | while ( g->valid(v) ) { |
---|
| 596 | level.set(v,n); |
---|
| 597 | v=right[v]; |
---|
| 598 | } |
---|
| 599 | level_list[i]=INVALID; |
---|
| 600 | if ( !what_heur ) { |
---|
| 601 | while ( !active[i].empty() ) { |
---|
| 602 | active[i].pop(); //FIXME: ezt szebben kene |
---|
| 603 | } |
---|
[615] | 604 | } |
---|
[478] | 605 | } |
---|
[615] | 606 | |
---|
[478] | 607 | level.set(w,n); |
---|
| 608 | b=lev-1; |
---|
| 609 | k=b; |
---|
| 610 | //gapping ends |
---|
[615] | 611 | |
---|
[478] | 612 | } else { |
---|
[615] | 613 | |
---|
| 614 | if ( newlevel == n ) level.set(w,n); |
---|
[478] | 615 | else { |
---|
| 616 | level.set(w,++newlevel); |
---|
| 617 | active[newlevel].push(w); |
---|
| 618 | if ( what_heur ) b=newlevel; |
---|
| 619 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 620 | Node first=level_list[newlevel]; |
---|
| 621 | if ( g->valid(first) ) left.set(first,w); |
---|
| 622 | right.set(w,first); |
---|
| 623 | left.set(w,INVALID); |
---|
| 624 | level_list[newlevel]=w; |
---|
| 625 | } |
---|
| 626 | } |
---|
[615] | 627 | |
---|
[478] | 628 | } //relabel |
---|
| 629 | |
---|
| 630 | |
---|
[615] | 631 | template<typename MapGraphWrapper> |
---|
[478] | 632 | class DistanceMap { |
---|
| 633 | protected: |
---|
| 634 | const MapGraphWrapper* g; |
---|
[615] | 635 | typename MapGraphWrapper::template NodeMap<int> dist; |
---|
[478] | 636 | public: |
---|
| 637 | DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
---|
[615] | 638 | void set(const typename MapGraphWrapper::Node& n, int a) { |
---|
| 639 | dist.set(n, a); |
---|
[478] | 640 | } |
---|
[615] | 641 | int operator[](const typename MapGraphWrapper::Node& n) |
---|
[485] | 642 | { return dist[n]; } |
---|
[615] | 643 | // int get(const typename MapGraphWrapper::Node& n) const { |
---|
[485] | 644 | // return dist[n]; } |
---|
[615] | 645 | // bool get(const typename MapGraphWrapper::Edge& e) const { |
---|
[485] | 646 | // return (dist.get(g->tail(e))<dist.get(g->head(e))); } |
---|
[615] | 647 | bool operator[](const typename MapGraphWrapper::Edge& e) const { |
---|
| 648 | return (dist[g->tail(e)]<dist[g->head(e)]); |
---|
[478] | 649 | } |
---|
| 650 | }; |
---|
[615] | 651 | |
---|
[478] | 652 | }; |
---|
| 653 | |
---|
| 654 | |
---|
| 655 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[631] | 656 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1( flowEnum fe ) |
---|
[478] | 657 | { |
---|
[615] | 658 | |
---|
| 659 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
[485] | 660 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
| 661 | int heur=heur1; //starting time interval (#of relabels) |
---|
| 662 | int numrelabel=0; |
---|
[615] | 663 | |
---|
| 664 | bool what_heur=1; |
---|
[485] | 665 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
---|
[478] | 666 | |
---|
[615] | 667 | bool end=false; |
---|
| 668 | //Needed for 'bound decrease', true means no active nodes are above bound |
---|
| 669 | //b. |
---|
[478] | 670 | |
---|
[485] | 671 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 672 | int b=k; //bound on the highest level under n of an active node |
---|
[615] | 673 | |
---|
[485] | 674 | VecStack active(n); |
---|
[615] | 675 | |
---|
[485] | 676 | NNMap left(*g, INVALID); |
---|
| 677 | NNMap right(*g, INVALID); |
---|
| 678 | VecNode level_list(n,INVALID); |
---|
| 679 | //List of the nodes in level i<n, set to n. |
---|
[478] | 680 | |
---|
[485] | 681 | NodeIt v; |
---|
| 682 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
---|
| 683 | //setting each node to level n |
