1 | // -*- C++ -*- |
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2 | /* |
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3 | preflow_hl4.h |
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4 | by jacint. |
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5 | Runs the two phase highest label preflow push algorithm. In phase 0 |
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6 | we maintain in a list the nodes in level i < n, and we maintain a |
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7 | bound k on the max level i < n containing a node, so we can do |
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8 | the gap heuristic fast. Phase 1 is the same. (The algorithm is the |
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9 | same as preflow.hl3, the only diff is that here we use the gap |
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10 | heuristic with the list of the nodes on level i, and not a bfs form the |
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11 | upgraded node.) |
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12 | |
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13 | In phase 1 we shift everything downwards by n. |
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14 | |
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15 | Member functions: |
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16 | |
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17 | void run() : runs the algorithm |
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18 | |
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19 | The following functions should be used after run() was already run. |
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20 | |
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21 | T maxflow() : returns the value of a maximum flow |
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22 | |
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23 | T flowonedge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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24 | |
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25 | FlowMap allflow() : returns a maximum flow |
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26 | |
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27 | void allflow(FlowMap& _flow ) : returns a maximum flow |
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28 | |
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29 | void mincut(CutMap& M) : sets M to the characteristic vector of a |
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30 | minimum cut. M should be a map of bools initialized to false. |
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31 | |
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32 | void min_mincut(CutMap& M) : sets M to the characteristic vector of the |
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33 | minimum min cut. M should be a map of bools initialized to false. |
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34 | |
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35 | void max_mincut(CutMap& M) : sets M to the characteristic vector of the |
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36 | maximum min cut. M should be a map of bools initialized to false. |
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37 | |
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38 | */ |
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39 | |
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40 | #ifndef PREFLOW_HL4_H |
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41 | #define PREFLOW_HL4_H |
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42 | |
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43 | #include <vector> |
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44 | #include <stack> |
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45 | #include <queue> |
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46 | |
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47 | namespace marci { |
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48 | |
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49 | template <typename Graph, typename T, |
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50 | typename FlowMap=typename Graph::EdgeMap<T>, |
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51 | typename CapMap=typename Graph::EdgeMap<T> > |
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52 | class preflow_hl4 { |
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53 | |
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54 | typedef typename Graph::NodeIt NodeIt; |
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55 | typedef typename Graph::EdgeIt EdgeIt; |
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56 | typedef typename Graph::EachNodeIt EachNodeIt; |
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57 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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58 | typedef typename Graph::InEdgeIt InEdgeIt; |
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59 | |
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60 | Graph& G; |
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61 | NodeIt s; |
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62 | NodeIt t; |
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63 | FlowMap flow; |
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64 | CapMap& capacity; |
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65 | T value; |
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66 | |
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67 | public: |
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68 | |
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69 | preflow_hl4(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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70 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) { } |
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71 | |
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72 | |
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73 | void run() { |
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74 | |
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75 | bool phase=0; |
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76 | int n=G.nodeNum(); |
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77 | int k=n-2; |
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78 | int b=k; |
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79 | /* |
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80 | b is a bound on the highest level of the stack. |
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81 | k is a bound on the highest nonempty level i < n. |
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82 | */ |
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83 | |
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84 | typename Graph::NodeMap<int> level(G,n); |
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85 | typename Graph::NodeMap<T> excess(G); |
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86 | std::vector<std::stack<NodeIt> > stack(n); |
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87 | //Stack of the active nodes in level i < n. |
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88 | //We use it in both phases. |
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89 | |
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90 | typename Graph::NodeMap<NodeIt> left(G); |
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91 | typename Graph::NodeMap<NodeIt> right(G); |
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92 | std::vector<NodeIt> level_list(n); |
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93 | /* |
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94 | Needed for the list of the nodes in level i. |
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95 | */ |
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96 | |
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97 | /*Reverse_bfs from t, to find the starting level.*/ |
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98 | level.set(t,0); |
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99 | std::queue<NodeIt> bfs_queue; |
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100 | bfs_queue.push(t); |
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101 | |
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102 | while (!bfs_queue.empty()) { |
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103 | |
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104 | NodeIt v=bfs_queue.front(); |
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105 | bfs_queue.pop(); |
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106 | int l=level.get(v)+1; |
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107 | |
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108 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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109 | NodeIt w=G.tail(e); |
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110 | if ( level.get(w) == n ) { |
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111 | bfs_queue.push(w); |
