COIN-OR::LEMON - Graph Library

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  • lemon/cycle_canceling.h

    r1013 r1053  
    4848  /// \ref CycleCanceling implements three different cycle-canceling
    4949  /// algorithms for finding a \ref min_cost_flow "minimum cost flow"
    50   /// \ref amo93networkflows, \ref klein67primal,
    51   /// \ref goldberg89cyclecanceling.
     50  /// \cite amo93networkflows, \cite klein67primal,
     51  /// \cite goldberg89cyclecanceling.
    5252  /// The most efficent one is the \ref CANCEL_AND_TIGHTEN
    5353  /// "Cancel-and-Tighten" algorithm, thus it is the default method.
    54   /// It runs in strongly polynomial time, but in practice, it is typically
    55   /// orders of magnitude slower than the scaling algorithms and
    56   /// \ref NetworkSimplex.
     54  /// It runs in strongly polynomial time O(n<sup>2</sup>e<sup>2</sup>log(n)),
     55  /// but in practice, it is typically orders of magnitude slower than
     56  /// the scaling algorithms and \ref NetworkSimplex.
    5757  /// (For more information, see \ref min_cost_flow_algs "the module page".)
    5858  ///
     
    132132      /// The "Minimum Mean Cycle-Canceling" algorithm, which is a
    133133      /// well-known strongly polynomial method
    134       /// \ref goldberg89cyclecanceling. It improves along a
     134      /// \cite goldberg89cyclecanceling. It improves along a
    135135      /// \ref min_mean_cycle "minimum mean cycle" in each iteration.
    136136      /// Its running time complexity is O(n<sup>2</sup>e<sup>3</sup>log(n)).
     
    138138      /// The "Cancel-and-Tighten" algorithm, which can be viewed as an
    139139      /// improved version of the previous method
    140       /// \ref goldberg89cyclecanceling.
     140      /// \cite goldberg89cyclecanceling.
    141141      /// It is faster both in theory and in practice, its running time
    142142      /// complexity is O(n<sup>2</sup>e<sup>2</sup>log(n)).
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