COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/preflow_push_hl.hh @ 30:10a3f2e0928c

Last change on this file since 30:10a3f2e0928c was 30:10a3f2e0928c, checked in by jacint, 17 years ago

is_valid changed to valid

File size: 8.0 KB
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[20]1/*
2preflow_push_hl.hh
3by jacint.
4Runs the highest label variant of the preflow push algorithm with
5running time O(n^2\sqrt(m)).
6
7Member functions:
8
9void run() : runs the algorithm
10
11 The following functions should be used after run() was already run.
12
13T maxflow() : returns the value of a maximum flow
14
15T flowonedge(edge_iterator e) : for a fixed maximum flow x it returns x(e)
16
17edge_property_vector<graph_type, T> allflow() : returns the fixed maximum flow x
18
19node_property_vector<graph_type, bool> mincut() : returns a
20     characteristic vector of a minimum cut. (An empty level
21     in the algorithm gives a minimum cut.)
22*/
23
24#ifndef PREFLOW_PUSH_HL_HH
25#define PREFLOW_PUSH_HL_HH
26
27#include <algorithm>
28#include <vector>
29#include <stack>
30
31#include <marci_graph_traits.hh>
32#include <marci_property_vector.hh>
33#include <reverse_bfs.hh>
34
35namespace marci {
36
37  template <typename graph_type, typename T>
38  class preflow_push_hl {
39   
40    typedef typename graph_traits<graph_type>::node_iterator node_iterator;
41    typedef typename graph_traits<graph_type>::edge_iterator edge_iterator;
42    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;
43    typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;
44    typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator;
45    typedef typename graph_traits<graph_type>::each_edge_iterator each_edge_iterator;
46   
47
48    graph_type& G;
49    node_iterator s;
50    node_iterator t;
51    edge_property_vector<graph_type, T> flow;
52    edge_property_vector<graph_type, T>& capacity;
53    T value;
54    node_property_vector<graph_type, bool> mincutvector;
55
56   
57  public:
58
59    preflow_push_hl(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), mincutvector(_G, true) { }
60
61
62
63
64    /*
65      The run() function runs the highest label preflow-push,
66      running time: O(n^2\sqrt(m))
67    */
68    void run() {
69 
70      node_property_vector<graph_type, int> level(G);         //level of node
71      node_property_vector<graph_type, T> excess(G);          //excess of node
72           
73      int n=number_of(G.first_node());                        //number of nodes
74      int b=n;
75      /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/
76
77      std::vector<std::stack<node_iterator> > stack(2*n-1);    //Stack of the active nodes in level i.
78
79
80
81
82      /*Reverse_bfs from t, to find the starting level.*/
83
84      reverse_bfs<list_graph> bfs(G, t);
85      bfs.run();
[30]86      for(each_node_iterator v=G.first_node(); v.valid(); ++v) {
[20]87        level.put(v, bfs.dist(v));
88        //std::cout << "the level of " << v << " is " << bfs.dist(v);
89      }
90
91      /*The level of s is fixed to n*/
92      level.put(s,n);
93
94
95
96
97
98      /* Starting flow. It is everywhere 0 at the moment. */
99     
[30]100      for(out_edge_iterator i=G.first_out_edge(s); i.valid(); ++i)
[20]101        {
102          node_iterator w=G.head(i);
103          flow.put(i, capacity.get(i));
104          stack[bfs.dist(w)].push(w);
105          excess.put(w, capacity.get(i));
106        }
107
108
109      /*
110         End of preprocessing
111      */
112
113
114
115      /*
116        Push/relabel on the highest level active nodes.
117      */
118       
119      /*While there exists active node.*/
120      while (b) {
121
122        /*We decrease the bound if there is no active node of level b.*/
123        if (stack[b].empty()) {
124          --b;
125        } else {
126
127          node_iterator w=stack[b].top();    //w is the highest label active node.
128          stack[b].pop();                    //We delete w from the stack.
129       
130          int newlevel=2*n-2;                   //In newlevel we maintain the next level of w.
131       
[30]132          for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) {
[20]133            node_iterator v=G.head(e);
134            /*e is the edge wv.*/
135
136            if (flow.get(e)<capacity.get(e)) {             
137              /*e is an edge of the residual graph */
138
139              if(level.get(w)==level.get(v)+1) {     
140                /*Push is allowed now*/
141
142                if (capacity.get(e)-flow.get(e) > excess.get(w)) {       
143                  /*A nonsaturating push.*/
144                 
145                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
146                  /*v becomes active.*/
147                 
148                  flow.put(e, flow.get(e)+excess.get(w));
149                  excess.put(v, excess.get(v)+excess.get(w));
150                  excess.put(w,0);
151                  //std::cout << w << " " << v <<" elore elen nonsat pump "  << std::endl;
152                  break;
153                } else {
