1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_hl2.h |
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4 | by jacint. |
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5 | Runs the highest label variant of the preflow push algorithm with |
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6 | running time O(n^2\sqrt(m)), with the 'empty level' and with the |
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7 | heuristic that the bound b on the active nodes is not increased |
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8 | only when b=0, when we put b=2*n-2. |
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9 | |
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10 | 'A' is a parameter for the empty_level heuristic |
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11 | |
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12 | Member functions: |
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13 | |
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14 | void run() : runs the algorithm |
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15 | |
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16 | The following functions should be used after run() was already run. |
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17 | |
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18 | T maxflow() : returns the value of a maximum flow |
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19 | |
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20 | T flowonedge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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21 | |
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22 | FlowMap allflow() : returns the fixed maximum flow x |
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23 | |
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24 | void mincut(CutMap& M) : sets M to the characteristic vector of a |
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25 | minimum cut. M should be a map of bools initialized to false. |
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26 | |
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27 | void min_mincut(CutMap& M) : sets M to the characteristic vector of the |
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28 | minimum min cut. M should be a map of bools initialized to false. |
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29 | |
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30 | void max_mincut(CutMap& M) : sets M to the characteristic vector of the |
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31 | maximum min cut. M should be a map of bools initialized to false. |
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32 | |
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33 | */ |
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34 | |
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35 | #ifndef PREFLOW_HL2_H |
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36 | #define PREFLOW_HL2_H |
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37 | |
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38 | #define A 1 |
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39 | |
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40 | #include <vector> |
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41 | #include <stack> |
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42 | #include <queue> |
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43 | |
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44 | namespace marci { |
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45 | |
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46 | template <typename Graph, typename T, |
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47 | typename FlowMap=typename Graph::EdgeMap<T>, typename CapMap=typename Graph::EdgeMap<T>, |
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48 | typename IntMap=typename Graph::NodeMap<int>, typename TMap=typename Graph::NodeMap<T> > |
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49 | class preflow_hl2 { |
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50 | |
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51 | typedef typename Graph::NodeIt NodeIt; |
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52 | typedef typename Graph::EdgeIt EdgeIt; |
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53 | typedef typename Graph::EachNodeIt EachNodeIt; |
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54 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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55 | typedef typename Graph::InEdgeIt InEdgeIt; |
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56 | |
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57 | Graph& G; |
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58 | NodeIt s; |
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59 | NodeIt t; |
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60 | FlowMap flow; |
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61 | CapMap& capacity; |
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62 | T value; |
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63 | |
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64 | public: |
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65 | |
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66 | preflow_hl2(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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67 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) { } |
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68 | |
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69 | |
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70 | void run() { |
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71 | |
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72 | bool no_end=true; |
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73 | int n=G.nodeNum(); |
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74 | int b=n-2; |
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75 | /* |
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76 | b is a bound on the highest level of an active node. |
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77 | In the beginning it is at most n-2. |
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78 | */ |
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79 | |
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80 | IntMap level(G,n); |
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81 | TMap excess(G); |
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82 | |
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83 | std::vector<int> numb(n); |
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84 | /* |
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85 | The number of nodes on level i < n. It is |
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86 | initialized to n+1, because of the reverse_bfs-part. |
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87 | */ |
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88 | |
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89 | std::vector<std::stack<NodeIt> > stack(2*n-1); |
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90 | //Stack of the active nodes in level i. |
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91 | |
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92 | |
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93 | /*Reverse_bfs from t, to find the starting level.*/ |
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94 | level.set(t,0); |
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95 | std::queue<NodeIt> bfs_queue; |
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96 | bfs_queue.push(t); |
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97 | |
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98 | while (!bfs_queue.empty()) { |
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99 | |
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100 | NodeIt v=bfs_queue.front(); |
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101 | bfs_queue.pop(); |
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102 | int l=level.get(v)+1; |
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103 | |
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104 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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105 | NodeIt w=G.tail(e); |
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106 | if ( level.get(w) == n ) { |
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107 | bfs_queue.push(w); |
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108 | ++numb[l]; |
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109 | level.set(w, l); |
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110 | } |
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111 | } |
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112 | } |
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113 | |
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114 | level.set(s,n); |
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115 | |
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116 | |
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117 | |
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118 | /* Starting flow. It is everywhere 0 at the moment. */ |
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119 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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120 | { |
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121 | T c=capacity.get(e); |
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122 | if ( c == 0 ) continue; |
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123 | NodeIt w=G.head(e); |
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124 | if ( w!=s ) { |
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125 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
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126 | flow.set(e, c); |
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127 | excess.set(w, excess.get(w)+c); |
