1 | /* -*- C++ -*- |
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2 | * lemon/preflow_matching.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_CIRCULATION_H |
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18 | #define LEMON_CIRCULATION_H |
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19 | |
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20 | #include <lemon/graph_utils.h> |
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21 | #include <iostream> |
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22 | #include <queue> |
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23 | #include <lemon/tolerance.h> |
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24 | #include <lemon/elevator.h> |
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25 | |
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26 | ///\ingroup max_flow |
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27 | ///\file |
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28 | ///\brief Push-prelabel algorithm for finding a feasible circulation. |
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29 | /// |
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30 | namespace lemon { |
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31 | |
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32 | ///Preflow algorithm for the Network Circulation Problem. |
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33 | |
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34 | ///\ingroup flowalgs |
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35 | ///This class implements a preflow algorithm |
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36 | ///for the Network Circulation Problem. |
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37 | ///The exact formulation of this problem is the following. |
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38 | /// \f[\sum_{e\in\rho(v)}x(e)-\sum_{e\in\delta(v)}x(e)\leq delta(v)\quad \forall v\in V \f] |
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39 | /// \f[ lo(e)\leq x(e) \leq up(e) \quad \forall e\in E \f] |
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40 | /// |
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41 | template<class Graph, |
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42 | class Value, |
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43 | class FlowMap=typename Graph::template EdgeMap<Value>, |
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44 | class LCapMap=typename Graph::template EdgeMap<Value>, |
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45 | class UCapMap=LCapMap, |
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46 | class DeltaMap=typename Graph::template NodeMap<Value> |
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47 | > |
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48 | class Circulation { |
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49 | typedef typename Graph::Node Node; |
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50 | typedef typename Graph::NodeIt NodeIt; |
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51 | typedef typename Graph::Edge Edge; |
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52 | typedef typename Graph::EdgeIt EdgeIt; |
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53 | typedef typename Graph::InEdgeIt InEdgeIt; |
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54 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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55 | |
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56 | |
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57 | const Graph &_g; |
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58 | int _node_num; |
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59 | |
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60 | const LCapMap &_lo; |
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61 | const UCapMap &_up; |
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62 | const DeltaMap &_delta; |
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63 | FlowMap &_x; |
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64 | Tolerance<Value> _tol; |
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65 | Elevator<Graph,typename Graph::Node> _levels; |
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66 | typename Graph::template NodeMap<Value> _excess; |
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67 | |
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68 | public: |
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69 | ///\e |
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70 | Circulation(const Graph &g,const LCapMap &lo,const UCapMap &up, |
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71 | const DeltaMap &delta,FlowMap &x) : |
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72 | _g(g), |
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73 | _node_num(countNodes(g)), |
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74 | _lo(lo),_up(up),_delta(delta),_x(x), |
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75 | _levels(g,_node_num), |
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76 | _excess(g) |
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77 | { |
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78 | } |
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79 | |
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80 | private: |
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81 | |
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82 | void addExcess(Node n,Value v) |
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83 | { |
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84 | if(_tol.positive(_excess[n]+=v)) |
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85 | { |
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86 | if(!_levels.active(n)) _levels.activate(n); |
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87 | } |
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88 | else if(_levels.active(n)) _levels.deactivate(n); |
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89 | } |
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90 | |
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91 | void init() |
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92 | { |
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93 | |
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94 | _x=_lo; |
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95 | |
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96 | for(NodeIt n(_g);n!=INVALID;++n) _excess[n]=-_delta[n]; |
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97 | |
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98 | for(EdgeIt e(_g);e!=INVALID;++e) |
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99 | { |
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100 | _excess[_g.target(e)]+=_x[e]; |
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101 | _excess[_g.source(e)]-=_x[e]; |
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102 | } |
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103 | |
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104 | _levels.initStart(); |
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105 | for(NodeIt n(_g);n!=INVALID;++n) |
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106 | _levels.initAddItem(n); |
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107 | _levels.initFinish(); |
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108 | for(NodeIt n(_g);n!=INVALID;++n) |
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109 | if(_tol.positive(_excess[n])) |
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110 | _levels.activate(n); |
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111 | } |
