1.1 --- a/lemon/cycle_canceling.h	Mon Jan 30 23:24:14 2012 +0100
     1.2 +++ b/lemon/cycle_canceling.h	Mon Jan 30 23:24:40 2012 +0100
     1.3 @@ -48,11 +48,12 @@
     1.4    /// algorithms for finding a \ref min_cost_flow "minimum cost flow"
     1.5    /// \ref amo93networkflows, \ref klein67primal,
     1.6    /// \ref goldberg89cyclecanceling.
     1.7 -  /// The most efficent one (both theoretically and practically)
     1.8 -  /// is the \ref CANCEL_AND_TIGHTEN "Cancel and Tighten" algorithm,
     1.9 -  /// thus it is the default method.
    1.10 -  /// It is strongly polynomial, but in practice, it is typically much
    1.11 -  /// slower than the scaling algorithms and NetworkSimplex.
    1.12 +  /// The most efficent one is the \ref CANCEL_AND_TIGHTEN
    1.13 +  /// "Cancel-and-Tighten" algorithm, thus it is the default method.
    1.14 +  /// It runs in strongly polynomial time, but in practice, it is typically
    1.15 +  /// orders of magnitude slower than the scaling algorithms and
    1.16 +  /// \ref NetworkSimplex.
    1.17 +  /// (For more information, see \ref min_cost_flow_algs "the module page".)
    1.18    ///
    1.19    /// Most of the parameters of the problem (except for the digraph)
    1.20    /// can be given using separate functions, and the algorithm can be
    1.21 @@ -116,26 +117,28 @@
    1.22      /// for the \ref run() function.
    1.23      ///
    1.24      /// \ref CycleCanceling provides three different cycle-canceling
    1.25 -    /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel and Tighten"
    1.26 +    /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel-and-Tighten"
    1.27      /// is used, which is by far the most efficient and the most robust.
    1.28      /// However, the other methods can be selected using the \ref run()
    1.29      /// function with the proper parameter.
    1.30      enum Method {
    1.31        /// A simple cycle-canceling method, which uses the
    1.32 -      /// \ref BellmanFord "Bellman-Ford" algorithm with limited iteration
    1.33 -      /// number for detecting negative cycles in the residual network.
    1.34 +      /// \ref BellmanFord "Bellman-Ford" algorithm for detecting negative
    1.35 +      /// cycles in the residual network.
    1.36 +      /// The number of Bellman-Ford iterations is bounded by a successively
    1.37 +      /// increased limit.
    1.38        SIMPLE_CYCLE_CANCELING,
    1.39        /// The "Minimum Mean Cycle-Canceling" algorithm, which is a
    1.40        /// well-known strongly polynomial method
    1.41        /// \ref goldberg89cyclecanceling. It improves along a
    1.42        /// \ref min_mean_cycle "minimum mean cycle" in each iteration.
    1.43 -      /// Its running time complexity is O(n<sup>2</sup>m<sup>3</sup>log(n)).
    1.44 +      /// Its running time complexity is O(n<sup>2</sup>e<sup>3</sup>log(n)).
    1.45        MINIMUM_MEAN_CYCLE_CANCELING,
    1.46 -      /// The "Cancel And Tighten" algorithm, which can be viewed as an
    1.47 +      /// The "Cancel-and-Tighten" algorithm, which can be viewed as an
    1.48        /// improved version of the previous method
    1.49        /// \ref goldberg89cyclecanceling.
    1.50        /// It is faster both in theory and in practice, its running time
    1.51 -      /// complexity is O(n<sup>2</sup>m<sup>2</sup>log(n)).
    1.52 +      /// complexity is O(n<sup>2</sup>e<sup>2</sup>log(n)).
    1.53        CANCEL_AND_TIGHTEN
    1.54      };
    1.55  
    1.56 @@ -610,7 +613,8 @@
    1.57        return _res_cap[_arc_idb[a]];
    1.58      }
    1.59  
    1.60 -    /// \brief Return the flow map (the primal solution).
    1.61 +    /// \brief Copy the flow values (the primal solution) into the
    1.62 +    /// given map.
    1.63      ///
    1.64      /// This function copies the flow value on each arc into the given
    1.65      /// map. The \c Value type of the algorithm must be convertible to
    1.66 @@ -634,7 +638,8 @@
    1.67        return static_cast<Cost>(_pi[_node_id[n]]);
    1.68      }
    1.69  
    1.70 -    /// \brief Return the potential map (the dual solution).
    1.71 +    /// \brief Copy the potential values (the dual solution) into the
    1.72 +    /// given map.
    1.73      ///
    1.74      /// This function copies the potential (dual value) of each node
    1.75      /// into the given map.
    1.76 @@ -954,7 +959,7 @@
    1.77        }
    1.78      }
    1.79  
    1.80 -    // Execute the "Cancel And Tighten" method
    1.81 +    // Execute the "Cancel-and-Tighten" method
    1.82      void startCancelAndTighten() {
    1.83        // Constants for the min mean cycle computations
    1.84        const double LIMIT_FACTOR = 1.0;