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112 | NodeIt first=level_list[l]; |
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113 | if ( first != 0 ) left.set(first,w); |
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114 | right.set(w,first); |
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115 | level_list[l]=w; |
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116 | level.set(w, l); |
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117 | } |
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118 | } |
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119 | } |
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120 | |
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121 | level.set(s,n); |
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122 | |
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123 | |
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124 | /* Starting flow. It is everywhere 0 at the moment. */ |
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125 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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126 | { |
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127 | T c=capacity.get(e); |
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128 | if ( c == 0 ) continue; |
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129 | NodeIt w=G.head(e); |
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130 | if ( level.get(w) < n ) { |
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131 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
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132 | flow.set(e, c); |
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133 | excess.set(w, excess.get(w)+c); |
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134 | } |
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135 | } |
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136 | /* |
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137 | End of preprocessing |
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138 | */ |
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139 | |
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140 | |
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141 | /* |
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142 | Push/relabel on the highest level active nodes. |
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143 | */ |
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144 | while ( true ) { |
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145 | |
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146 | if ( b == 0 ) { |
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147 | if ( phase ) break; |
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148 | |
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149 | /* |
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150 | In the end of phase 0 we apply a bfs from s in |
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151 | the residual graph. |
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152 | */ |
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153 | phase=1; |
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154 | level.set(s,0); |
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155 | std::queue<NodeIt> bfs_queue; |
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156 | bfs_queue.push(s); |
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157 | |
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158 | while (!bfs_queue.empty()) { |
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159 | |
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160 | NodeIt v=bfs_queue.front(); |
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161 | bfs_queue.pop(); |
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162 | int l=level.get(v)+1; |
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163 | |
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164 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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165 | if ( capacity.get(e) == flow.get(e) ) continue; |
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166 | NodeIt u=G.tail(e); |
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167 | if ( level.get(u) >= n ) { |
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168 | bfs_queue.push(u); |
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169 | level.set(u, l); |
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170 | if ( excess.get(u) > 0 ) stack[l].push(u); |
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171 | } |
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172 | } |
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173 | |
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174 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) { |
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175 | if ( 0 == flow.get(e) ) continue; |
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176 | NodeIt u=G.head(e); |
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177 | if ( level.get(u) >= n ) { |
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178 | bfs_queue.push(u); |
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179 | level.set(u, l); |
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180 | if ( excess.get(u) > 0 ) stack[l].push(u); |
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181 | } |
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182 | } |
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183 | } |
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184 | b=n-2; |
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185 | } |
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186 | |
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187 | |
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188 | if ( stack[b].empty() ) --b; |
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189 | else { |
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190 | |
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191 | NodeIt w=stack[b].top(); //w is a highest label active node. |
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192 | stack[b].pop(); |
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193 | int lev=level.get(w); |
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194 | T exc=excess.get(w); |
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195 | int newlevel=n; //In newlevel we bound the next level of w. |
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196 | |
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197 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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198 | |
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199 | if ( flow.get(e) == capacity.get(e) ) continue; |
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200 | NodeIt v=G.head(e); |
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201 | //e=wv |
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202 | |
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203 | if( lev > level.get(v) ) { |
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204 | /*Push is allowed now*/ |
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205 | |
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206 | if ( excess.get(v)==0 && v!=t && v!=s ) |
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207 | stack[level.get(v)].push(v); |
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208 | /*v becomes active.*/ |
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209 | |
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210 | T cap=capacity.get(e); |
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211 | T flo=flow.get(e); |
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212 | T remcap=cap-flo; |
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213 | |
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214 | if ( remcap >= exc ) { |
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215 | /*A nonsaturating push.*/ |
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216 | |
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217 | flow.set(e, flo+exc); |
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218 | excess.set(v, excess.get(v)+exc); |
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219 | exc=0; |
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220 | break; |
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221 | |
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222 | } else { |
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223 | /*A saturating push.*/ |
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224 | |
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225 | flow.set(e, cap); |
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226 | excess.set(v, excess.get(v)+remcap); |
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227 | exc-=remcap; |
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228 | } |
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229 | } else if ( newlevel > level.get(v) ){ |
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230 | newlevel = level.get(v); |