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112 | |
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113 | public: |
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114 | ///Check if \c x is a feasible circulation |
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115 | template<class FT> |
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116 | bool checkX(FT &x) { |
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117 | for(EdgeIt e(_g);e!=INVALID;++e) |
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118 | if(x[e]<_lo[e]||x[e]>_up[e]) return false; |
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119 | for(NodeIt n(_g);n!=INVALID;++n) |
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120 | { |
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121 | Value dif=_delta[n]; |
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122 | for(InEdgeIt e(_g,n);e!=INVALID;++e) dif-=x[e]; |
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123 | for(OutEdgeIt e(_g,n);e!=INVALID;++e) dif+=x[e]; |
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124 | if(_tol.negative(dif)) return false; |
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125 | } |
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126 | return true; |
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127 | }; |
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128 | ///Check if the default \c x is a feasible circulation |
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129 | bool checkX() { return checkX(_x); } |
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130 | |
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131 | ///Chech if \c bar is a real barrier |
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132 | |
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133 | ///Chech if \c bar is a real barrier |
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134 | ///\sa barrier() |
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135 | template<class GT> |
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136 | bool checkBarrier(GT &bar) |
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137 | { |
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138 | Value delta=0; |
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139 | for(NodeIt n(_g);n!=INVALID;++n) |
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140 | if(bar[n]) |
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141 | delta+=_delta[n]; |
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142 | for(EdgeIt e(_g);e!=INVALID;++e) |
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143 | { |
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144 | Node s=_g.source(e); |
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145 | Node t=_g.target(e); |
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146 | if(bar[s]&&!bar[t]) delta+=_up[e]; |
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147 | else if(bar[t]&&!bar[s]) delta-=_lo[e]; |
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148 | } |
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149 | return _tol.negative(delta); |
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150 | } |
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151 | ///Chech whether or not the last execution provides a barrier |
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152 | |
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153 | ///Chech whether or not the last execution provides a barrier |
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154 | ///\sa barrier() |
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155 | bool checkBarrier() |
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156 | { |
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157 | typename Graph:: template NodeMap<bool> bar(_g); |
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158 | barrier(bar); |
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159 | return checkBarrier(bar); |
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160 | } |
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161 | ///Run the algorithm |
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162 | |
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163 | ///This function runs the algorithm. |
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164 | ///\return This function returns -1 if it found a feasible circulation. |
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165 | /// nonnegative values (including 0) mean that no feasible solution is |
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166 | /// found. In this case the return value means an "empty level". |
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167 | /// |
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168 | ///\sa barrier() |
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169 | int run() |
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170 | { |
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171 | init(); |
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172 | |
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173 | #ifdef LEMON_CIRCULATION_DEBUG |
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174 | for(NodeIt n(_g);n!=INVALID;++n) |
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175 | std::cerr<< _levels[n] << ' '; |
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176 | std::cerr << std::endl; |
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177 | #endif |
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178 | Node act; |
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179 | Node bact=INVALID; |
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180 | Node last_activated=INVALID; |
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181 | while((act=_levels.highestActive())!=INVALID) { |
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182 | int actlevel=_levels[act]; |
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183 | int tlevel; |
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184 | int mlevel=_node_num; |
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185 | Value exc=_excess[act]; |
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186 | Value fc; |
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187 | |
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188 | #ifdef LEMON_CIRCULATION_DEBUG |
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189 | for(NodeIt n(_g);n!=INVALID;++n) |
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190 | std::cerr<< _levels[n] << ' '; |
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191 | std::cerr << std::endl; |
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192 | std::cerr << "Process node " << _g.id(act) |
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193 | << " on level " << actlevel |
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194 | << " with excess " << exc |
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195 | << std::endl; |
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196 | #endif |
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197 | for(OutEdgeIt e(_g,act);e!=INVALID; ++e) |
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198 | if((fc=_up[e]-_x[e])>0) |
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199 | if((tlevel=_levels[_g.target(e)])<actlevel) |
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200 | if(fc<=exc) { |
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201 | _x[e]=_up[e]; |
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202 | addExcess(_g.target(e),fc); |
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203 | exc-=fc; |
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204 | #ifdef LEMON_CIRCULATION_DEBUG |
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205 | std::cerr << " Push " << fc |
