[109] | 1 | // -*- C++ -*- |
---|
| 2 | /* |
---|
| 3 | preflow_max_flow.h |
---|
| 4 | by jacint. |
---|
| 5 | Runs the first phase of preflow.h |
---|
| 6 | |
---|
| 7 | The constructor runs the algorithm. |
---|
| 8 | |
---|
| 9 | Members: |
---|
| 10 | |
---|
| 11 | T maxFlow() : returns the value of a maximum flow |
---|
| 12 | |
---|
| 13 | CutMap minCut() : returns the characteristic vector of a min cut. |
---|
| 14 | */ |
---|
| 15 | |
---|
| 16 | #ifndef PREFLOW_MAX_FLOW_H |
---|
| 17 | #define PREFLOW_MAX_FLOW_H |
---|
| 18 | |
---|
| 19 | #define H0 20 |
---|
| 20 | #define H1 1 |
---|
| 21 | |
---|
| 22 | #include <vector> |
---|
| 23 | #include <queue> |
---|
| 24 | |
---|
| 25 | namespace hugo { |
---|
| 26 | |
---|
| 27 | template <typename Graph, typename T, |
---|
| 28 | typename FlowMap=typename Graph::EdgeMap<T>, |
---|
| 29 | typename CapMap=typename Graph::EdgeMap<T>, |
---|
| 30 | typename CutMap=typename Graph::NodeMap<bool> > |
---|
| 31 | class preflow_max_flow { |
---|
| 32 | |
---|
| 33 | typedef typename Graph::NodeIt NodeIt; |
---|
| 34 | typedef typename Graph::EdgeIt EdgeIt; |
---|
| 35 | typedef typename Graph::EachNodeIt EachNodeIt; |
---|
| 36 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
| 37 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
| 38 | |
---|
| 39 | Graph& G; |
---|
| 40 | NodeIt s; |
---|
| 41 | NodeIt t; |
---|
| 42 | FlowMap flow; |
---|
| 43 | CapMap& capacity; |
---|
| 44 | CutMap cut; |
---|
| 45 | T value; |
---|
| 46 | |
---|
| 47 | public: |
---|
| 48 | |
---|
| 49 | preflow_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) : |
---|
| 50 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), cut(_G, false) |
---|
| 51 | { |
---|
| 52 | |
---|
| 53 | int n=G.nodeNum(); |
---|
| 54 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
| 55 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
| 56 | int heur=heur1; //starting time interval (#of relabels) |
---|
| 57 | bool what_heur=1; |
---|
| 58 | /* |
---|
| 59 | what_heur is 0 in case 'bound decrease' |
---|
| 60 | and 1 in case 'highest label' |
---|
| 61 | */ |
---|
| 62 | bool end=false; |
---|
| 63 | /* |
---|
| 64 | Needed for 'bound decrease', 'true' |
---|
| 65 | means no active nodes are above bound b. |
---|
| 66 | */ |
---|
| 67 | int relabel=0; |
---|
| 68 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 69 | int b=k; //bound on the highest level under n of an active node |
---|
| 70 | |
---|
| 71 | typename Graph::NodeMap<int> level(G,n); |
---|
| 72 | typename Graph::NodeMap<T> excess(G); |
---|
| 73 | |
---|
| 74 | std::vector<NodeIt> active(n); |
---|
| 75 | typename Graph::NodeMap<NodeIt> next(G); |
---|
| 76 | //Stack of the active nodes in level i < n. |
---|
| 77 | //We use it in both phases. |
---|
| 78 | |
---|
| 79 | typename Graph::NodeMap<NodeIt> left(G); |
---|
| 80 | typename Graph::NodeMap<NodeIt> right(G); |
---|
| 81 | std::vector<NodeIt> level_list(n); |
---|
| 82 | /* |
---|
| 83 | List of the nodes in level i<n. |
---|
| 84 | */ |
---|
| 85 | |
---|
| 86 | /*Reverse_bfs from t, to find the starting level.*/ |
---|
| 87 | level.set(t,0); |
---|
| 88 | std::queue<NodeIt> bfs_queue; |
---|
| 89 | bfs_queue.push(t); |
---|
| 90 | |
---|
| 91 | while (!bfs_queue.empty()) { |
---|
| 92 | |
---|
| 93 | NodeIt v=bfs_queue.front(); |
---|
| 94 | bfs_queue.pop(); |
---|
| 95 | int l=level.get(v)+1; |
---|
| 96 | |
---|
| 97 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
---|
| 98 | NodeIt w=G.tail(e); |
---|
| 99 | if ( level.get(w) == n && w != s ) { |
---|
| 100 | bfs_queue.push(w); |
---|
| 101 | NodeIt first=level_list[l]; |
---|
| 102 | if ( first != 0 ) left.set(first,w); |
