1 // -*- C++ -*- |
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2 #ifndef LEMON_MAX_FLOW_H |
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3 #define LEMON_MAX_FLOW_H |
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4 |
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5 ///\ingroup galgs |
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6 ///\file |
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7 ///\brief Maximum flow algorithm. |
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8 |
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9 #define H0 20 |
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10 #define H1 1 |
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11 |
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12 #include <vector> |
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13 #include <queue> |
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14 #include <stack> |
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15 |
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16 #include <graph_wrapper.h> |
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17 #include <bfs_iterator.h> |
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18 #include <invalid.h> |
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19 #include <maps.h> |
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20 #include <for_each_macros.h> |
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21 |
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22 /// \file |
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23 /// \brief Dimacs file format reader. |
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24 |
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25 namespace lemon { |
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26 |
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27 /// \addtogroup galgs |
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28 /// @{ |
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29 |
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30 ///Maximum flow algorithms class. |
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31 |
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32 ///This class provides various algorithms for finding a flow of |
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33 ///maximum value in a directed graph. The \e source node, the \e |
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34 ///target node, the \e capacity of the edges and the \e starting \e |
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35 ///flow value of the edges can be passed to the algorithm by the |
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36 ///constructor. It is possible to change these quantities using the |
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37 ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
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38 ///\ref resetFlow. Before any subsequent runs of any algorithm of |
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39 ///the class \ref resetFlow should be called, otherwise it will |
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40 ///start from a maximum flow. |
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41 |
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42 ///After running an algorithm of the class, the maximum value of a |
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43 ///value can be obtained by calling \ref flowValue(). The minimum |
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44 ///value cut can be written into a \c node map of \c bools by |
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45 ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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46 ///the inclusionwise minimum and maximum of the minimum value |
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47 ///cuts, resp.) |
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48 |
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49 ///\param Graph The undirected graph type the algorithm runs on. |
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50 ///\param Num The number type of the capacities and the flow values. |
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51 ///\param The type of the capacity map. |
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52 ///\param The type of the flow map. |
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53 |
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54 ///\author Marton Makai, Jacint Szabo |
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55 template <typename Graph, typename Num, |
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56 typename CapMap=typename Graph::template EdgeMap<Num>, |
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57 typename FlowMap=typename Graph::template EdgeMap<Num> > |
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58 class MaxFlow { |
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59 |
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60 typedef typename Graph::Node Node; |
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61 typedef typename Graph::NodeIt NodeIt; |
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62 typedef typename Graph::OutEdgeIt OutEdgeIt; |
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63 typedef typename Graph::InEdgeIt InEdgeIt; |
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64 |
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65 typedef typename std::vector<std::stack<Node> > VecStack; |
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66 typedef typename Graph::template NodeMap<Node> NNMap; |
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67 typedef typename std::vector<Node> VecNode; |
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68 |
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69 typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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70 typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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71 typedef typename ResGW::Edge ResGWEdge; |
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72 //typedef typename ResGW::template NodeMap<bool> ReachedMap; //fixme |
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73 typedef typename Graph::template NodeMap<int> ReachedMap; |
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74 |
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75 const Graph* g; |
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76 Node s; |
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77 Node t; |
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78 const CapMap* capacity; |
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79 FlowMap* flow; |
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80 int n; //the number of nodes of G |
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81 |
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82 //level works as a bool map in augmenting path algorithms and is |
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83 //used by bfs for storing reached information. In preflow, it |
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84 //shows the levels of nodes. |
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85 ReachedMap level; |
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86 |
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87 //excess is needed only in preflow |
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88 typename Graph::template NodeMap<Num> excess; |
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89 |
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90 |
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91 //fixme |
