COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/preflow_push_max_flow.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: 7.9 KB
Line 
1/*
2preflow_push_max_flow_hh
3by jacint.
4Runs a preflow push algorithm with the modification,
5that we do not push on nodes with level at least n.
6Moreover, if a level gets empty, we put all nodes above that
7level to level n. Hence, in the end, we arrive at a maximum preflow
8with value of a max flow value. An empty level gives a minimum cut.
9
10Member functions:
11
12void run() : runs the algorithm
13
14  The following functions should be used after run() was already run.
15
16T maxflow() : returns the value of a maximum flow
17
18node_property_vector<graph_type, bool> mincut(): returns a
19     characteristic vector of a minimum cut.
20*/
21
22#ifndef PREFLOW_PUSH_MAX_FLOW_HH
23#define PREFLOW_PUSH_MAX_FLOW_HH
24
25#include <algorithm>
26#include <vector>
27#include <stack>
28
29#include <marci_list_graph.hh>
30#include <marci_graph_traits.hh>
31#include <marci_property_vector.hh>
32#include <reverse_bfs.hh>
33
34
35namespace marci {
36
37  template <typename graph_type, typename T>
38  class preflow_push_max_flow {
39   
40    typedef typename graph_traits<graph_type>::node_iterator node_iterator;
41    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;
42    typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;
43    typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator;
44   
45    graph_type& G;
46    node_iterator s;
47    node_iterator t;
48    edge_property_vector<graph_type, T>& capacity;
49    T value;
50    node_property_vector<graph_type, bool> mincutvector;   
51
52
53     
54  public:
55       
56    preflow_push_max_flow(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { }
57
58
59    /*
60      The run() function runs a modified version of the highest label preflow-push, which only
61      finds a maximum preflow, hence giving the value of a maximum flow.
62    */
63    void run() {
64 
65      edge_property_vector<graph_type, T> flow(G, 0);         //the flow value, 0 everywhere 
66      node_property_vector<graph_type, int> level(G);         //level of node
67      node_property_vector<graph_type, T> excess(G);          //excess of node
68           
69      int n=number_of(G.first_node());                        //number of nodes
70      int b=n-2;
71      /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/
72     
73      std::vector<int> numb(n);                                //The number of nodes on level i < n.
74
75      std::vector<std::stack<node_iterator> > stack(2*n-1);    //Stack of the active nodes in level i.
76
77
78
79      /*Reverse_bfs from t, to find the starting level.*/
80
81      reverse_bfs<list_graph> bfs(G, t);
82      bfs.run();
83      for(each_node_iterator v=G.first_node(); v.valid(); ++v)
84        {
85          int dist=bfs.dist(v);
86          level.put(v, dist);
87          ++numb[dist];
88        }
89
90      /*The level of s is fixed to n*/
91      level.put(s,n);
92
93
94      /* Starting flow. It is everywhere 0 at the moment. */
95     
96      for(out_edge_iterator i=G.first_out_edge(s); i.valid(); ++i)
97        {
98          node_iterator w=G.head(i);
99          flow.put(i, capacity.get(i));
100          stack[bfs.dist(w)].push(w);
101          excess.put(w, capacity.get(i));
102        }
103
104
105      /*
106         End of preprocessing
107      */
108
109
110
111
112      /*
113        Push/relabel on the highest level active nodes.
114      */
115       
116      /*While there exists an active node.*/
117      while (b) {
118
119        /*We decrease the bound if there is no active node of level b.*/
120        if (stack[b].empty()) {
121          --b;
122        } else {
123
124          node_iterator w=stack[b].top();    //w is the highest label active node.
125          stack[b].pop();                    //We delete w from the stack.
126       
127          int newlevel=2*n-2;                //In newlevel we maintain the next level of w.