---|
| 103 | right.set(w,first); |
---|
| 104 | level_list[l]=w; |
---|
| 105 | level.set(w, l); |
---|
| 106 | } |
---|
| 107 | } |
---|
| 108 | } |
---|
| 109 | |
---|
| 110 | level.set(s,n); |
---|
| 111 | |
---|
| 112 | |
---|
| 113 | /* Starting flow. It is everywhere 0 at the moment. */ |
---|
| 114 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
---|
| 115 | { |
---|
| 116 | T c=capacity.get(e); |
---|
| 117 | if ( c == 0 ) continue; |
---|
| 118 | NodeIt w=G.head(e); |
---|
| 119 | if ( level.get(w) < n ) { |
---|
| 120 | if ( excess.get(w) == 0 && w!=t ) { |
---|
| 121 | next.set(w,active[level.get(w)]); |
---|
| 122 | active[level.get(w)]=w; |
---|
| 123 | } |
---|
| 124 | flow.set(e, c); |
---|
| 125 | excess.set(w, excess.get(w)+c); |
---|
| 126 | } |
---|
| 127 | } |
---|
| 128 | |
---|
| 129 | /* |
---|
| 130 | End of preprocessing |
---|
| 131 | */ |
---|
| 132 | |
---|
| 133 | |
---|
| 134 | |
---|
| 135 | /* |
---|
| 136 | Push/relabel on the highest level active nodes. |
---|
| 137 | */ |
---|
| 138 | while ( true ) { |
---|
| 139 | |
---|
| 140 | if ( b == 0 ) { |
---|
| 141 | if ( !what_heur && !end && k > 0 ) { |
---|
| 142 | b=k; |
---|
| 143 | end=true; |
---|
| 144 | } else break; |
---|
| 145 | } |
---|
| 146 | |
---|
| 147 | |
---|
| 148 | if ( active[b] == 0 ) --b; |
---|
| 149 | else { |
---|
| 150 | end=false; |
---|
| 151 | |
---|
| 152 | NodeIt w=active[b]; |
---|
| 153 | active[b]=next.get(w); |
---|
| 154 | int lev=level.get(w); |
---|
| 155 | T exc=excess.get(w); |
---|
| 156 | int newlevel=n; //bound on the next level of w |
---|
| 157 | |
---|
| 158 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
---|
| 159 | |
---|
| 160 | if ( flow.get(e) == capacity.get(e) ) continue; |
---|
| 161 | NodeIt v=G.head(e); |
---|
| 162 | //e=wv |
---|
| 163 | |
---|
| 164 | if( lev > level.get(v) ) { |
---|
| 165 | /*Push is allowed now*/ |
---|
| 166 | |
---|
| 167 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
---|
| 168 | int lev_v=level.get(v); |
---|
| 169 | next.set(v,active[lev_v]); |
---|
| 170 | active[lev_v]=v; |
---|
| 171 | } |
---|
| 172 | |
---|
| 173 | T cap=capacity.get(e); |
---|
| 174 | T flo=flow.get(e); |
---|
| 175 | T remcap=cap-flo; |
---|
| 176 | |
---|
| 177 | if ( remcap >= exc ) { |
---|
| 178 | /*A nonsaturating push.*/ |
---|
| 179 | |
---|
| 180 | flow.set(e, flo+exc); |
---|
| 181 | excess.set(v, excess.get(v)+exc); |
---|
| 182 | exc=0; |
---|
| 183 | break; |
---|
| 184 | |
---|
| 185 | } else { |
---|
| 186 | /*A saturating push.*/ |
---|
| 187 | |
---|
| 188 | flow.set(e, cap); |
---|
| 189 | excess.set(v, excess.get(v)+remcap); |
---|
| 190 | exc-=remcap; |
---|
| 191 | } |
---|
| 192 | } else if ( newlevel > level.get(v) ){ |
---|
| 193 | newlevel = level.get(v); |
---|
| 194 | } |
---|
| 195 | |
---|
| 196 | } //for out edges wv |
---|
| 197 | |
---|
| 198 | |
---|
| 199 | if ( exc > 0 ) { |
---|
| 200 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
---|
| 201 | |
---|
| 202 | if( flow.get(e) == 0 ) continue; |
---|
| 203 | NodeIt v=G.tail(e); |
---|
| 204 | //e=vw |
---|
| 205 | |
---|
| 206 | if( lev > level.get(v) ) { |
---|
| 207 | /*Push is allowed now*/ |
---|
| 208 | |
---|
| 209 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
---|
| 210 | int lev_v=level.get(v); |
---|
| 211 | next.set(v,active[lev_v]); |
---|
| 212 | active[lev_v]=v; |
---|
| 213 | } |
---|
| 214 | |
---|
| 215 | T flo=flow.get(e); |
---|
| 216 | |
---|
| 217 | if ( flo >= exc ) { |
---|
| 218 | /*A nonsaturating push.*/ |
---|
| 219 | |
---|
| 220 | flow.set(e, flo-exc); |
---|
| 221 | excess.set(v, excess.get(v)+exc); |
---|
| 222 | exc=0; |
---|
| 223 | break; |
