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 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms

 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms

 @ingroup algs

 @ingroup algs

 \brief Algorithms for finding minimum mean cycles.

 \brief Algorithms for finding minimum mean cycles.

 The \e minimum \e mean \e cycle \e problem is to find a directed cycle

 The \e minimum \e mean \e cycle \e problem is to find a directed cycle

 of minimum mean length (cost) in a digraph.

 of minimum mean length (cost) in a digraph.

 The mean length of a cycle is the average length of its arcs, i.e. the

 The mean length of a cycle is the average length of its arcs, i.e. the

 ratio between the total length of the cycle and the number of arcs on it.

 ratio between the total length of the cycle and the number of arcs on it.

 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the

 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the

 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length

 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length

 function.

 function.

 LEMON contains three algorithms for solving the minimum mean cycle problem:

 LEMON contains three algorithms for solving the minimum mean cycle problem:

 - \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved

 - \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved

 In practice, the Howard algorithm proved to be by far the most efficient

 In practice, the Howard algorithm proved to be by far the most efficient

 one, though the best known theoretical bound on its running time is

 one, though the best known theoretical bound on its running time is

 exponential.

 exponential.

 Both Karp and HartmannOrlin algorithms run in time O(ne) and use space

 Both Karp and HartmannOrlin algorithms run in time O(ne) and use space