---|
[615] | 684 | |
---|
[631] | 685 | if ( fe == NO_FLOW ) { |
---|
| 686 | EdgeIt e; |
---|
| 687 | for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
---|
| 688 | } |
---|
| 689 | |
---|
| 690 | switch (fe) { //computing the excess |
---|
[615] | 691 | case PRE_FLOW: |
---|
[485] | 692 | { |
---|
| 693 | NodeIt v; |
---|
| 694 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
[478] | 695 | Num exc=0; |
---|
[615] | 696 | |
---|
[478] | 697 | InEdgeIt e; |
---|
[485] | 698 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
[478] | 699 | OutEdgeIt f; |
---|
[485] | 700 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
[615] | 701 | |
---|
| 702 | excess.set(v,exc); |
---|
| 703 | |
---|
[485] | 704 | //putting the active nodes into the stack |
---|
| 705 | int lev=level[v]; |
---|
| 706 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
---|
[478] | 707 | } |
---|
| 708 | break; |
---|
| 709 | } |
---|
[485] | 710 | case GEN_FLOW: |
---|
| 711 | { |
---|
[631] | 712 | NodeIt v; |
---|
| 713 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 714 | |
---|
[485] | 715 | Num exc=0; |
---|
| 716 | InEdgeIt e; |
---|
| 717 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
| 718 | OutEdgeIt f; |
---|
| 719 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
[615] | 720 | excess.set(t,exc); |
---|
[485] | 721 | break; |
---|
| 722 | } |
---|
[631] | 723 | case ZERO_FLOW: |
---|
| 724 | case NO_FLOW: |
---|
| 725 | { |
---|
| 726 | NodeIt v; |
---|
| 727 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 728 | break; |
---|
| 729 | } |
---|
[485] | 730 | } |
---|
[615] | 731 | |
---|
| 732 | preflowPreproc(fe, active, level_list, left, right); |
---|
| 733 | //End of preprocessing |
---|
| 734 | |
---|
| 735 | |
---|
[485] | 736 | //Push/relabel on the highest level active nodes. |
---|
| 737 | while ( true ) { |
---|
| 738 | if ( b == 0 ) { |
---|
| 739 | if ( !what_heur && !end && k > 0 ) { |
---|
| 740 | b=k; |
---|
| 741 | end=true; |
---|
| 742 | } else break; |
---|
| 743 | } |
---|
[615] | 744 | |
---|
| 745 | if ( active[b].empty() ) --b; |
---|
[485] | 746 | else { |
---|
[615] | 747 | end=false; |
---|
[485] | 748 | Node w=active[b].top(); |
---|
| 749 | active[b].pop(); |
---|
| 750 | int newlevel=push(w,active); |
---|
[615] | 751 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
---|
[485] | 752 | left, right, b, k, what_heur); |
---|
[615] | 753 | |
---|
| 754 | ++numrelabel; |
---|
[485] | 755 | if ( numrelabel >= heur ) { |
---|
| 756 | numrelabel=0; |
---|
| 757 | if ( what_heur ) { |
---|
| 758 | what_heur=0; |
---|
| 759 | heur=heur0; |
---|
| 760 | end=false; |
---|
| 761 | } else { |
---|
| 762 | what_heur=1; |
---|
| 763 | heur=heur1; |
---|
[615] | 764 | b=k; |
---|
[485] | 765 | } |
---|
[478] | 766 | } |
---|
[615] | 767 | } |
---|
| 768 | } |
---|
[485] | 769 | } |
---|
[478] | 770 | |
---|
| 771 | |
---|
| 772 | |
---|
| 773 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[631] | 774 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() |
---|
[478] | 775 | { |
---|
[615] | 776 | |
---|
[485] | 777 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 778 | int b=k; //bound on the highest level under n of an active node |
---|
[615] | 779 | |
---|
[485] | 780 | VecStack active(n); |
---|
| 781 | level.set(s,0); |
---|
| 782 | std::queue<Node> bfs_queue; |
---|
| 783 | bfs_queue.push(s); |
---|
[615] | 784 | |
---|
[485] | 785 | while (!bfs_queue.empty()) { |
---|
[615] | 786 | |
---|
| 787 | Node v=bfs_queue.front(); |
---|