154                  /*A saturating push.*/
155
156                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
157                  /*v becomes active.*/
158
159                  excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e));
160                  excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e));
161                  flow.put(e, capacity.get(e));
162                  //std::cout << w<<" " <<v<<" elore elen sat pump "   << std::endl;
163                  if (excess.get(w)==0) break;
164                  /*If w is not active any more, then we go on to the next node.*/
165                 
166                } // if (capacity.get(e)-flow.get(e) > excess.get(w))
167              } // if(level.get(w)==level.get(v)+1)
168           
169              else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
170           
171            } //if (flow.get(e)<capacity.get(e))
172         
[30]173          } //for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e)
[20]174         
175
176
[30]177          for(in_edge_iterator e=G.first_in_edge(w); e.valid(); ++e) {
[20]178            node_iterator v=G.tail(e);
179            /*e is the edge vw.*/
180
181            if (excess.get(w)==0) break;
182            /*It may happen, that w became inactive in the first for cycle.*/           
183            if(flow.get(e)>0) {             
184              /*e is an edge of the residual graph */
185
186              if(level.get(w)==level.get(v)+1) { 
187                /*Push is allowed now*/
188               
189                if (flow.get(e) > excess.get(w)) {
190                  /*A nonsaturating push.*/
191                 
192                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
193                  /*v becomes active.*/
194
195                  flow.put(e, flow.get(e)-excess.get(w));
196                  excess.put(v, excess.get(v)+excess.get(w));
197                  excess.put(w,0);
198                  //std::cout << v << " " << w << " vissza elen nonsat pump "     << std::endl;
199                  break;
200                } else {                                               
201                  /*A saturating push.*/
202                 
203                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
204                  /*v becomes active.*/
205                 
206                  excess.put(v, excess.get(v)+flow.get(e));
207                  excess.put(w, excess.get(w)-flow.get(e));
208                  flow.put(e,0);
209                  //std::cout << v <<" " << w << " vissza elen sat pump "     << std::endl;
210                  if (excess.get(w)==0) { break;}
211                } //if (flow.get(e) > excess.get(v))
212              } //if(level.get(w)==level.get(v)+1)
213             
214              else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
215             
216
217            } //if (flow.get(e)>0)
218
219          } //for
220
221
222          if (excess.get(w)>0) {
223            level.put(w,++newlevel);
224            stack[newlevel].push(w);
225            b=newlevel;
226            //std::cout << "The new level of " << w << " is "<< newlevel <<std::endl;
227          }
228
229
230        } //else
231       
232      } //while(b)
233
234      value = excess.get(t);
235      /*Max flow value.*/
236
237
238
239
240    } //void run()
241
242
243
244
245
246    /*
247      Returns the maximum value of a flow.
248     */
249
250    T maxflow() {
251      return value;
252    }
253
254
255
256    /*
257      For the maximum flow x found by the algorithm, it returns the flow value on edge e, i.e. x(e).
258    */
259
260    T flowonedge(edge_iterator e) {
261      return flow.get(e);
262    }
263
264
265
266    /*
267      Returns the maximum flow x found by the algorithm.
268    */
269
270    edge_property_vector<graph_type, T> allflow() {
271      return flow;
272    }
273
274
275
276    /*
277      Returns a minimum cut by using a reverse bfs from t in the residual graph.
278    */
279   
280    node_property_vector<graph_type, bool> mincut() {
281   
282      std::queue<node_iterator> queue;
283     
284      mincutvector.put(t,false);     
285      queue.push(t);
286
287      while (!queue.empty()) {
288        node_iterator w=queue.front();
289        queue.pop();
290
[30]291        for(in_edge_iterator e=G.first_in_edge(w) ; e.valid(); ++e) {
[20]292          node_iterator v=G.tail(e);
293          if (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) {
294            queue.push(v);
295            mincutvector.put(v, false);
296          }
297        } // for
298
[30]299        for(out_edge_iterator e=G.first_out_edge(w) ; e.valid(); ++e) {
[20]300          node_iterator v=G.head(e);
301          if (mincutvector.get(v) && flow.get(e) > 0 ) {
302            queue.push(v);
303            mincutvector.put(v, false);
304          }
305        } // for
306
307      }
308
309      return mincutvector;
310   
311    }
312
313
314  };
315}//namespace marci
316#endif
317
318
319
320
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