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92 // protected: |
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93 // MaxFlow() { } |
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94 // void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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95 // FlowMap& _flow) |
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96 // { |
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97 // g=&_G; |
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98 // s=_s; |
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99 // t=_t; |
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100 // capacity=&_capacity; |
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101 // flow=&_flow; |
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102 // n=_G.nodeNum; |
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103 // level.set (_G); //kellene vmi ilyesmi fv |
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104 // excess(_G,0); //itt is |
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105 // } |
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106 |
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107 public: |
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108 |
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109 ///Indicates the property of the starting flow. |
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110 |
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111 ///Indicates the property of the starting flow. The meanings: |
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112 ///- \c ZERO_FLOW: constant zero flow |
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113 ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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114 ///the sum of the out-flows in every node except the source and |
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115 ///the target. |
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116 ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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117 ///least the sum of the out-flows in every node except the source. |
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118 enum flowEnum{ |
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119 ZERO_FLOW=0, |
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120 GEN_FLOW=1, |
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121 PRE_FLOW=2 |
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122 }; |
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123 |
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124 MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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125 FlowMap& _flow) : |
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126 g(&_G), s(_s), t(_t), capacity(&_capacity), |
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127 flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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128 |
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129 ///Runs a maximum flow algorithm. |
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130 |
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131 ///Runs a preflow algorithm, which is the fastest maximum flow |
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132 ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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133 ///\pre The starting flow must be a |
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134 /// - constant zero flow if \c fe is \c ZERO_FLOW, |
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135 /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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136 /// - an arbitary preflow if \c fe is \c PRE_FLOW. |
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137 void run( flowEnum fe=ZERO_FLOW ) { |
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138 preflow(fe); |
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139 } |
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140 |
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141 ///Runs a preflow algorithm. |
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142 |
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143 ///Runs a preflow algorithm. The preflow algorithms provide the |
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144 ///fastest way to compute a maximum flow in a directed graph. |
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145 ///\pre The starting flow must be a |
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146 /// - constant zero flow if \c fe is \c ZERO_FLOW, |
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147 /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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148 /// - an arbitary preflow if \c fe is \c PRE_FLOW. |
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149 void preflow(flowEnum fe) { |
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150 preflowPhase1(fe); |
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151 preflowPhase2(); |
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152 } |
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153 // Heuristics: |
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154 // 2 phase |
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155 // gap |
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156 // list 'level_list' on the nodes on level i implemented by hand |
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157 // stack 'active' on the active nodes on level i |
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158 // runs heuristic 'highest label' for H1*n relabels |
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159 // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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160 // Parameters H0 and H1 are initialized to 20 and 1. |
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161 |
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162 ///Runs the first phase of the preflow algorithm. |
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163 |
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164 ///The preflow algorithm consists of two phases, this method runs the |
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165 ///first phase. After the first phase the maximum flow value and a |
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166 ///minimum value cut can already be computed, though a maximum flow |
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167 ///is net yet obtained. So after calling this method \ref flowValue |
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168 ///and \ref actMinCut gives proper results. |
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169 ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
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170 ///give minimum value cuts unless calling \ref preflowPhase2. |
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171 ///\pre The starting flow must be a |
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172 /// - constant zero flow if \c fe is \c ZERO_FLOW, |
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173 /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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174 /// - an arbitary preflow if \c fe is \c PRE_FLOW. |
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175 void preflowPhase1( flowEnum fe ); |
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176 |
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177 ///Runs the second phase of the preflow algorithm. |
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178 |