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206 | << " toward " << _g.id(_g.target(e)) << std::endl; |
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207 | #endif |
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208 | } |
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209 | else { |
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210 | _x[e]+=exc; |
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211 | addExcess(_g.target(e),exc); |
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212 | //exc=0; |
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213 | _excess[act]=0; |
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214 | _levels.deactivate(act); |
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215 | #ifdef LEMON_CIRCULATION_DEBUG |
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216 | std::cerr << " Push " << exc |
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217 | << " toward " << _g.id(_g.target(e)) << std::endl; |
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218 | std::cerr << " Deactivate\n"; |
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219 | #endif |
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220 | goto next_l; |
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221 | } |
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222 | else if(tlevel<mlevel) mlevel=tlevel; |
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223 | |
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224 | for(InEdgeIt e(_g,act);e!=INVALID; ++e) |
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225 | if((fc=_x[e]-_lo[e])>0) |
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226 | if((tlevel=_levels[_g.source(e)])<actlevel) |
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227 | if(fc<=exc) { |
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228 | _x[e]=_lo[e]; |
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229 | addExcess(_g.source(e),fc); |
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230 | exc-=fc; |
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231 | #ifdef LEMON_CIRCULATION_DEBUG |
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232 | std::cerr << " Push " << fc |
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233 | << " toward " << _g.id(_g.source(e)) << std::endl; |
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234 | #endif |
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235 | } |
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236 | else { |
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237 | _x[e]-=exc; |
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238 | addExcess(_g.source(e),exc); |
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239 | //exc=0; |
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240 | _excess[act]=0; |
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241 | _levels.deactivate(act); |
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242 | #ifdef LEMON_CIRCULATION_DEBUG |
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243 | std::cerr << " Push " << exc |
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244 | << " toward " << _g.id(_g.source(e)) << std::endl; |
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245 | std::cerr << " Deactivate\n"; |
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246 | #endif |
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247 | goto next_l; |
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248 | } |
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249 | else if(tlevel<mlevel) mlevel=tlevel; |
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250 | |
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251 | _excess[act]=exc; |
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252 | if(!_tol.positive(exc)) _levels.deactivate(act); |
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253 | else if(mlevel==_node_num) { |
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254 | _levels.liftHighestActiveTo(_node_num); |
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255 | #ifdef LEMON_CIRCULATION_DEBUG |
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256 | std::cerr << " Lift to level " << _node_num << std::endl; |
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257 | #endif |
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258 | return _levels.onLevel(_node_num-1)==0?_node_num-1:actlevel; |
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259 | } |
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260 | else { |
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261 | _levels.liftHighestActiveTo(mlevel+1); |
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262 | #ifdef LEMON_CIRCULATION_DEBUG |
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263 | std::cerr << " Lift to level " << mlevel+1 << std::endl; |
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264 | #endif |
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265 | if(_levels.onLevel(actlevel)==0) |
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266 | return actlevel; |
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267 | } |
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268 | next_l: |
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269 | ; |
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270 | } |
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271 | #ifdef LEMON_CIRCULATION_DEBUG |
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272 | std::cerr << "Feasible flow found.\n"; |
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273 | #endif |
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274 | return -1; |
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275 | } |
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276 | |
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277 | ///Return a barrier |
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278 | |
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279 | ///Barrier is a set \e B of nodes for which |
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280 | /// \f[ \sum_{v\in B}delta(v)<\sum_{e\in\rho(B)}lo(e)-\sum_{e\in\delta(B)}up(e) \f] |
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281 | ///holds. The existence of a set with this property prooves that a feasible |
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282 | ///flow cannot exists. |
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283 | ///\pre The run() must have been executed, and its return value was -1. |
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284 | ///\sa checkBarrier() |
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285 | ///\sa run() |
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286 | template<class GT> |
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287 | void barrier(GT &bar,int empty_level=-1) |
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288 | { |
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289 | if(empty_level==-1) |
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290 | for(empty_level=0;_levels.onLevel(empty_level);empty_level++) ; |
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291 | for(NodeIt n(_g);n!=INVALID;++n) |
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292 | bar[n] = _levels[n]>empty_level; |
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293 | } |
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294 | |
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295 | }; |
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296 | |
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297 | } |
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298 | |
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299 | #endif |
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