[485] | 788 | bfs_queue.pop(); |
---|
| 789 | int l=level[v]+1; |
---|
[615] | 790 | |
---|
[485] | 791 | InEdgeIt e; |
---|
| 792 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 793 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 794 | Node u=g->tail(e); |
---|
[615] | 795 | if ( level[u] >= n ) { |
---|
[485] | 796 | bfs_queue.push(u); |
---|
| 797 | level.set(u, l); |
---|
| 798 | if ( excess[u] > 0 ) active[l].push(u); |
---|
[478] | 799 | } |
---|
| 800 | } |
---|
[615] | 801 | |
---|
[485] | 802 | OutEdgeIt f; |
---|
| 803 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 804 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 805 | Node u=g->head(f); |
---|
[615] | 806 | if ( level[u] >= n ) { |
---|
[485] | 807 | bfs_queue.push(u); |
---|
| 808 | level.set(u, l); |
---|
| 809 | if ( excess[u] > 0 ) active[l].push(u); |
---|
| 810 | } |
---|
| 811 | } |
---|
| 812 | } |
---|
| 813 | b=n-2; |
---|
[478] | 814 | |
---|
[485] | 815 | while ( true ) { |
---|
[615] | 816 | |
---|
[485] | 817 | if ( b == 0 ) break; |
---|
[478] | 818 | |
---|
[615] | 819 | if ( active[b].empty() ) --b; |
---|
[485] | 820 | else { |
---|
| 821 | Node w=active[b].top(); |
---|
| 822 | active[b].pop(); |
---|
[615] | 823 | int newlevel=push(w,active); |
---|
[478] | 824 | |
---|
[485] | 825 | //relabel |
---|
| 826 | if ( excess[w] > 0 ) { |
---|
| 827 | level.set(w,++newlevel); |
---|
| 828 | active[newlevel].push(w); |
---|
| 829 | b=newlevel; |
---|
| 830 | } |
---|
| 831 | } // if stack[b] is nonempty |
---|
| 832 | } // while(true) |
---|
| 833 | } |
---|
[478] | 834 | |
---|
| 835 | |
---|
| 836 | |
---|
| 837 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[615] | 838 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
---|
[478] | 839 | { |
---|
[485] | 840 | ResGW res_graph(*g, *capacity, *flow); |
---|
| 841 | bool _augment=false; |
---|
[615] | 842 | |
---|
[485] | 843 | //ReachedMap level(res_graph); |
---|
| 844 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 845 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
| 846 | bfs.pushAndSetReached(s); |
---|
[615] | 847 | |
---|
| 848 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
---|
[485] | 849 | pred.set(s, INVALID); |
---|
[615] | 850 | |
---|
[485] | 851 | typename ResGW::template NodeMap<Num> free(res_graph); |
---|
[615] | 852 | |
---|
[485] | 853 | //searching for augmenting path |
---|
[615] | 854 | while ( !bfs.finished() ) { |
---|
[485] | 855 | ResGWOutEdgeIt e=bfs; |
---|
| 856 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 857 | Node v=res_graph.tail(e); |
---|
| 858 | Node w=res_graph.head(e); |
---|
| 859 | pred.set(w, e); |
---|
| 860 | if (res_graph.valid(pred[v])) { |
---|
| 861 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
---|
| 862 | } else { |
---|
[615] | 863 | free.set(w, res_graph.resCap(e)); |
---|
[478] | 864 | } |
---|
[485] | 865 | if (res_graph.head(e)==t) { _augment=true; break; } |
---|
| 866 | } |
---|
[615] | 867 | |
---|
[485] | 868 | ++bfs; |
---|
| 869 | } //end of searching augmenting path |
---|
[478] | 870 | |
---|
[485] | 871 | if (_augment) { |
---|
| 872 | Node n=t; |
---|
| 873 | Num augment_value=free[t]; |
---|
[615] | 874 | while (res_graph.valid(pred[n])) { |
---|
[485] | 875 | ResGWEdge e=pred[n]; |
---|
[615] | 876 | res_graph.augment(e, augment_value); |
---|
[485] | 877 | n=res_graph.tail(e); |
---|
[478] | 878 | } |
---|
[485] | 879 | } |
---|
[478] | 880 | |
---|
[485] | 881 | return _augment; |
---|
| 882 | } |
---|
[478] | 883 | |
---|
| 884 | |
---|
| 885 | |
---|
| 886 | |