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179 ///The preflow algorithm consists of two phases, this method runs |
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180 ///the second phase. After calling \ref preflowPhase1 and then |
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181 ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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182 ///\ref minMinCut and \ref maxMinCut give proper results. |
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183 ///\pre \ref preflowPhase1 must be called before. |
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184 void preflowPhase2(); |
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185 |
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186 /// Starting from a flow, this method searches for an augmenting path |
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187 /// according to the Edmonds-Karp algorithm |
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188 /// and augments the flow on if any. |
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189 /// The return value shows if the augmentation was successful. |
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190 bool augmentOnShortestPath(); |
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191 |
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192 /// Starting from a flow, this method searches for an augmenting blockin |
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193 /// flow according to Dinits' algorithm and augments the flow on if any. |
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194 /// The blocking flow is computed in a physically constructed |
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195 /// residual graph of type \c Mutablegraph. |
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196 /// The return value show sif the augmentation was succesful. |
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197 template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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198 |
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199 /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
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200 /// residual graph is not constructed physically. |
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201 /// The return value shows if the augmentation was succesful. |
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202 bool augmentOnBlockingFlow2(); |
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203 |
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204 /// Returns the actual flow value. |
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205 /// More precisely, it returns the negative excess of s, thus |
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206 /// this works also for preflows. |
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207 ///Can be called already after \ref preflowPhase1. |
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208 |
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209 Num flowValue() { |
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210 Num a=0; |
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211 FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e]; |
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212 FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e]; |
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213 return a; |
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214 //marci figyu: excess[t] epp ezt adja preflow 0. fazisa utan |
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215 } |
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216 |
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217 ///Returns a minimum value cut after calling \ref preflowPhase1. |
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218 |
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219 ///After the first phase of the preflow algorithm the maximum flow |
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220 ///value and a minimum value cut can already be computed. This |
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221 ///method can be called after running \ref preflowPhase1 for |
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222 ///obtaining a minimum value cut. |
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223 ///\warning: Gives proper result only right after calling \ref |
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224 ///preflowPhase1. |
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225 ///\todo We have to make some status variable which shows the actual state |
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226 /// of the class. This enables us to determine which methods are valid |
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227 /// for MinCut computation |
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228 template<typename _CutMap> |
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229 void actMinCut(_CutMap& M) { |
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230 NodeIt v; |
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231 for(g->first(v); g->valid(v); g->next(v)) { |
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232 if ( level[v] < n ) { |
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233 M.set(v,false); |
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234 } else { |
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235 M.set(v,true); |
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236 } |
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237 } |
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238 } |
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239 |
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240 ///Returns the inclusionwise minimum of the minimum value cuts. |
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241 |
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242 ///Sets \c M to the characteristic vector of the minimum value cut |
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243 ///which is inclusionwise minimum. It is computed by processing |
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244 ///a bfs from the source node \c s in the residual graph. |
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245 ///\pre M should be a node map of bools initialized to false. |
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246 ///\pre \c flow must be a maximum flow. |
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247 template<typename _CutMap> |
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248 void minMinCut(_CutMap& M) { |
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249 |
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250 std::queue<Node> queue; |
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251 |
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252 M.set(s,true); |
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253 queue.push(s); |
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254 |
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255 while (!queue.empty()) { |
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256 Node w=queue.front(); |
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257 queue.pop(); |
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258 |
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259 OutEdgeIt e; |
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260 for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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261 Node v=g->target(e); |
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262 if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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263 queue.push(v); |