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128 | } |
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129 | } |
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130 | |
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131 | /* |
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132 | End of preprocessing |
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133 | */ |
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134 | |
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135 | |
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136 | |
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137 | /* |
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138 | Push/relabel on the highest level active nodes. |
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139 | */ |
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140 | /*While there exists an active node.*/ |
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141 | while (b) { |
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142 | if ( stack[b].empty() ) { |
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143 | if ( b==1 ) { |
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144 | if ( !no_end ) break; |
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145 | else { |
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146 | b=2*n-2; |
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147 | no_end=false; |
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148 | } |
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149 | } |
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150 | --b; |
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151 | } else { |
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152 | |
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153 | no_end=true; |
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154 | |
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155 | NodeIt w=stack[b].top(); //w is a highest label active node. |
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156 | stack[b].pop(); |
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157 | int lev=level.get(w); |
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158 | int exc=excess.get(w); |
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159 | int newlevel=2*n; //In newlevel we bound the next level of w. |
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160 | |
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161 | // if ( level.get(w) < n ) { //Nem tudom ez mukodik-e |
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162 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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163 | |
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164 | if ( flow.get(e) == capacity.get(e) ) continue; |
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165 | NodeIt v=G.head(e); |
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166 | //e=wv |
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167 | |
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168 | if( lev > level.get(v) ) { |
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169 | /*Push is allowed now*/ |
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170 | |
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171 | if ( excess.get(v)==0 && v != s && v !=t ) |
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172 | stack[level.get(v)].push(v); |
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173 | /*v becomes active.*/ |
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174 | |
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175 | int cap=capacity.get(e); |
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176 | int flo=flow.get(e); |
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177 | int remcap=cap-flo; |
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178 | |
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179 | if ( remcap >= exc ) { |
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180 | /*A nonsaturating push.*/ |
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181 | |
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182 | flow.set(e, flo+exc); |
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183 | excess.set(v, excess.get(v)+exc); |
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184 | exc=0; |
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185 | break; |
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186 | |
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187 | } else { |
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188 | /*A saturating push.*/ |
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189 | |
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190 | flow.set(e, cap ); |
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191 | excess.set(v, excess.get(v)+remcap); |
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192 | exc-=remcap; |
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193 | } |
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194 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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195 | |
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196 | } //for out edges wv |
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197 | |
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198 | |
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199 | if ( exc > 0 ) { |
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200 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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201 | |
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202 | if( flow.get(e) == 0 ) continue; |
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203 | NodeIt v=G.tail(e); |
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204 | //e=vw |
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205 | |
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206 | if( lev > level.get(v) ) { |
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207 | /*Push is allowed now*/ |
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208 | |
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209 | if ( excess.get(v)==0 && v != s && v !=t) |
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210 | stack[level.get(v)].push(v); |
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211 | /*v becomes active.*/ |
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212 | |
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213 | int flo=flow.get(e); |
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214 | |
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215 | if ( flo >= exc ) { |
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216 | /*A nonsaturating push.*/ |
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217 | |
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218 | flow.set(e, flo-exc); |
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219 | excess.set(v, excess.get(v)+exc); |
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220 | exc=0; |
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221 | break; |
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222 | } else { |
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223 | /*A saturating push.*/ |
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224 | |
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225 | excess.set(v, excess.get(v)+flo); |
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226 | exc-=flo; |
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227 | flow.set(e,0); |
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228 | } |
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229 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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230 | |
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231 | } //for in edges vw |
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232 | |
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233 | } // if w still has excess after the out edge for cycle |
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234 | |
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235 | excess.set(w, exc); |
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236 | |
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237 | |
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238 | /* |
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239 | Relabel |
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240 | */ |
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241 | |
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242 | if ( exc > 0 ) { |
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243 | //now 'lev' is the old level of w |
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244 | level.set(w,++newlevel); |
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245 | |
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246 | if ( lev < n ) { |
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247 | --numb[lev]; |
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248 | |
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249 | if ( !numb[lev] && lev < A*n ) { //If the level of w gets empty. |
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250 | |
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251 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
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252 | if (level.get(v) > lev && level.get(v) < n ) level.set(v,n); |
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253 | } |
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254 | for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; |
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255 | if ( newlevel < n ) newlevel=n; |
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256 | } else { |
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257 | if ( newlevel < n ) ++numb[newlevel]; |
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258 | } |
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259 | } |
