1.1 --- a/doc/groups.dox	Tue Aug 11 22:52:35 2009 +0200
     1.2 +++ b/doc/groups.dox	Wed Aug 12 09:45:15 2009 +0200
     1.3 @@ -391,6 +391,40 @@
     1.4  */
     1.5  
     1.6  /**
     1.7 +@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
     1.8 +@ingroup algs
     1.9 +\brief Algorithms for finding minimum mean cycles.
    1.10 +
    1.11 +This group contains the algorithms for finding minimum mean cycles.
    1.12 +
    1.13 +The \e minimum \e mean \e cycle \e problem is to find a directed cycle
    1.14 +of minimum mean length (cost) in a digraph.
    1.15 +The mean length of a cycle is the average length of its arcs, i.e. the
    1.16 +ratio between the total length of the cycle and the number of arcs on it.
    1.17 +
    1.18 +This problem has an important connection to \e conservative \e length
    1.19 +\e functions, too. A length function on the arcs of a digraph is called
    1.20 +conservative if and only if there is no directed cycle of negative total
    1.21 +length. For an arbitrary length function, the negative of the minimum
    1.22 +cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
    1.23 +arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
    1.24 +function.
    1.25 +
    1.26 +LEMON contains three algorithms for solving the minimum mean cycle problem:
    1.27 +- \ref Karp "Karp"'s original algorithm.
    1.28 +- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
    1.29 +  version of Karp's algorithm.
    1.30 +- \ref Howard "Howard"'s policy iteration algorithm.
    1.31 +
    1.32 +In practice, the Howard algorithm proved to be by far the most efficient
    1.33 +one, though the best known theoretical bound on its running time is
    1.34 +exponential.
    1.35 +Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
    1.36 +O(n<sup>2</sup>+e), but the latter one is typically faster due to the
    1.37 +applied early termination scheme.
    1.38 +*/
    1.39 +
    1.40 +/**
    1.41  @defgroup graph_properties Connectivity and Other Graph Properties
    1.42  @ingroup algs
    1.43  \brief Algorithms for discovering the graph properties