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264 M.set(v, true); |
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265 } |
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266 } |
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267 |
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268 InEdgeIt f; |
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269 for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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270 Node v=g->source(f); |
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271 if (!M[v] && (*flow)[f] > 0 ) { |
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272 queue.push(v); |
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273 M.set(v, true); |
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274 } |
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275 } |
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276 } |
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277 } |
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278 |
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279 |
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280 ///Returns the inclusionwise maximum of the minimum value cuts. |
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281 |
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282 ///Sets \c M to the characteristic vector of the minimum value cut |
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283 ///which is inclusionwise maximum. It is computed by processing a |
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284 ///backward bfs from the target node \c t in the residual graph. |
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285 ///\pre M should be a node map of bools initialized to false. |
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286 ///\pre \c flow must be a maximum flow. |
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287 template<typename _CutMap> |
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288 void maxMinCut(_CutMap& M) { |
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289 |
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290 NodeIt v; |
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291 for(g->first(v) ; g->valid(v); g->next(v)) { |
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292 M.set(v, true); |
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293 } |
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294 |
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295 std::queue<Node> queue; |
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296 |
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297 M.set(t,false); |
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298 queue.push(t); |
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299 |
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300 while (!queue.empty()) { |
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301 Node w=queue.front(); |
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302 queue.pop(); |
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303 |
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304 |
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305 InEdgeIt e; |
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306 for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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307 Node v=g->source(e); |
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308 if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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309 queue.push(v); |
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310 M.set(v, false); |
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311 } |
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312 } |
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313 |
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314 OutEdgeIt f; |
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315 for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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316 Node v=g->target(f); |
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317 if (M[v] && (*flow)[f] > 0 ) { |
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318 queue.push(v); |
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319 M.set(v, false); |
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320 } |
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321 } |
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322 } |
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323 } |
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324 |
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325 |
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326 ///Returns a minimum value cut. |
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327 |
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328 ///Sets \c M to the characteristic vector of a minimum value cut. |
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329 ///\pre M should be a node map of bools initialized to false. |
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330 ///\pre \c flow must be a maximum flow. |
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331 template<typename CutMap> |
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332 void minCut(CutMap& M) { minMinCut(M); } |
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333 |
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334 ///Resets the source node to \c _s. |
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335 |
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336 ///Resets the source node to \c _s. |
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337 /// |
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338 void resetSource(Node _s) { s=_s; } |
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339 |
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340 |
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341 ///Resets the target node to \c _t. |
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342 |
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343 ///Resets the target node to \c _t. |
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344 /// |
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345 void resetTarget(Node _t) { t=_t; } |
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346 |
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347 /// Resets the edge map of the capacities to _cap. |
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348 |
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349 /// Resets the edge map of the capacities to _cap. |
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350 /// |
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351 void resetCap(const CapMap& _cap) { capacity=&_cap; } |
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352 |
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353 /// Resets the edge map of the flows to _flow. |
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354 |
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355 /// Resets the edge map of the flows to _flow. |
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356 /// |
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357 void resetFlow(FlowMap& _flow) { flow=&_flow; } |
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358 |
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359 |
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360 private: |
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361 |
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362 int push(Node w, VecStack& active) { |
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363 |
