Changeset 768:0a42883c8221 in lemon1.2 for doc/groups.dox
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 08/12/09 09:45:15 (10 years ago)
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 default
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doc/groups.dox
r663 r768 392 392 393 393 /** 394 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms 395 @ingroup algs 396 \brief Algorithms for finding minimum mean cycles. 397 398 This group contains the algorithms for finding minimum mean cycles. 399 400 The \e minimum \e mean \e cycle \e problem is to find a directed cycle 401 of minimum mean length (cost) in a digraph. 402 The mean length of a cycle is the average length of its arcs, i.e. the 403 ratio between the total length of the cycle and the number of arcs on it. 404 405 This problem has an important connection to \e conservative \e length 406 \e functions, too. A length function on the arcs of a digraph is called 407 conservative if and only if there is no directed cycle of negative total 408 length. For an arbitrary length function, the negative of the minimum 409 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the 410 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length 411 function. 412 413 LEMON contains three algorithms for solving the minimum mean cycle problem: 414  \ref Karp "Karp"'s original algorithm. 415  \ref HartmannOrlin "HartmannOrlin"'s algorithm, which is an improved 416 version of Karp's algorithm. 417  \ref Howard "Howard"'s policy iteration algorithm. 418 419 In practice, the Howard algorithm proved to be by far the most efficient 420 one, though the best known theoretical bound on its running time is 421 exponential. 422 Both Karp and HartmannOrlin algorithms run in time O(ne) and use space 423 O(n<sup>2</sup>+e), but the latter one is typically faster due to the 424 applied early termination scheme. 425 */ 426 427 /** 394 428 @defgroup graph_properties Connectivity and Other Graph Properties 395 429 @ingroup algs
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