COIN-OR::LEMON - Graph Library

1 edited


  • doc/groups.dox

    r755 r770  
     456@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
     457@ingroup algs
     458\brief Algorithms for finding minimum mean cycles.
     460This group contains the algorithms for finding minimum mean cycles.
     462The \e minimum \e mean \e cycle \e problem is to find a directed cycle
     463of minimum mean length (cost) in a digraph.
     464The mean length of a cycle is the average length of its arcs, i.e. the
     465ratio between the total length of the cycle and the number of arcs on it.
     467This problem has an important connection to \e conservative \e length
     468\e functions, too. A length function on the arcs of a digraph is called
     469conservative if and only if there is no directed cycle of negative total
     470length. For an arbitrary length function, the negative of the minimum
     471cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
     472arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
     475LEMON contains three algorithms for solving the minimum mean cycle problem:
     476- \ref Karp "Karp"'s original algorithm.
     477- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
     478  version of Karp's algorithm.
     479- \ref Howard "Howard"'s policy iteration algorithm.
     481In practice, the Howard algorithm proved to be by far the most efficient
     482one, though the best known theoretical bound on its running time is
     484Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
     485O(n<sup>2</sup>+e), but the latter one is typically faster due to the
     486applied early termination scheme.
    456490@defgroup matching Matching Algorithms
    457491@ingroup algs
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