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364 int lev=level[w]; |
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365 Num exc=excess[w]; |
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366 int newlevel=n; //bound on the next level of w |
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367 |
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368 OutEdgeIt e; |
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369 for(g->first(e,w); g->valid(e); g->next(e)) { |
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370 |
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371 if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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372 Node v=g->target(e); |
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373 |
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374 if( lev > level[v] ) { //Push is allowed now |
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375 |
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376 if ( excess[v]<=0 && v!=t && v!=s ) { |
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377 int lev_v=level[v]; |
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378 active[lev_v].push(v); |
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379 } |
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380 |
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381 Num cap=(*capacity)[e]; |
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382 Num flo=(*flow)[e]; |
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383 Num remcap=cap-flo; |
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384 |
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385 if ( remcap >= exc ) { //A nonsaturating push. |
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386 |
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387 flow->set(e, flo+exc); |
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388 excess.set(v, excess[v]+exc); |
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389 exc=0; |
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390 break; |
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391 |
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392 } else { //A saturating push. |
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393 flow->set(e, cap); |
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394 excess.set(v, excess[v]+remcap); |
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395 exc-=remcap; |
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396 } |
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397 } else if ( newlevel > level[v] ) newlevel = level[v]; |
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398 } //for out edges wv |
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399 |
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400 if ( exc > 0 ) { |
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401 InEdgeIt e; |
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402 for(g->first(e,w); g->valid(e); g->next(e)) { |
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403 |
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404 if( (*flow)[e] <= 0 ) continue; |
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405 Node v=g->source(e); |
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406 |
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407 if( lev > level[v] ) { //Push is allowed now |
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408 |
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409 if ( excess[v]<=0 && v!=t && v!=s ) { |
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410 int lev_v=level[v]; |
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411 active[lev_v].push(v); |
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412 } |
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413 |
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414 Num flo=(*flow)[e]; |
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415 |
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416 if ( flo >= exc ) { //A nonsaturating push. |
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417 |
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418 flow->set(e, flo-exc); |
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419 excess.set(v, excess[v]+exc); |
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420 exc=0; |
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421 break; |
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422 } else { //A saturating push. |
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423 |
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424 excess.set(v, excess[v]+flo); |
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425 exc-=flo; |
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426 flow->set(e,0); |
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427 } |
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428 } else if ( newlevel > level[v] ) newlevel = level[v]; |
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429 } //for in edges vw |
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430 |
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431 } // if w still has excess after the out edge for cycle |
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432 |
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433 excess.set(w, exc); |
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434 |
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435 return newlevel; |
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436 } |
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437 |
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438 |
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439 void preflowPreproc ( flowEnum fe, VecStack& active, |
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440 VecNode& level_list, NNMap& left, NNMap& right ) { |
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441 |
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442 std::queue<Node> bfs_queue; |
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443 |
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444 switch ( fe ) { |
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445 case ZERO_FLOW: |
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446 { |
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447 //Reverse_bfs from t, to find the starting level. |
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448 level.set(t,0); |
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449 bfs_queue.push(t); |
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450 |
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451 while (!bfs_queue.empty()) { |
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452 |
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453 Node v=bfs_queue.front(); |
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454 bfs_queue.pop(); |
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455 int l=level[v]+1; |
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456 |
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457 InEdgeIt e; |
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458 for(g->first(e,v); g->valid(e); g->next(e)) { |
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459 Node w=g->source(e); |
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460 if ( level[w] == n && w != s ) { |
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461 bfs_queue.push(w); |
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462 Node first=level_list[l]; |
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463 if ( g->valid(first) ) left.set(first,w); |
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464 right.set(w,first); |
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465 level_list[l]=w; |
