@defgroup min_mean_cycle Minimum Mean Cycle Algorithms

 @ingroup algs

 \brief Algorithms for finding minimum mean cycles.

 This group contains the algorithms for finding minimum mean cycles.

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

 of minimum mean length (cost) in a digraph.

 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.

 This problem has an important connection to \e conservative \e length

 \e functions, too. A length function on the arcs of a digraph is called

 conservative if and only if there is no directed cycle of negative total

 length. For an arbitrary length function, the negative of the minimum

 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

 function.

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

 - \ref Karp "Karp"'s original algorithm.

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

   version of Karp's algorithm.

 - \ref Howard "Howard"'s policy iteration algorithm.

 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

 exponential.

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

 O(n<sup>2</sup>+e), but the latter one is typically faster due to the

 applied early termination scheme.

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