COIN-OR::LEMON - Graph Library

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  • lemon/cost_scaling.h

    r1298 r1297  
    33 * This file is a part of LEMON, a generic C++ optimization library.
    44 *
    5  * Copyright (C) 2003-2013
     5 * Copyright (C) 2003-2010
    66 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    77 * (Egervary Research Group on Combinatorial Optimization, EGRES).
     
    9292  /// \ref CostScaling implements a cost scaling algorithm that performs
    9393  /// push/augment and relabel operations for finding a \ref min_cost_flow
    94   /// "minimum cost flow" \cite amo93networkflows,
    95   /// \cite goldberg90approximation,
    96   /// \cite goldberg97efficient, \cite bunnagel98efficient.
     94  /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation,
     95  /// \ref goldberg97efficient, \ref bunnagel98efficient.
    9796  /// It is a highly efficient primal-dual solution method, which
    9897  /// can be viewed as the generalization of the \ref Preflow
    9998  /// "preflow push-relabel" algorithm for the maximum flow problem.
    100   /// It is a polynomial algorithm, its running time complexity is
    101   /// \f$O(n^2m\log(nK))\f$, where <i>K</i> denotes the maximum arc cost.
    10299  ///
    103100  /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
     
    154151    typedef typename TR::LargeCost LargeCost;
    155152
    156     /// \brief The \ref lemon::CostScalingDefaultTraits "traits class"
    157     /// of the algorithm
     153    /// The \ref CostScalingDefaultTraits "traits class" of the algorithm
    158154    typedef TR Traits;
    159155
     
    215211    typedef std::vector<LargeCost> LargeCostVector;
    216212    typedef std::vector<char> BoolVector;
    217     // Note: vector<char> is used instead of vector<bool>
    218     // for efficiency reasons
     213    // Note: vector<char> is used instead of vector<bool> for efficiency reasons
    219214
    220215  private:
     
    672667    ///
    673668    /// This function returns the total cost of the found flow.
    674     /// Its complexity is O(m).
     669    /// Its complexity is O(e).
    675670    ///
    676671    /// \note The return type of the function can be specified as a
     
    906901      return OPTIMAL;
    907902    }
    908 
     903   
    909904    // Check if the upper bound is greater than or equal to the lower bound
    910905    // on each forward arc.
     
    12871282          _buckets[r] = _bucket_next[u];
    12881283
    1289           // Search the incoming arcs of u
     1284          // Search the incomming arcs of u
    12901285          LargeCost pi_u = _pi[u];
    12911286          int last_out = _first_out[u+1];
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