---|
| 887 | |
---|
| 888 | |
---|
| 889 | |
---|
| 890 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[615] | 891 | template<typename MutableGraph> |
---|
| 892 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
---|
| 893 | { |
---|
[485] | 894 | typedef MutableGraph MG; |
---|
| 895 | bool _augment=false; |
---|
[478] | 896 | |
---|
[485] | 897 | ResGW res_graph(*g, *capacity, *flow); |
---|
[478] | 898 | |
---|
[485] | 899 | //bfs for distances on the residual graph |
---|
| 900 | //ReachedMap level(res_graph); |
---|
| 901 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 902 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
| 903 | bfs.pushAndSetReached(s); |
---|
[615] | 904 | typename ResGW::template NodeMap<int> |
---|
[485] | 905 | dist(res_graph); //filled up with 0's |
---|
[478] | 906 | |
---|
[485] | 907 | //F will contain the physical copy of the residual graph |
---|
| 908 | //with the set of edges which are on shortest paths |
---|
| 909 | MG F; |
---|
[615] | 910 | typename ResGW::template NodeMap<typename MG::Node> |
---|
[485] | 911 | res_graph_to_F(res_graph); |
---|
| 912 | { |
---|
| 913 | typename ResGW::NodeIt n; |
---|
| 914 | for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
---|
| 915 | res_graph_to_F.set(n, F.addNode()); |
---|
[478] | 916 | } |
---|
[485] | 917 | } |
---|
[478] | 918 | |
---|
[485] | 919 | typename MG::Node sF=res_graph_to_F[s]; |
---|
| 920 | typename MG::Node tF=res_graph_to_F[t]; |
---|
| 921 | typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
---|
| 922 | typename MG::template EdgeMap<Num> residual_capacity(F); |
---|
[478] | 923 | |
---|
[615] | 924 | while ( !bfs.finished() ) { |
---|
[485] | 925 | ResGWOutEdgeIt e=bfs; |
---|
| 926 | if (res_graph.valid(e)) { |
---|
| 927 | if (bfs.isBNodeNewlyReached()) { |
---|
| 928 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
[615] | 929 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
---|
| 930 | res_graph_to_F[res_graph.head(e)]); |
---|
[485] | 931 | original_edge.update(); |
---|
| 932 | original_edge.set(f, e); |
---|
| 933 | residual_capacity.update(); |
---|
| 934 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
| 935 | } else { |
---|
| 936 | if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
---|
[615] | 937 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
---|
| 938 | res_graph_to_F[res_graph.head(e)]); |
---|
[478] | 939 | original_edge.update(); |
---|
| 940 | original_edge.set(f, e); |
---|
| 941 | residual_capacity.update(); |
---|
| 942 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
| 943 | } |
---|
| 944 | } |
---|
[485] | 945 | } |
---|
| 946 | ++bfs; |
---|
| 947 | } //computing distances from s in the residual graph |
---|
[478] | 948 | |
---|
[485] | 949 | bool __augment=true; |
---|
[478] | 950 | |
---|
[485] | 951 | while (__augment) { |
---|
| 952 | __augment=false; |
---|
| 953 | //computing blocking flow with dfs |
---|
| 954 | DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
---|
| 955 | typename MG::template NodeMap<typename MG::Edge> pred(F); |
---|
| 956 | pred.set(sF, INVALID); |
---|
| 957 | //invalid iterators for sources |
---|
[478] | 958 | |
---|
[485] | 959 | typename MG::template NodeMap<Num> free(F); |
---|
[478] | 960 | |
---|
[615] | 961 | dfs.pushAndSetReached(sF); |
---|
[485] | 962 | while (!dfs.finished()) { |
---|
| 963 | ++dfs; |
---|
| 964 | if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
---|
| 965 | if (dfs.isBNodeNewlyReached()) { |
---|
| 966 | typename MG::Node v=F.aNode(dfs); |
---|
