[98] | 1 | // -*- C++ -*- |
---|
| 2 | /* |
---|
| 3 | preflow_hl2.h |
---|
| 4 | by jacint. |
---|
| 5 | Runs the highest label variant of the preflow push algorithm with |
---|
[109] | 6 | running time O(n^2\sqrt(m)). |
---|
[98] | 7 | |
---|
[109] | 8 | Heuristics: |
---|
[98] | 9 | |
---|
[109] | 10 | gap: we iterate through the nodes for finding the nodes above |
---|
| 11 | the gap and under level n. So it is quite slow. |
---|
| 12 | numb: we maintain the number of nodes in level i. |
---|
| 13 | highest label |
---|
| 14 | |
---|
| 15 | 'A' is a parameter for the gap, we only upgrade the nodes to level n, |
---|
| 16 | if the gap is under A*n. |
---|
[98] | 17 | |
---|
[109] | 18 | The constructor runs the algorithm. |
---|
[98] | 19 | |
---|
[109] | 20 | Members: |
---|
[98] | 21 | |
---|
[109] | 22 | T maxFlow() : returns the value of a maximum flow |
---|
[98] | 23 | |
---|
[109] | 24 | T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
---|
[98] | 25 | |
---|
[109] | 26 | FlowMap Flow() : returns the fixed maximum flow x |
---|
[98] | 27 | |
---|
[109] | 28 | void minCut(CutMap& M) : sets M to the characteristic vector of a |
---|
[98] | 29 | minimum cut. M should be a map of bools initialized to false. |
---|
| 30 | |
---|
[109] | 31 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
---|
[98] | 32 | minimum min cut. M should be a map of bools initialized to false. |
---|
| 33 | |
---|
[109] | 34 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
---|
[98] | 35 | maximum min cut. M should be a map of bools initialized to false. |
---|
| 36 | |
---|
| 37 | */ |
---|
| 38 | |
---|
| 39 | #ifndef PREFLOW_HL2_H |
---|
| 40 | #define PREFLOW_HL2_H |
---|
| 41 | |
---|
[109] | 42 | #define A .9 |
---|
[98] | 43 | |
---|
| 44 | #include <vector> |
---|
| 45 | #include <stack> |
---|
| 46 | #include <queue> |
---|
| 47 | |
---|
[105] | 48 | namespace hugo { |
---|
[98] | 49 | |
---|
| 50 | template <typename Graph, typename T, |
---|
[109] | 51 | typename FlowMap=typename Graph::EdgeMap<T>, |
---|
| 52 | typename CapMap=typename Graph::EdgeMap<T> > |
---|
[98] | 53 | class preflow_hl2 { |
---|
| 54 | |
---|
| 55 | typedef typename Graph::NodeIt NodeIt; |
---|
| 56 | typedef typename Graph::EdgeIt EdgeIt; |
---|
| 57 | typedef typename Graph::EachNodeIt EachNodeIt; |
---|
| 58 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
| 59 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
| 60 | |
---|
| 61 | Graph& G; |
---|
| 62 | NodeIt s; |
---|
| 63 | NodeIt t; |
---|
| 64 | FlowMap flow; |
---|
| 65 | CapMap& capacity; |
---|
| 66 | T value; |
---|
| 67 | |
---|
| 68 | public: |
---|
| 69 | |
---|
| 70 | preflow_hl2(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
---|
[109] | 71 | G(_G), s(_s), t(_t), flow(_G), capacity(_capacity) { |
---|
[98] | 72 | |
---|
| 73 | int n=G.nodeNum(); |
---|
| 74 | int b=n-2; |
---|
| 75 | /* |
---|
| 76 | b is a bound on the highest level of an active node. |
---|
| 77 | */ |
---|
| 78 | |
---|
[109] | 79 | typename Graph::NodeMap<int> level(G,n); |
---|
| 80 | typename Graph::NodeMap<T> excess(G); |
---|
| 81 | |
---|
[101] | 82 | std::vector<int> numb(n); |