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231 | } |
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232 | |
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233 | } //for out edges wv |
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234 | |
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235 | |
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236 | if ( exc > 0 ) { |
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237 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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238 | |
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239 | if( flow.get(e) == 0 ) continue; |
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240 | NodeIt v=G.tail(e); |
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241 | //e=vw |
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242 | |
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243 | if( lev > level.get(v) ) { |
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244 | /*Push is allowed now*/ |
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245 | |
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246 | if ( excess.get(v)==0 && v!=t && v!=s ) |
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247 | stack[level.get(v)].push(v); |
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248 | /*v becomes active.*/ |
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249 | |
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250 | T flo=flow.get(e); |
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251 | |
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252 | if ( flo >= exc ) { |
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253 | /*A nonsaturating push.*/ |
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254 | |
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255 | flow.set(e, flo-exc); |
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256 | excess.set(v, excess.get(v)+exc); |
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257 | exc=0; |
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258 | break; |
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259 | } else { |
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260 | /*A saturating push.*/ |
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261 | |
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262 | excess.set(v, excess.get(v)+flo); |
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263 | exc-=flo; |
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264 | flow.set(e,0); |
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265 | } |
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266 | } else if ( newlevel > level.get(v) ) { |
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267 | newlevel = level.get(v); |
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268 | } |
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269 | } //for in edges vw |
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270 | |
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271 | } // if w still has excess after the out edge for cycle |
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272 | |
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273 | excess.set(w, exc); |
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274 | |
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275 | /* |
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276 | Relabel |
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277 | */ |
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278 | |
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279 | if ( exc > 0 ) { |
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280 | //now 'lev' is the old level of w |
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281 | |
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282 | if ( phase ) { |
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283 | level.set(w,++newlevel); |
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284 | stack[newlevel].push(w); |
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285 | b=newlevel; |
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286 | } else { |
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287 | //unlacing |
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288 | NodeIt right_n=right.get(w); |
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289 | NodeIt left_n=left.get(w); |
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290 | |
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291 | if ( right_n != 0 ) { |
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292 | if ( left_n != 0 ) { |
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293 | right.set(left_n, right_n); |
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294 | left.set(right_n, left_n); |
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295 | } else { |
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296 | level_list[lev]=right_n; |
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297 | left.set(right_n, 0); |
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298 | } |
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299 | } else { |
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300 | if ( left_n != 0 ) { |
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301 | right.set(left_n, 0); |
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302 | } else { |
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303 | level_list[lev]=0; |
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304 | } |
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305 | } |
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306 | |
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307 | |
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308 | if ( level_list[lev]==0 ) { |
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309 | |
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310 | for (int i=lev; i!=k ; ) { |
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311 | NodeIt v=level_list[++i]; |
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312 | while ( v != 0 ) { |
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313 | level.set(v,n); |
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314 | v=right.get(v); |
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315 | } |
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316 | level_list[i]=0; |
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317 | } |
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318 | |
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319 | level.set(w,n); |
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320 | |
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321 | b=--lev; |
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322 | k=b; |
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323 | |
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324 | } else { |
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325 | |
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326 | if ( newlevel == n ) { |
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327 | level.set(w,n); |
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328 | } else { |
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329 | |
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330 | level.set(w,++newlevel); |
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331 | stack[newlevel].push(w); |
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332 | b=newlevel; |
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333 | if ( k < newlevel ) ++k; |
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334 | NodeIt first=level_list[newlevel]; |
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335 | if ( first != 0 ) left.set(first,w); |
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336 | right.set(w,first); |
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337 | left.set(w,0); |
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338 | level_list[newlevel]=w; |
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339 | } |
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340 | } |
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341 | } //phase 0 |
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342 | } // if ( exc > 0 ) |
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343 | |
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344 | |
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345 | } // if stack[b] is nonempty |
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346 | |
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347 | } // while(true) |
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348 | |
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349 | |
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350 | value = excess.get(t); |
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351 | /*Max flow value.*/ |
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352 | |
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353 | |
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354 | } //void run() |
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355 | |
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356 | |