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466 level.set(w, l); |
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467 } |
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468 } |
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469 } |
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470 |
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471 //the starting flow |
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472 OutEdgeIt e; |
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473 for(g->first(e,s); g->valid(e); g->next(e)) |
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474 { |
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475 Num c=(*capacity)[e]; |
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476 if ( c <= 0 ) continue; |
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477 Node w=g->target(e); |
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478 if ( level[w] < n ) { |
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479 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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480 flow->set(e, c); |
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481 excess.set(w, excess[w]+c); |
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482 } |
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483 } |
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484 break; |
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485 } |
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486 |
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487 case GEN_FLOW: |
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488 case PRE_FLOW: |
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489 { |
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490 //Reverse_bfs from t in the residual graph, |
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491 //to find the starting level. |
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492 level.set(t,0); |
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493 bfs_queue.push(t); |
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494 |
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495 while (!bfs_queue.empty()) { |
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496 |
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497 Node v=bfs_queue.front(); |
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498 bfs_queue.pop(); |
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499 int l=level[v]+1; |
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500 |
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501 InEdgeIt e; |
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502 for(g->first(e,v); g->valid(e); g->next(e)) { |
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503 if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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504 Node w=g->source(e); |
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505 if ( level[w] == n && w != s ) { |
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506 bfs_queue.push(w); |
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507 Node first=level_list[l]; |
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508 if ( g->valid(first) ) left.set(first,w); |
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509 right.set(w,first); |
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510 level_list[l]=w; |
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511 level.set(w, l); |
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512 } |
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513 } |
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514 |
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515 OutEdgeIt f; |
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516 for(g->first(f,v); g->valid(f); g->next(f)) { |
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517 if ( 0 >= (*flow)[f] ) continue; |
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518 Node w=g->target(f); |
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519 if ( level[w] == n && w != s ) { |
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520 bfs_queue.push(w); |
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521 Node first=level_list[l]; |
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522 if ( g->valid(first) ) left.set(first,w); |
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523 right.set(w,first); |
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524 level_list[l]=w; |
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525 level.set(w, l); |
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526 } |
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527 } |
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528 } |
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529 |
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530 |
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531 //the starting flow |
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532 OutEdgeIt e; |
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533 for(g->first(e,s); g->valid(e); g->next(e)) |
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534 { |
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535 Num rem=(*capacity)[e]-(*flow)[e]; |
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536 if ( rem <= 0 ) continue; |
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537 Node w=g->target(e); |
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538 if ( level[w] < n ) { |
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539 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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540 flow->set(e, (*capacity)[e]); |
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541 excess.set(w, excess[w]+rem); |
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542 } |
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543 } |
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544 |
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545 InEdgeIt f; |
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546 for(g->first(f,s); g->valid(f); g->next(f)) |
|
547 { |
|
548 if ( (*flow)[f] <= 0 ) continue; |
|
549 Node w=g->source(f); |
|
550 if ( level[w] < n ) { |
|
551 if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
|
552 excess.set(w, excess[w]+(*flow)[f]); |
|
553 flow->set(f, 0); |
|
554 } |
|
555 } |
|
556 break; |
|
557 } //case PRE_FLOW |
|
558 } |
|
559 } //preflowPreproc |
|
560 |
|
561 |
|
562 |
|
563 void relabel(Node w, int newlevel, VecStack& active, |
|
564 VecNode& level_list, NNMap& left, |
|
565 NNMap& right, int& b, int& k, bool what_heur ) |
|
566 { |
|
567 |
|
568 Num lev=level[w]; |
|
569 |
|
570 Node right_n=right[w]; |
|
571 Node left_n=left[w]; |
|
572 |
|
573 //unlacing starts |
|
574 if ( g->valid(right_n) ) { |
|
575 if ( g->valid(left_n) ) { |
|
576 right.set(left_n, right_n); |
|
577 left.set(right_n, left_n); |
|
578 } else { |
|
579 level_list[lev]=right_n; |
|
580 left.set(right_n, INVALID); |
|
581 } |
|
582 } else { |
|
583 if ( g->valid(left_n) ) { |
|
584 right.set(left_n, INVALID); |
|
585 } else { |
|
586 level_list[lev]=INVALID; |
|
587 } |
|
588 } |
|
589 //unlacing ends |
|
590 |
|
591 if ( !g->valid(level_list[lev]) ) { |
|
592 |
|
593 //gapping starts |
|
594 for (int i=lev; i!=k ; ) { |
|
595 Node v=level_list[++i]; |
|
596 while ( g->valid(v) ) { |
|
597 level.set(v,n); |
|
598 v=right[v]; |
|
599 } |
|
600 level_list[i]=INVALID; |
|
601 if ( !what_heur ) { |
|
602 while ( !active[i].empty() ) { |
|
603 active[i].pop(); //FIXME: ezt szebben kene |
|
604 } |
|
605 } |
|
606 } |
|
607 |
|
608 level.set(w,n); |
|
609 b=lev-1; |
|
610 k=b; |
|
611 //gapping ends |
|
612 |
|
613 } else { |
|
614 |
|
615 if ( newlevel == n ) level.set(w,n); |
