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46 /// This algorithm is a highly efficient specialized version of the |
46 /// This algorithm is a highly efficient specialized version of the |
47 /// linear programming simplex method directly for the minimum cost |
47 /// linear programming simplex method directly for the minimum cost |
48 /// flow problem. |
48 /// flow problem. |
49 /// |
49 /// |
50 /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest |
50 /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest |
51 /// implementations available in LEMON for this problem. |
51 /// implementations available in LEMON for solving this problem. |
|
52 /// (For more information, see \ref min_cost_flow_algs "the module page".) |
52 /// Furthermore, this class supports both directions of the supply/demand |
53 /// Furthermore, this class supports both directions of the supply/demand |
53 /// inequality constraints. For more information, see \ref SupplyType. |
54 /// inequality constraints. For more information, see \ref SupplyType. |
54 /// |
55 /// |
55 /// Most of the parameters of the problem (except for the digraph) |
56 /// Most of the parameters of the problem (except for the digraph) |
56 /// can be given using separate functions, and the algorithm can be |
57 /// can be given using separate functions, and the algorithm can be |
1007 /// \pre \ref run() must be called before using this function. |
1008 /// \pre \ref run() must be called before using this function. |
1008 Value flow(const Arc& a) const { |
1009 Value flow(const Arc& a) const { |
1009 return _flow[_arc_id[a]]; |
1010 return _flow[_arc_id[a]]; |
1010 } |
1011 } |
1011 |
1012 |
1012 /// \brief Return the flow map (the primal solution). |
1013 /// \brief Copy the flow values (the primal solution) into the |
|
1014 /// given map. |
1013 /// |
1015 /// |
1014 /// This function copies the flow value on each arc into the given |
1016 /// This function copies the flow value on each arc into the given |
1015 /// map. The \c Value type of the algorithm must be convertible to |
1017 /// map. The \c Value type of the algorithm must be convertible to |
1016 /// the \c Value type of the map. |
1018 /// the \c Value type of the map. |
1017 /// |
1019 /// |
1031 /// \pre \ref run() must be called before using this function. |
1033 /// \pre \ref run() must be called before using this function. |
1032 Cost potential(const Node& n) const { |
1034 Cost potential(const Node& n) const { |
1033 return _pi[_node_id[n]]; |
1035 return _pi[_node_id[n]]; |
1034 } |
1036 } |
1035 |
1037 |
1036 /// \brief Return the potential map (the dual solution). |
1038 /// \brief Copy the potential values (the dual solution) into the |
|
1039 /// given map. |
1037 /// |
1040 /// |
1038 /// This function copies the potential (dual value) of each node |
1041 /// This function copies the potential (dual value) of each node |
1039 /// into the given map. |
1042 /// into the given map. |
1040 /// The \c Cost type of the algorithm must be convertible to the |
1043 /// The \c Cost type of the algorithm must be convertible to the |
1041 /// \c Value type of the map. |
1044 /// \c Value type of the map. |