128       
129          for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) {
130            node_iterator v=G.head(e);
131            /*e is the edge wv.*/
132
133            if (flow.get(e)<capacity.get(e)) {             
134              /*e is an edge of the residual graph */
135
136              if(level.get(w)==level.get(v)+1) {     
137                /*Push is allowed now*/
138
139                if (capacity.get(e)-flow.get(e) > excess.get(w)) {       
140                  /*A nonsaturating push.*/
141                 
142                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
143                  /*v becomes active.*/
144                 
145                  flow.put(e, flow.get(e)+excess.get(w));
146                  excess.put(v, excess.get(v)+excess.get(w));
147                  excess.put(w,0);
148                  //std::cout << w << " " << v <<" elore elen nonsat pump "  << std::endl;
149                  break;
150                } else {
151                  /*A saturating push.*/
152
153                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
154                  /*v becomes active.*/
155
156                  excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e));
157                  excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e));
158                  flow.put(e, capacity.get(e));
159                  //std::cout << w <<" " << v <<" elore elen sat pump "   << std::endl;
160                  if (excess.get(w)==0) break;
161                  /*If w is not active any more, then we go on to the next node.*/
162                 
163                } // if (capacity.get(e)-flow.get(e) > excess.get(w))
164              } // if (level.get(w)==level.get(v)+1)
165           
166              else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
167           
168            } //if (flow.get(e)<capacity.get(e))
169         
170          } //for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e)
171         
172
173
174          for(in_edge_iterator e=G.first_in_edge(w); e.valid(); ++e) {
175            node_iterator v=G.tail(e);
176            /*e is the edge vw.*/
177
178            if (excess.get(w)==0) break;
179            /*It may happen, that w became inactive in the first 'for' cycle.*/         
180 
181            if(flow.get(e)>0) {             
182              /*e is an edge of the residual graph */
183
184              if(level.get(w)==level.get(v)+1) { 
185                /*Push is allowed now*/
186               
187                if (flow.get(e) > excess.get(w)) {
188                  /*A nonsaturating push.*/
189                 
190                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
191                  /*v becomes active.*/
192
193                  flow.put(e, flow.get(e)-excess.get(w));
194                  excess.put(v, excess.get(v)+excess.get(w));
195                  excess.put(w,0);
196                  //std::cout << v << " " << w << " vissza elen nonsat pump "     << std::endl;
197                  break;
198                } else {                                               
199                  /*A saturating push.*/
200                 
201                  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v);
202                  /*v becomes active.*/
203                 
204                  flow.put(e,0);
205                  excess.put(v, excess.get(v)+flow.get(e));
206                  excess.put(w, excess.get(w)-flow.get(e));
207                  //std::cout << v <<" " << w << " vissza elen sat pump "     << std::endl;
208                  if (excess.get(w)==0) { break;}
209                } //if (flow.get(e) > excess.get(v))
210              } //if(level.get(w)==level.get(v)+1)
211             
212              else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
213              //std::cout << "Leveldecrease of node " << w << " to " << newlevel << std::endl;
214
215            } //if (flow.get(e)>0)
216
217          } //for in-edge
218
219
220
221
222          /*
223            Relabel
224          */
225          if (excess.get(w)>0) {
226            /*Now newlevel <= n*/
227
228            int l=level.get(w);         //l is the old level of w.
229            --numb[l];
230           
231            if (newlevel == n) {
232              level.put(w,n);
233             
234            } else {
235             
236              if (numb[l]) {
237                /*If the level of w remains nonempty.*/
238               
239                level.put(w,++newlevel);
240                ++numb[newlevel];
241                stack[newlevel].push(w);
242                b=newlevel;
243              } else {
244                /*If the level of w gets empty.*/
245             
246                for (each_node_iterator v=G.first_node() ; v.valid() ; ++v) {
247                  if (level.get(v) >= l ) {
248                    level.put(v,n); 
249                  }
250                }
251               
252                for (int i=l+1 ; i!=n ; ++i) numb[i]=0;
253              } //if (numb[l])
254       
255            } // if (newlevel = n)
256         
257          } // if (excess.get(w)>0)
258
259
260        } //else
261       
262      } //while(b)
263
264      value=excess.get(t);
265      /*Max flow value.*/
266     
267
268
269      /*
270        We find an empty level, e. The nodes above this level give
271        a minimum cut.
272      */
273     
274      int e=1;
275     
276      while(e) {
277        if(numb[e]) ++e;
278        else break;
279      }
280      for (each_node_iterator v=G.first_node(); v.valid(); ++v) {
281        if (level.get(v) > e) mincutvector.put(v, true);
282      }
283     
284
285    } // void run()
286
287
288
289    /*
290      Returns the maximum value of a flow.
291     */
292
293    T maxflow() {
294      return value;
295    }
296
297
298
299    /*
300      Returns a minimum cut.
301    */
302   
303    node_property_vector<graph_type, bool> mincut() {
304      return mincutvector;
305    }
306   
307
308  };
309}//namespace marci
310#endif
311
312
313
314
315
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