|
616 else { |
|
617 level.set(w,++newlevel); |
|
618 active[newlevel].push(w); |
|
619 if ( what_heur ) b=newlevel; |
|
620 if ( k < newlevel ) ++k; //now k=newlevel |
|
621 Node first=level_list[newlevel]; |
|
622 if ( g->valid(first) ) left.set(first,w); |
|
623 right.set(w,first); |
|
624 left.set(w,INVALID); |
|
625 level_list[newlevel]=w; |
|
626 } |
|
627 } |
|
628 |
|
629 } //relabel |
|
630 |
|
631 |
|
632 template<typename MapGraphWrapper> |
|
633 class DistanceMap { |
|
634 protected: |
|
635 const MapGraphWrapper* g; |
|
636 typename MapGraphWrapper::template NodeMap<int> dist; |
|
637 public: |
|
638 DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
|
639 void set(const typename MapGraphWrapper::Node& n, int a) { |
|
640 dist.set(n, a); |
|
641 } |
|
642 int operator[](const typename MapGraphWrapper::Node& n) |
|
643 { return dist[n]; } |
|
644 // int get(const typename MapGraphWrapper::Node& n) const { |
|
645 // return dist[n]; } |
|
646 // bool get(const typename MapGraphWrapper::Edge& e) const { |
|
647 // return (dist.get(g->source(e))<dist.get(g->target(e))); } |
|
648 bool operator[](const typename MapGraphWrapper::Edge& e) const { |
|
649 return (dist[g->source(e)]<dist[g->target(e)]); |
|
650 } |
|
651 }; |
|
652 |
|
653 }; |
|
654 |
|
655 |
|
656 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
657 void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1( flowEnum fe ) |
|
658 { |
|
659 |
|
660 int heur0=(int)(H0*n); //time while running 'bound decrease' |
|
661 int heur1=(int)(H1*n); //time while running 'highest label' |
|
662 int heur=heur1; //starting time interval (#of relabels) |
|
663 int numrelabel=0; |
|
664 |
|
665 bool what_heur=1; |
|
666 //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
|
667 |
|
668 bool end=false; |
|
669 //Needed for 'bound decrease', true means no active nodes are above bound b. |
|
670 |
|
671 int k=n-2; //bound on the highest level under n containing a node |
|
672 int b=k; //bound on the highest level under n of an active node |
|
673 |
|
674 VecStack active(n); |
|
675 |
|
676 NNMap left(*g, INVALID); |
|
677 NNMap right(*g, INVALID); |
|
678 VecNode level_list(n,INVALID); |
|
679 //List of the nodes in level i<n, set to n. |
|
680 |
|
681 NodeIt v; |
|
682 for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
|
683 //setting each node to level n |
|
684 |
|
685 switch ( fe ) { |
|
686 case PRE_FLOW: |
|
687 { |
|
688 //counting the excess |
|
689 NodeIt v; |
|
690 for(g->first(v); g->valid(v); g->next(v)) { |
|
691 Num exc=0; |
|
692 |
|
693 InEdgeIt e; |
|
694 for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
|
695 OutEdgeIt f; |
|
696 for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
|
697 |
|
698 excess.set(v,exc); |
|
699 |
|
700 //putting the active nodes into the stack |
|
701 int lev=level[v]; |
|
702 if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
|
703 } |
|
704 break; |
|
705 } |
|
706 case GEN_FLOW: |
|
707 { |
|
708 //Counting the excess of t |
|
709 Num exc=0; |
|
710 |
|
711 InEdgeIt e; |
|
712 for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
|
713 OutEdgeIt f; |
|
714 for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
|
715 |
|
716 excess.set(t,exc); |
|
717 |
|
718 break; |
|
719 } |
|
720 default: |
|
721 break; |
|
722 } |
|
723 |
|
724 preflowPreproc( fe, active, level_list, left, right ); |
|
725 //End of preprocessing |
|
726 |
|
727 |
|
728 //Push/relabel on the highest level active nodes. |
|
729 while ( true ) { |
|
730 if ( b == 0 ) { |
|
731 if ( !what_heur && !end && k > 0 ) { |
|
732 b=k; |
|
733 end=true; |
|
734 } else break; |
|
735 } |
|
736 |
|
737 if ( active[b].empty() ) --b; |
|
738 else { |
|
739 end=false; |
|
740 Node w=active[b].top(); |
|
741 active[b].pop(); |
|
742 int newlevel=push(w,active); |
|
743 if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
|
744 left, right, b, k, what_heur); |
|
745 |
|
746 ++numrelabel; |
|
747 if ( numrelabel >= heur ) { |
|
748 numrelabel=0; |
|
749 if ( what_heur ) { |
|
750 what_heur=0; |
|
751 heur=heur0; |
|
752 end=false; |
|
753 } else { |
|
754 what_heur=1; |
|
755 heur=heur1; |
|
756 b=k; |
|
757 } |
|
758 } |
|
759 } |
|
760 } |
|
761 } |
|
762 |
|
763 |
|
764 |
|
765 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
766 void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() |
|
767 { |
|
768 |
|
769 int k=n-2; //bound on the highest level under n containing a node |
|
770 int b=k; //bound on the highest level under n of an active node |
|
771 |
|
772 VecStack active(n); |
|
773 level.set(s,0); |
|
774 std::queue<Node> bfs_queue; |
|
775 bfs_queue.push(s); |
|
776 |
|
777 while (!bfs_queue.empty()) { |
|
778 |
|
779 Node v=bfs_queue.front(); |
|
780 bfs_queue.pop(); |
|
781 int l=level[v]+1; |
|
782 |
|
783 InEdgeIt e; |
|
784 for(g->first(e,v); g->valid(e); g->next(e)) { |
|
785 if ( (*capacity)[e] <= (*flow)[e] ) continue; |
|
786 Node u=g->source(e); |
|
787 if ( level[u] >= n ) { |
|
788 bfs_queue.push(u); |
|
789 level.set(u, l); |
|
790 if ( excess[u] > 0 ) active[l].push(u); |
|
791 } |
|
792 } |
|
793 |
|
794 OutEdgeIt f; |
|
795 for(g->first(f,v); g->valid(f); g->next(f)) { |
|
796 if ( 0 >= (*flow)[f] ) continue; |
|
797 Node u=g->target(f); |
|
798 if ( level[u] >= n ) { |
|
799 bfs_queue.push(u); |
|
800 level.set(u, l); |
|
801 if ( excess[u] > 0 ) active[l].push(u); |
|
802 } |
|
803 } |
|
804 } |
|
805 b=n-2; |
|
806 |
|
807 while ( true ) { |
|
808 |
|
809 if ( b == 0 ) break; |
|
810 |
|
811 if ( active[b].empty() ) --b; |
|
812 else { |
|
813 Node w=active[b].top(); |
|
814 active[b].pop(); |
|
815 int newlevel=push(w,active); |
|
816 |
|
817 //relabel |
|
818 if ( excess[w] > 0 ) { |
|
819 level.set(w,++newlevel); |
|
820 active[newlevel].push(w); |
|
821 b=newlevel; |
|
822 } |
|
823 } // if stack[b] is nonempty |
|
824 } // while(true) |
|
825 } |
|
826 |
|
827 |
|
828 |
|
829 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
830 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
|
831 { |
|
832 ResGW res_graph(*g, *capacity, *flow); |
|
833 bool _augment=false; |
|
834 |
|
835 //ReachedMap level(res_graph); |
|
836 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
837 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
838 bfs.pushAndSetReached(s); |
|
839 |
|
840 typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
|
841 pred.set(s, INVALID); |
|
842 |
|
843 typename ResGW::template NodeMap<Num> free(res_graph); |
|
844 |
|
845 //searching for augmenting path |
|
846 while ( !bfs.finished() ) { |
|
847 ResGWOutEdgeIt e=bfs; |
|
848 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
849 Node v=res_graph.source(e); |
|
850 Node w=res_graph.target(e); |
|
851 pred.set(w, e); |
|
852 if (res_graph.valid(pred[v])) { |
|
853 free.set(w, std::min(free[v], res_graph.resCap(e))); |
|
854 } else { |
|
855 free.set(w, res_graph.resCap(e)); |
|
856 } |
|
857 if (res_graph.target(e)==t) { _augment=true; break; } |
|
858 } |
|
859 |
|
860 ++bfs; |
|
861 } //end of searching augmenting path |
|
862 |
|
863 if (_augment) { |
|
864 Node n=t; |
|
865 Num augment_value=free[t]; |
|
866 while (res_graph.valid(pred[n])) { |
|
867 ResGWEdge e=pred[n]; |
|
868 res_graph.augment(e, augment_value); |
|
869 n=res_graph.source(e); |
|
870 } |
|
871 } |
|
872 |
|
873 return _augment; |
|
874 } |
|
875 |
|
876 |
|
877 |
|
878 |
|
879 |
|
880 |
|
881 |
|
882 |
|
883 |
|
884 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
885 template<typename MutableGraph> |
|
886 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
|
887 { |
|
888 typedef MutableGraph MG; |
|
889 bool _augment=false; |
|
890 |
|
891 ResGW res_graph(*g, *capacity, *flow); |
|
892 |
|
893 //bfs for distances on the residual graph |
|
894 //ReachedMap level(res_graph); |
|
895 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