---|
[98] | 83 | /* |
---|
| 84 | The number of nodes on level i < n. It is |
---|
| 85 | initialized to n+1, because of the reverse_bfs-part. |
---|
| 86 | */ |
---|
| 87 | |
---|
| 88 | std::vector<std::stack<NodeIt> > stack(2*n-1); |
---|
| 89 | //Stack of the active nodes in level i. |
---|
| 90 | |
---|
| 91 | |
---|
| 92 | /*Reverse_bfs from t, to find the starting level.*/ |
---|
| 93 | level.set(t,0); |
---|
| 94 | std::queue<NodeIt> bfs_queue; |
---|
| 95 | bfs_queue.push(t); |
---|
| 96 | |
---|
| 97 | while (!bfs_queue.empty()) { |
---|
| 98 | |
---|
| 99 | NodeIt v=bfs_queue.front(); |
---|
| 100 | bfs_queue.pop(); |
---|
| 101 | int l=level.get(v)+1; |
---|
| 102 | |
---|
| 103 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
---|
| 104 | NodeIt w=G.tail(e); |
---|
| 105 | if ( level.get(w) == n ) { |
---|
| 106 | bfs_queue.push(w); |
---|
| 107 | ++numb[l]; |
---|
| 108 | level.set(w, l); |
---|
| 109 | } |
---|
| 110 | } |
---|
| 111 | } |
---|
[109] | 112 | |
---|
[98] | 113 | level.set(s,n); |
---|
| 114 | |
---|
| 115 | |
---|
| 116 | |
---|
| 117 | /* Starting flow. It is everywhere 0 at the moment. */ |
---|
| 118 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
---|
| 119 | { |
---|
[101] | 120 | T c=capacity.get(e); |
---|
| 121 | if ( c == 0 ) continue; |
---|
[98] | 122 | NodeIt w=G.head(e); |
---|
| 123 | if ( w!=s ) { |
---|
| 124 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
---|
[101] | 125 | flow.set(e, c); |
---|
| 126 | excess.set(w, excess.get(w)+c); |
---|
| 127 | } |
---|
[98] | 128 | } |
---|
[109] | 129 | |
---|
[98] | 130 | /* |
---|
| 131 | End of preprocessing |
---|
| 132 | */ |
---|
| 133 | |
---|
| 134 | |
---|
| 135 | /* |
---|
| 136 | Push/relabel on the highest level active nodes. |
---|
[109] | 137 | */ |
---|
[98] | 138 | /*While there exists an active node.*/ |
---|
| 139 | while (b) { |
---|
[109] | 140 | if ( stack[b].empty() ) { |
---|
[98] | 141 | --b; |
---|
[109] | 142 | continue; |
---|
| 143 | } |
---|
| 144 | |
---|
| 145 | NodeIt w=stack[b].top(); |
---|
| 146 | stack[b].pop(); |
---|
| 147 | int lev=level.get(w); |
---|
| 148 | T exc=excess.get(w); |
---|
| 149 | int newlevel=2*n; //In newlevel we bound the next level of w. |
---|
| 150 | |
---|
[98] | 151 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
---|
| 152 | |
---|
| 153 | if ( flow.get(e) == capacity.get(e) ) continue; |
---|
| 154 | NodeIt v=G.head(e); |
---|
| 155 | //e=wv |
---|
| 156 | |
---|
| 157 | if( lev > level.get(v) ) { |
---|
| 158 | /*Push is allowed now*/ |
---|
| 159 | |
---|
| 160 | if ( excess.get(v)==0 && v != s && v !=t ) |
---|
| 161 | stack[level.get(v)].push(v); |
---|
| 162 | /*v becomes active.*/ |
---|
| 163 | |
---|
[109] | 164 | T cap=capacity.get(e); |
---|
| 165 | T flo=flow.get(e); |
---|
| 166 | T remcap=cap-flo; |
---|
[98] | 167 | |
---|
| 168 | if ( remcap >= exc ) { |
---|
| 169 | /*A nonsaturating push.*/ |
---|
| 170 | |
---|
| 171 | flow.set(e, flo+exc); |
---|
| 172 | excess.set(v, excess.get(v)+exc); |
---|
| 173 | exc=0; |
---|
| 174 | break; |
---|
| 175 | |
---|
| 176 | } else { |
---|
| 177 | /*A saturating push.*/ |
---|