| 967 | typename MG::Node w=F.bNode(dfs); |
---|
| 968 | pred.set(w, dfs); |
---|
| 969 | if (F.valid(pred[v])) { |
---|
| 970 | free.set(w, std::min(free[v], residual_capacity[dfs])); |
---|
| 971 | } else { |
---|
[615] | 972 | free.set(w, residual_capacity[dfs]); |
---|
[485] | 973 | } |
---|
[615] | 974 | if (w==tF) { |
---|
| 975 | __augment=true; |
---|
[485] | 976 | _augment=true; |
---|
[615] | 977 | break; |
---|
[485] | 978 | } |
---|
[615] | 979 | |
---|
[485] | 980 | } else { |
---|
| 981 | F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
---|
| 982 | } |
---|
[615] | 983 | } |
---|
[485] | 984 | } |
---|
| 985 | |
---|
| 986 | if (__augment) { |
---|
| 987 | typename MG::Node n=tF; |
---|
| 988 | Num augment_value=free[tF]; |
---|
[615] | 989 | while (F.valid(pred[n])) { |
---|
[485] | 990 | typename MG::Edge e=pred[n]; |
---|
[615] | 991 | res_graph.augment(original_edge[e], augment_value); |
---|
[485] | 992 | n=F.tail(e); |
---|
[615] | 993 | if (residual_capacity[e]==augment_value) |
---|
| 994 | F.erase(e); |
---|
| 995 | else |
---|
[485] | 996 | residual_capacity.set(e, residual_capacity[e]-augment_value); |
---|
[478] | 997 | } |
---|
[485] | 998 | } |
---|
[615] | 999 | |
---|
[485] | 1000 | } |
---|
[615] | 1001 | |
---|
[485] | 1002 | return _augment; |
---|
| 1003 | } |
---|
[478] | 1004 | |
---|
| 1005 | |
---|
| 1006 | |
---|
| 1007 | |
---|
| 1008 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[615] | 1009 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
---|
[478] | 1010 | { |
---|
[485] | 1011 | bool _augment=false; |
---|
[478] | 1012 | |
---|
[485] | 1013 | ResGW res_graph(*g, *capacity, *flow); |
---|
[615] | 1014 | |
---|
[485] | 1015 | //ReachedMap level(res_graph); |
---|
| 1016 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 1017 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
[478] | 1018 | |
---|
[485] | 1019 | bfs.pushAndSetReached(s); |
---|
| 1020 | DistanceMap<ResGW> dist(res_graph); |
---|
[615] | 1021 | while ( !bfs.finished() ) { |
---|
[485] | 1022 | ResGWOutEdgeIt e=bfs; |
---|
| 1023 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 1024 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
| 1025 | } |
---|
| 1026 | ++bfs; |
---|
| 1027 | } //computing distances from s in the residual graph |
---|
[478] | 1028 | |
---|
| 1029 | //Subgraph containing the edges on some shortest paths |
---|
[485] | 1030 | ConstMap<typename ResGW::Node, bool> true_map(true); |
---|
[615] | 1031 | typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
---|
[485] | 1032 | DistanceMap<ResGW> > FilterResGW; |
---|
| 1033 | FilterResGW filter_res_graph(res_graph, true_map, dist); |
---|
[478] | 1034 | |
---|
[615] | 1035 | //Subgraph, which is able to delete edges which are already |
---|
[485] | 1036 | //met by the dfs |
---|
[615] | 1037 | typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
---|
[485] | 1038 | first_out_edges(filter_res_graph); |
---|
| 1039 | typename FilterResGW::NodeIt v; |
---|
[615] | 1040 | for(filter_res_graph.first(v); filter_res_graph.valid(v); |
---|
| 1041 | filter_res_graph.next(v)) |
---|
[478] | 1042 | { |
---|
| 1043 | typename FilterResGW::OutEdgeIt e; |
---|
| 1044 | filter_res_graph.first(e, v); |
---|
| 1045 | first_out_edges.set(v, e); |
---|
| 1046 | } |
---|
[485] | 1047 | typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
---|
| 1048 | template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
---|
| 1049 | ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
---|
[478] | 1050 | |
---|