896 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
897 bfs.pushAndSetReached(s); |
|
898 typename ResGW::template NodeMap<int> |
|
899 dist(res_graph); //filled up with 0's |
|
900 |
|
901 //F will contain the physical copy of the residual graph |
|
902 //with the set of edges which are on shortest paths |
|
903 MG F; |
|
904 typename ResGW::template NodeMap<typename MG::Node> |
|
905 res_graph_to_F(res_graph); |
|
906 { |
|
907 typename ResGW::NodeIt n; |
|
908 for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
|
909 res_graph_to_F.set(n, F.addNode()); |
|
910 } |
|
911 } |
|
912 |
|
913 typename MG::Node sF=res_graph_to_F[s]; |
|
914 typename MG::Node tF=res_graph_to_F[t]; |
|
915 typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
|
916 typename MG::template EdgeMap<Num> residual_capacity(F); |
|
917 |
|
918 while ( !bfs.finished() ) { |
|
919 ResGWOutEdgeIt e=bfs; |
|
920 if (res_graph.valid(e)) { |
|
921 if (bfs.isBNodeNewlyReached()) { |
|
922 dist.set(res_graph.target(e), dist[res_graph.source(e)]+1); |
|
923 typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.source(e)], res_graph_to_F[res_graph.target(e)]); |
|
924 original_edge.update(); |
|
925 original_edge.set(f, e); |
|
926 residual_capacity.update(); |
|
927 residual_capacity.set(f, res_graph.resCap(e)); |
|
928 } else { |
|
929 if (dist[res_graph.target(e)]==(dist[res_graph.source(e)]+1)) { |
|
930 typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.source(e)], res_graph_to_F[res_graph.target(e)]); |
|
931 original_edge.update(); |
|
932 original_edge.set(f, e); |
|
933 residual_capacity.update(); |
|
934 residual_capacity.set(f, res_graph.resCap(e)); |
|
935 } |
|
936 } |
|
937 } |
|
938 ++bfs; |
|
939 } //computing distances from s in the residual graph |
|
940 |
|
941 bool __augment=true; |
|
942 |
|
943 while (__augment) { |
|
944 __augment=false; |
|
945 //computing blocking flow with dfs |
|
946 DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
|
947 typename MG::template NodeMap<typename MG::Edge> pred(F); |
|
948 pred.set(sF, INVALID); |
|
949 //invalid iterators for sources |
|
950 |
|
951 typename MG::template NodeMap<Num> free(F); |
|
952 |
|
953 dfs.pushAndSetReached(sF); |
|
954 while (!dfs.finished()) { |
|
955 ++dfs; |
|
956 if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
|
957 if (dfs.isBNodeNewlyReached()) { |
|
958 typename MG::Node v=F.aNode(dfs); |
|
959 typename MG::Node w=F.bNode(dfs); |
|
960 pred.set(w, dfs); |
|
961 if (F.valid(pred[v])) { |
|
962 free.set(w, std::min(free[v], residual_capacity[dfs])); |
|
963 } else { |
|
964 free.set(w, residual_capacity[dfs]); |
|
965 } |
|
966 if (w==tF) { |
|
967 __augment=true; |
|
968 _augment=true; |
|
969 break; |
|
970 } |
|
971 |
|
972 } else { |
|
973 F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
|
974 } |
|
975 } |
|
976 } |
|
977 |
|
978 if (__augment) { |
|
979 typename MG::Node n=tF; |
|
980 Num augment_value=free[tF]; |
|
981 while (F.valid(pred[n])) { |
|
982 typename MG::Edge e=pred[n]; |
|
983 res_graph.augment(original_edge[e], augment_value); |
|
984 n=F.source(e); |
|
985 if (residual_capacity[e]==augment_value) |
|
986 F.erase(e); |
|
987 else |
|
988 residual_capacity.set(e, residual_capacity[e]-augment_value); |
|
989 } |
|
990 } |
|
991 |
|
992 } |
|
993 |
|
994 return _augment; |
|
995 } |
|
996 |
|
997 |
|
998 |
|
999 |
|
1000 |
|
1001 |
|
1002 template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
|
1003 bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
|
1004 { |
|
1005 bool _augment=false; |
|
1006 |
|
1007 ResGW res_graph(*g, *capacity, *flow); |
|
1008 |
|
1009 //ReachedMap level(res_graph); |
|
1010 FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
|
1011 BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
|
1012 |
|
1013 bfs.pushAndSetReached(s); |
|
1014 DistanceMap<ResGW> dist(res_graph); |
|
1015 while ( !bfs.finished() ) { |
|
1016 ResGWOutEdgeIt e=bfs; |
|
1017 if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
|
1018 dist.set(res_graph.target(e), dist[res_graph.source(e)]+1); |
|
1019 } |
|
1020 ++bfs; |
|
1021 } //computing distances from s in the residual graph |
|
1022 |
|
1023 //Subgraph containing the edges on some shortest paths |
|
1024 ConstMap<typename ResGW::Node, bool> true_map(true); |
|
1025 typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
|
1026 DistanceMap<ResGW> > FilterResGW; |
|
1027 FilterResGW filter_res_graph(res_graph, true_map, dist); |
|
1028 |
|
1029 //Subgraph, which is able to delete edges which are already |
|
1030 //met by the dfs |
|
1031 typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
|
1032 first_out_edges(filter_res_graph); |
|
1033 typename FilterResGW::NodeIt v; |
|
1034 for(filter_res_graph.first(v); filter_res_graph.valid(v); |
|
1035 filter_res_graph.next(v)) |
|
1036 { |
|
1037 typename FilterResGW::OutEdgeIt e; |
|
1038 filter_res_graph.first(e, v); |
|
1039 first_out_edges.set(v, e); |
|
1040 } |
|
1041 typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
|
1042 template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
|
1043 ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
|
1044 |
|
1045 bool __augment=true; |
|
1046 |
|
1047 while (__augment) { |
|
1048 |
|
1049 __augment=false; |
|
1050 //computing blocking flow with dfs |
|
1051 DfsIterator< ErasingResGW, |
|
1052 typename ErasingResGW::template NodeMap<bool> > |
|
1053 dfs(erasing_res_graph); |
|
1054 typename ErasingResGW:: |
|
1055 template NodeMap<typename ErasingResGW::OutEdgeIt> |
|
1056 pred(erasing_res_graph); |
|
1057 pred.set(s, INVALID); |
|
1058 //invalid iterators for sources |
|
1059 |
|
1060 typename ErasingResGW::template NodeMap<Num> |
|
1061 free1(erasing_res_graph); |
|
1062 |
|
1063 dfs.pushAndSetReached( |
|
1064 typename ErasingResGW::Node( |
|
1065 typename FilterResGW::Node( |
|
1066 typename ResGW::Node(s) |
|
1067 ) |
|
1068 ) |
|
1069 ); |
|
1070 while (!dfs.finished()) { |
|
1071 ++dfs; |
|
1072 if (erasing_res_graph.valid( |
|
1073 typename ErasingResGW::OutEdgeIt(dfs))) |
|
1074 { |
|
1075 if (dfs.isBNodeNewlyReached()) { |
|
1076 |
|
1077 typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
|
1078 typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
|
1079 |
|
1080 pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
|
1081 if (erasing_res_graph.valid(pred[v])) { |
|
1082 free1.set(w, std::min(free1[v], res_graph.resCap( |
|
1083 typename ErasingResGW::OutEdgeIt(dfs)))); |
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1084 } else { |
|
1085 free1.set(w, res_graph.resCap( |
|
1086 typename ErasingResGW::OutEdgeIt(dfs))); |
|
1087 } |
|
1088 |
|
1089 if (w==t) { |
|
1090 __augment=true; |
|
1091 _augment=true; |
|
1092 break; |
|
1093 } |
|
1094 } else { |
|
1095 erasing_res_graph.erase(dfs); |
|
1096 } |
|
1097 } |
|
1098 } |
|
1099 |
|
1100 if (__augment) { |
|
1101 typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t)); |
|
1102 // typename ResGW::NodeMap<Num> a(res_graph); |
|
1103 // typename ResGW::Node b; |
|
1104 // Num j=a[b]; |
|
1105 // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
|
1106 // typename FilterResGW::Node b1; |
|
1107 // Num j1=a1[b1]; |
|
1108 // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
|
1109 // typename ErasingResGW::Node b2; |
|
1110 // Num j2=a2[b2]; |
|
1111 Num augment_value=free1[n]; |
|
1112 while (erasing_res_graph.valid(pred[n])) { |
|
1113 typename ErasingResGW::OutEdgeIt e=pred[n]; |
|
1114 res_graph.augment(e, augment_value); |
|
1115 n=erasing_res_graph.source(e); |
|
1116 if (res_graph.resCap(e)==0) |
|
1117 erasing_res_graph.erase(e); |
|
1118 } |
|
1119 } |
|
1120 |
|
1121 } //while (__augment) |
|
1122 |
|
1123 return _augment; |
|
1124 } |
|
1125 |
|
1126 |
|
1127 |
|
1128 /// @} |
|
1129 |
|
1130 } //END OF NAMESPACE LEMON |
|
1131 |
|
1132 #endif //LEMON_MAX_FLOW_H |
|
1133 |
|
1134 |
|
1135 |
|
1136 |
|