| 178 | |
---|
| 179 | flow.set(e, cap ); |
---|
| 180 | excess.set(v, excess.get(v)+remcap); |
---|
| 181 | exc-=remcap; |
---|
| 182 | } |
---|
| 183 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
---|
| 184 | |
---|
| 185 | } //for out edges wv |
---|
| 186 | |
---|
| 187 | |
---|
| 188 | if ( exc > 0 ) { |
---|
| 189 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
---|
| 190 | |
---|
| 191 | if( flow.get(e) == 0 ) continue; |
---|
| 192 | NodeIt v=G.tail(e); |
---|
| 193 | //e=vw |
---|
| 194 | |
---|
| 195 | if( lev > level.get(v) ) { |
---|
| 196 | /*Push is allowed now*/ |
---|
| 197 | |
---|
| 198 | if ( excess.get(v)==0 && v != s && v !=t) |
---|
| 199 | stack[level.get(v)].push(v); |
---|
| 200 | /*v becomes active.*/ |
---|
| 201 | |
---|
[109] | 202 | T flo=flow.get(e); |
---|
[98] | 203 | |
---|
| 204 | if ( flo >= exc ) { |
---|
| 205 | /*A nonsaturating push.*/ |
---|
| 206 | |
---|
| 207 | flow.set(e, flo-exc); |
---|
| 208 | excess.set(v, excess.get(v)+exc); |
---|
| 209 | exc=0; |
---|
| 210 | break; |
---|
| 211 | } else { |
---|
| 212 | /*A saturating push.*/ |
---|
| 213 | |
---|
| 214 | excess.set(v, excess.get(v)+flo); |
---|
| 215 | exc-=flo; |
---|
| 216 | flow.set(e,0); |
---|
| 217 | } |
---|
| 218 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
---|
| 219 | |
---|
| 220 | } //for in edges vw |
---|
| 221 | |
---|
| 222 | } // if w still has excess after the out edge for cycle |
---|
[109] | 223 | |
---|
| 224 | excess.set(w, exc); |
---|
| 225 | |
---|
| 226 | |
---|
| 227 | |
---|
| 228 | |
---|
| 229 | /* |
---|
| 230 | Relabel |
---|
| 231 | */ |
---|
| 232 | |
---|
| 233 | if ( exc > 0 ) { |
---|
| 234 | //now 'lev' is the old level of w |
---|
| 235 | level.set(w,++newlevel); |
---|
[98] | 236 | |
---|
[109] | 237 | if ( lev < n ) { |
---|
| 238 | --numb[lev]; |
---|
| 239 | |
---|
| 240 | if ( !numb[lev] && lev < A*n ) { //If the level of w gets empty. |
---|
| 241 | |
---|
| 242 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
---|
| 243 | if (level.get(v) > lev && level.get(v) < n ) level.set(v,n); |
---|
| 244 | } |
---|
| 245 | for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; |
---|
| 246 | if ( newlevel < n ) newlevel=n; |
---|
| 247 | } else { |
---|
| 248 | if ( newlevel < n ) ++numb[newlevel]; |
---|
| 249 | } |
---|
| 250 | } |
---|
[98] | 251 | |
---|
[109] | 252 | stack[newlevel].push(w); |
---|
| 253 | b=newlevel; |
---|
| 254 | |
---|
| 255 | } |
---|
| 256 | |
---|
[98] | 257 | } // while(b) |
---|
[109] | 258 | |
---|
| 259 | |
---|
[98] | 260 | value = excess.get(t); |
---|
| 261 | /*Max flow value.*/ |
---|
| 262 | |
---|
| 263 | |
---|
| 264 | } //void run() |
---|
| 265 | |
---|
| 266 | |
---|
| 267 | |
---|
| 268 | |
---|
| 269 | |
---|
| 270 | /* |
---|
| 271 | Returns the maximum value of a flow. |
---|
| 272 | */ |
---|
| 273 | |
---|
[109] | 274 | T maxFlow() { |
---|
[98] | 275 | return value; |
---|
| 276 | } |
---|
| 277 | |
---|
| 278 | |
---|
| 279 | |
---|
| 280 | /* |
---|
[109] | 281 | For the maximum flow x found by the algorithm, |
---|
| 282 | it returns the flow value on edge e, i.e. x(e). |
---|
[98] | 283 | */ |