[485] | 1051 | bool __augment=true; |
---|
[478] | 1052 | |
---|
[485] | 1053 | while (__augment) { |
---|
[478] | 1054 | |
---|
[485] | 1055 | __augment=false; |
---|
| 1056 | //computing blocking flow with dfs |
---|
[615] | 1057 | DfsIterator< ErasingResGW, |
---|
| 1058 | typename ErasingResGW::template NodeMap<bool> > |
---|
[485] | 1059 | dfs(erasing_res_graph); |
---|
| 1060 | typename ErasingResGW:: |
---|
[615] | 1061 | template NodeMap<typename ErasingResGW::OutEdgeIt> |
---|
| 1062 | pred(erasing_res_graph); |
---|
[485] | 1063 | pred.set(s, INVALID); |
---|
| 1064 | //invalid iterators for sources |
---|
[478] | 1065 | |
---|
[615] | 1066 | typename ErasingResGW::template NodeMap<Num> |
---|
[485] | 1067 | free1(erasing_res_graph); |
---|
[478] | 1068 | |
---|
[615] | 1069 | dfs.pushAndSetReached |
---|
| 1070 | ///\bug hugo 0.2 |
---|
| 1071 | (typename ErasingResGW::Node |
---|
| 1072 | (typename FilterResGW::Node |
---|
| 1073 | (typename ResGW::Node(s) |
---|
| 1074 | ) |
---|
| 1075 | ) |
---|
| 1076 | ); |
---|
[485] | 1077 | while (!dfs.finished()) { |
---|
| 1078 | ++dfs; |
---|
[615] | 1079 | if (erasing_res_graph.valid(typename ErasingResGW::OutEdgeIt(dfs))) |
---|
| 1080 | { |
---|
[478] | 1081 | if (dfs.isBNodeNewlyReached()) { |
---|
[615] | 1082 | |
---|
[478] | 1083 | typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
---|
| 1084 | typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
---|
| 1085 | |
---|
| 1086 | pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
---|
| 1087 | if (erasing_res_graph.valid(pred[v])) { |
---|
[615] | 1088 | free1.set |
---|
| 1089 | (w, std::min(free1[v], res_graph.resCap |
---|
| 1090 | (typename ErasingResGW::OutEdgeIt(dfs)))); |
---|
[478] | 1091 | } else { |
---|
[615] | 1092 | free1.set |
---|
| 1093 | (w, res_graph.resCap |
---|
| 1094 | (typename ErasingResGW::OutEdgeIt(dfs))); |
---|
[478] | 1095 | } |
---|
[615] | 1096 | |
---|
| 1097 | if (w==t) { |
---|
| 1098 | __augment=true; |
---|
[478] | 1099 | _augment=true; |
---|
[615] | 1100 | break; |
---|
[478] | 1101 | } |
---|
| 1102 | } else { |
---|
| 1103 | erasing_res_graph.erase(dfs); |
---|
| 1104 | } |
---|
| 1105 | } |
---|
[615] | 1106 | } |
---|
[478] | 1107 | |
---|
[485] | 1108 | if (__augment) { |
---|
[615] | 1109 | typename ErasingResGW::Node |
---|
| 1110 | n=typename FilterResGW::Node(typename ResGW::Node(t)); |
---|
[485] | 1111 | // typename ResGW::NodeMap<Num> a(res_graph); |
---|
| 1112 | // typename ResGW::Node b; |
---|
| 1113 | // Num j=a[b]; |
---|
| 1114 | // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
---|
| 1115 | // typename FilterResGW::Node b1; |
---|
| 1116 | // Num j1=a1[b1]; |
---|
| 1117 | // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
---|
| 1118 | // typename ErasingResGW::Node b2; |
---|
| 1119 | // Num j2=a2[b2]; |
---|
| 1120 | Num augment_value=free1[n]; |
---|
[615] | 1121 | while (erasing_res_graph.valid(pred[n])) { |
---|
[485] | 1122 | typename ErasingResGW::OutEdgeIt e=pred[n]; |
---|
| 1123 | res_graph.augment(e, augment_value); |
---|
| 1124 | n=erasing_res_graph.tail(e); |
---|
| 1125 | if (res_graph.resCap(e)==0) |
---|
| 1126 | erasing_res_graph.erase(e); |
---|
[478] | 1127 | } |
---|
| 1128 | } |
---|
[615] | 1129 | |
---|
| 1130 | } //while (__augment) |
---|
| 1131 | |
---|
[485] | 1132 | return _augment; |
---|
| 1133 | } |
---|
[478] | 1134 | |
---|
| 1135 | |
---|
| 1136 | } //namespace hugo |
---|
| 1137 | |
---|
[480] | 1138 | #endif //HUGO_MAX_FLOW_H |
---|
[478] | 1139 | |
---|
| 1140 | |
---|
| 1141 | |
---|
| 1142 | |
---|