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357 | |
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358 | |
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359 | |
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360 | /* |
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361 | Returns the maximum value of a flow. |
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362 | */ |
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363 | |
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364 | T maxflow() { |
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365 | return value; |
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366 | } |
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367 | |
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368 | |
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369 | |
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370 | /* |
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371 | 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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372 | */ |
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373 | |
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374 | T flowonedge(EdgeIt e) { |
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375 | return flow.get(e); |
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376 | } |
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377 | |
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378 | |
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379 | |
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380 | FlowMap allflow() { |
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381 | return flow; |
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382 | } |
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383 | |
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384 | |
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385 | |
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386 | void allflow(FlowMap& _flow ) { |
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387 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) |
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388 | _flow.set(v,flow.get(v)); |
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389 | } |
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390 | |
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391 | |
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392 | |
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393 | /* |
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394 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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395 | */ |
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396 | |
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397 | template<typename CutMap> |
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398 | void mincut(CutMap& M) { |
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399 | |
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400 | std::queue<NodeIt> queue; |
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401 | |
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402 | M.set(s,true); |
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403 | queue.push(s); |
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404 | |
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405 | while (!queue.empty()) { |
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406 | NodeIt w=queue.front(); |
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407 | queue.pop(); |
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408 | |
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409 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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410 | NodeIt v=G.head(e); |
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411 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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412 | queue.push(v); |
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413 | M.set(v, true); |
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414 | } |
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415 | } |
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416 | |
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417 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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418 | NodeIt v=G.tail(e); |
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419 | if (!M.get(v) && flow.get(e) > 0 ) { |
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420 | queue.push(v); |
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421 | M.set(v, true); |
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422 | } |
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423 | } |
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424 | |
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425 | } |
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426 | |
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427 | } |
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428 | |
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429 | |
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430 | |
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431 | /* |
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432 | Returns the maximum min cut, by a reverse bfs |
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433 | from t in the residual graph. |
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434 | */ |
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435 | |
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436 | template<typename CutMap> |
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437 | void max_mincut(CutMap& M) { |
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438 | |
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439 | std::queue<NodeIt> queue; |
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440 | |
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441 | M.set(t,true); |
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442 | queue.push(t); |
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443 | |
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444 | while (!queue.empty()) { |
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445 | NodeIt w=queue.front(); |
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446 | queue.pop(); |
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447 | |
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448 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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449 | NodeIt v=G.tail(e); |
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450 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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451 | queue.push(v); |
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452 | M.set(v, true); |
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453 | } |
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454 | } |
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455 | |
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456 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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457 | NodeIt v=G.head(e); |
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458 | if (!M.get(v) && flow.get(e) > 0 ) { |
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459 | queue.push(v); |
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460 | M.set(v, true); |
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461 | } |
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462 | } |
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463 | } |
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464 | |
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465 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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466 | M.set(v, !M.get(v)); |
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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 | |
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472 | |
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473 | template<typename CutMap> |
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474 | void min_mincut(CutMap& M) { |
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475 | mincut(M); |
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476 | } |
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477 | |
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478 | |
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479 | |
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480 | }; |
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481 | }//namespace marci |
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482 | #endif |
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483 | |
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484 | |
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485 | |
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486 | |
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