---|
| 284 | |
---|
[109] | 285 | T flowOnEdge(const EdgeIt e) { |
---|
[98] | 286 | return flow.get(e); |
---|
| 287 | } |
---|
| 288 | |
---|
| 289 | |
---|
| 290 | |
---|
| 291 | /* |
---|
| 292 | Returns the maximum flow x found by the algorithm. |
---|
| 293 | */ |
---|
| 294 | |
---|
[109] | 295 | FlowMap Flow() { |
---|
[98] | 296 | return flow; |
---|
| 297 | } |
---|
| 298 | |
---|
| 299 | |
---|
| 300 | |
---|
| 301 | |
---|
| 302 | /* |
---|
| 303 | Returns the minimum min cut, by a bfs from s in the residual graph. |
---|
| 304 | */ |
---|
| 305 | |
---|
| 306 | template<typename CutMap> |
---|
[109] | 307 | void minCut(CutMap& M) { |
---|
[98] | 308 | |
---|
| 309 | std::queue<NodeIt> queue; |
---|
| 310 | |
---|
| 311 | M.set(s,true); |
---|
| 312 | queue.push(s); |
---|
| 313 | |
---|
| 314 | while (!queue.empty()) { |
---|
| 315 | NodeIt w=queue.front(); |
---|
| 316 | queue.pop(); |
---|
[109] | 317 | |
---|
[98] | 318 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
---|
| 319 | NodeIt v=G.head(e); |
---|
| 320 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
---|
| 321 | queue.push(v); |
---|
| 322 | M.set(v, true); |
---|
| 323 | } |
---|
| 324 | } |
---|
| 325 | |
---|
| 326 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
---|
| 327 | NodeIt v=G.tail(e); |
---|
| 328 | if (!M.get(v) && flow.get(e) > 0 ) { |
---|
| 329 | queue.push(v); |
---|
| 330 | M.set(v, true); |
---|
| 331 | } |
---|
[109] | 332 | } |
---|
[98] | 333 | |
---|
| 334 | } |
---|
| 335 | } |
---|
| 336 | |
---|
| 337 | |
---|
| 338 | |
---|
| 339 | /* |
---|
| 340 | Returns the maximum min cut, by a reverse bfs |
---|
| 341 | from t in the residual graph. |
---|
| 342 | */ |
---|
| 343 | |
---|
| 344 | template<typename CutMap> |
---|
[109] | 345 | void maxMinCut(CutMap& M) { |
---|
[98] | 346 | |
---|
| 347 | std::queue<NodeIt> queue; |
---|
| 348 | |
---|
| 349 | M.set(t,true); |
---|
| 350 | queue.push(t); |
---|
| 351 | |
---|
| 352 | while (!queue.empty()) { |
---|
| 353 | NodeIt w=queue.front(); |
---|
| 354 | queue.pop(); |
---|
| 355 | |
---|
| 356 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
---|
| 357 | NodeIt v=G.tail(e); |
---|
| 358 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
---|
| 359 | queue.push(v); |
---|
| 360 | M.set(v, true); |
---|
| 361 | } |
---|
| 362 | } |
---|
| 363 | |
---|
| 364 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
---|
| 365 | NodeIt v=G.head(e); |
---|
| 366 | if (!M.get(v) && flow.get(e) > 0 ) { |
---|
| 367 | queue.push(v); |
---|
| 368 | M.set(v, true); |
---|
| 369 | } |
---|
| 370 | } |
---|
| 371 | } |
---|
| 372 | |
---|
| 373 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
---|
| 374 | M.set(v, !M.get(v)); |
---|
| 375 | } |
---|
| 376 | |
---|
| 377 | } |
---|
| 378 | |
---|
| 379 | |
---|
| 380 | |
---|
| 381 | template<typename CutMap> |
---|
[109] | 382 | void minMinCut(CutMap& M) { |
---|
| 383 | minCut(M); |
---|
[98] | 384 | } |
---|
| 385 | |
---|
| 386 | |
---|
| 387 | |
---|
| 388 | }; |
---|
[109] | 389 | }//namespace marci |
---|
[98] | 390 | #endif |
---|
| 391 | |
---|
| 392 | |
---|
| 393 | |
---|
| 394 | |
---|