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260 | |
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261 | stack[newlevel].push(w); |
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262 | |
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263 | } |
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264 | |
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265 | } // if stack[b] is nonempty |
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266 | |
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267 | } // while(b) |
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268 | |
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269 | |
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270 | value = excess.get(t); |
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271 | /*Max flow value.*/ |
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272 | |
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273 | |
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274 | } //void run() |
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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 | /* |
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281 | Returns the maximum value of a flow. |
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282 | */ |
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283 | |
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284 | T maxflow() { |
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285 | return value; |
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286 | } |
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287 | |
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288 | |
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289 | |
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290 | /* |
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291 | For the maximum flow x found by the algorithm, it returns the flow value on Edge e, i.e. x(e). |
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292 | */ |
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293 | |
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294 | T flowonedge(EdgeIt e) { |
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295 | return flow.get(e); |
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296 | } |
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297 | |
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298 | |
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299 | |
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300 | /* |
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301 | Returns the maximum flow x found by the algorithm. |
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302 | */ |
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303 | |
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304 | FlowMap allflow() { |
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305 | return flow; |
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306 | } |
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307 | |
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308 | |
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309 | |
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310 | |
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311 | /* |
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312 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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313 | */ |
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314 | |
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315 | template<typename CutMap> |
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316 | void mincut(CutMap& M) { |
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317 | |
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318 | std::queue<NodeIt> queue; |
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319 | |
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320 | M.set(s,true); |
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321 | queue.push(s); |
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322 | |
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323 | while (!queue.empty()) { |
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324 | NodeIt w=queue.front(); |
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325 | queue.pop(); |
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326 | |
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327 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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328 | NodeIt v=G.head(e); |
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329 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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330 | queue.push(v); |
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331 | M.set(v, true); |
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332 | } |
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333 | } |
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334 | |
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335 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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336 | NodeIt v=G.tail(e); |
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337 | if (!M.get(v) && flow.get(e) > 0 ) { |
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338 | queue.push(v); |
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339 | M.set(v, true); |
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340 | } |
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341 | } |
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342 | |
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343 | } |
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344 | |
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345 | } |
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346 | |
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347 | |
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348 | |
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349 | /* |
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350 | Returns the maximum min cut, by a reverse bfs |
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351 | from t in the residual graph. |
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352 | */ |
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353 | |
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354 | template<typename CutMap> |
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355 | void max_mincut(CutMap& M) { |
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356 | |
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357 | std::queue<NodeIt> queue; |
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358 | |
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359 | M.set(t,true); |
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360 | queue.push(t); |
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361 | |
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362 | while (!queue.empty()) { |
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363 | NodeIt w=queue.front(); |
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364 | queue.pop(); |
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365 | |
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366 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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367 | NodeIt v=G.tail(e); |
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368 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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369 | queue.push(v); |
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370 | M.set(v, true); |
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371 | } |
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372 | } |
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373 | |
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374 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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375 | NodeIt v=G.head(e); |
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376 | if (!M.get(v) && flow.get(e) > 0 ) { |
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377 | queue.push(v); |
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378 | M.set(v, true); |
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379 | } |
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380 | } |
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381 | } |
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382 | |
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383 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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384 | M.set(v, !M.get(v)); |
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385 | } |
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386 | |
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387 | } |
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388 | |
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389 | |
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390 | |
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391 | template<typename CutMap> |
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392 | void min_mincut(CutMap& M) { |
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393 | mincut(M); |
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394 | } |
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395 | |
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396 | |
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397 | |
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398 | }; |
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399 | }//namespace marci |
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400 | #endif |
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401 | |
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402 | |
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403 | |
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404 | |
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