---|
| 224 | } else { |
---|
| 225 | /*A saturating push.*/ |
---|
| 226 | |
---|
| 227 | excess.set(v, excess.get(v)+flo); |
---|
| 228 | exc-=flo; |
---|
| 229 | flow.set(e,0); |
---|
| 230 | } |
---|
| 231 | } else if ( newlevel > level.get(v) ) { |
---|
| 232 | newlevel = level.get(v); |
---|
| 233 | } |
---|
| 234 | } //for in edges vw |
---|
| 235 | |
---|
| 236 | } // if w still has excess after the out edge for cycle |
---|
| 237 | |
---|
| 238 | excess.set(w, exc); |
---|
| 239 | |
---|
| 240 | /* |
---|
| 241 | Relabel |
---|
| 242 | */ |
---|
| 243 | |
---|
| 244 | |
---|
| 245 | if ( exc > 0 ) { |
---|
| 246 | //now 'lev' is the old level of w |
---|
| 247 | |
---|
| 248 | //unlacing starts |
---|
| 249 | NodeIt right_n=right.get(w); |
---|
| 250 | NodeIt left_n=left.get(w); |
---|
| 251 | |
---|
| 252 | if ( right_n != 0 ) { |
---|
| 253 | if ( left_n != 0 ) { |
---|
| 254 | right.set(left_n, right_n); |
---|
| 255 | left.set(right_n, left_n); |
---|
| 256 | } else { |
---|
| 257 | level_list[lev]=right_n; |
---|
| 258 | left.set(right_n, 0); |
---|
| 259 | } |
---|
| 260 | } else { |
---|
| 261 | if ( left_n != 0 ) { |
---|
| 262 | right.set(left_n, 0); |
---|
| 263 | } else { |
---|
| 264 | level_list[lev]=0; |
---|
| 265 | |
---|
| 266 | } |
---|
| 267 | } |
---|
| 268 | //unlacing ends |
---|
| 269 | |
---|
| 270 | //gapping starts |
---|
| 271 | if ( level_list[lev]==0 ) { |
---|
| 272 | |
---|
| 273 | for (int i=lev; i!=k ; ) { |
---|
| 274 | NodeIt v=level_list[++i]; |
---|
| 275 | while ( v != 0 ) { |
---|
| 276 | level.set(v,n); |
---|
| 277 | v=right.get(v); |
---|
| 278 | } |
---|
| 279 | level_list[i]=0; |
---|
| 280 | if ( !what_heur ) active[i]=0; |
---|
| 281 | } |
---|
| 282 | |
---|
| 283 | level.set(w,n); |
---|
| 284 | b=lev-1; |
---|
| 285 | k=b; |
---|
| 286 | //gapping ends |
---|
| 287 | } else { |
---|
| 288 | |
---|
| 289 | if ( newlevel == n ) level.set(w,n); |
---|
| 290 | else { |
---|
| 291 | level.set(w,++newlevel); |
---|
| 292 | next.set(w,active[newlevel]); |
---|
| 293 | active[newlevel]=w; |
---|
| 294 | if ( what_heur ) b=newlevel; |
---|
| 295 | if ( k < newlevel ) ++k; |
---|
| 296 | NodeIt first=level_list[newlevel]; |
---|
| 297 | if ( first != 0 ) left.set(first,w); |
---|
| 298 | right.set(w,first); |
---|
| 299 | left.set(w,0); |
---|
| 300 | level_list[newlevel]=w; |
---|
| 301 | } |
---|
| 302 | } |
---|
| 303 | |
---|
| 304 | |
---|
| 305 | ++relabel; |
---|
| 306 | if ( relabel >= heur ) { |
---|
| 307 | relabel=0; |
---|
| 308 | if ( what_heur ) { |
---|
| 309 | what_heur=0; |
---|
| 310 | heur=heur0; |
---|
| 311 | end=false; |
---|
| 312 | } else { |
---|
| 313 | what_heur=1; |
---|
| 314 | heur=heur1; |
---|
| 315 | b=k; |
---|
| 316 | } |
---|
| 317 | } |
---|
| 318 | |
---|
| 319 | |
---|
| 320 | } // if ( exc > 0 ) |
---|
| 321 | |
---|
| 322 | |
---|
| 323 | } // if stack[b] is nonempty |
---|
| 324 | |
---|
| 325 | } // while(true) |
---|
| 326 | |
---|
| 327 | |
---|
| 328 | |
---|
| 329 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
---|
| 330 | v.valid(); ++v) |
---|
| 331 | if (level.get(v) >= n ) cut.set(v,true); |
---|
| 332 | |
---|
| 333 | value = excess.get(t); |
---|
| 334 | /*Max flow value.*/ |
---|
| 335 | |
---|
| 336 | } //void run() |
---|
| 337 | |
---|
| 338 | |
---|
| 339 | |
---|
| 340 | |
---|
| 341 | T maxFlow() { |
---|
| 342 | return value; |
---|
| 343 | } |
---|
| 344 | |
---|
| 345 | |
---|
| 346 | |
---|
| 347 | CutMap minCut() { |
---|
| 348 | return cut; |
---|
| 349 | } |
---|
| 350 | |
---|
| 351 | |
---|
| 352 | }; |
---|
| 353 | }//namespace |
---|
| 354 | #endif |
---|
| 355 | |
---|
| 356 | |
---|
| 357 | |
---|
| 358 | |
---|