r967:38213abd2911
Thu, 18 Mar 2010 00:30:25
[Not Reviewed]
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LEMON code without an explicit copyright notice is covered by the following |
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copyright/license. |
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Copyright (C) 2003- |
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Copyright (C) 2003-2010 Egervary Jeno Kombinatorikus Optimalizalasi |
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Kutatocsoport (Egervary Combinatorial Optimization Research Group, |
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EGRES). |
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=========================================================================== |
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Boost Software License, Version 1.0 |
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=========================================================================== |
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used easily in such algorithms. |
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\sa \ref concepts::Heap "Heap concept" |
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*/ |
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/** |
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@defgroup matrices Matrices |
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@ingroup datas |
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\brief Two dimensional data storages implemented in LEMON. |
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This group contains two dimensional data storages implemented in LEMON. |
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*/ |
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/** |
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@defgroup auxdat Auxiliary Data Structures |
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@ingroup datas |
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\brief Auxiliary data structures implemented in LEMON. |
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This group contains some data structures implemented in LEMON in |
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order to make it easier to implement combinatorial algorithms. |
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length. For an arbitrary length function, the negative of the minimum |
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cycle mean is the smallest \f$\epsilon\f$ value so that increasing the |
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arc lengths uniformly by \f$\epsilon\f$ results in a conservative length |
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function. |
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LEMON contains three algorithms for solving the minimum mean cycle problem: |
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- \ref |
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- \ref KarpMmc Karp's original algorithm \ref amo93networkflows, |
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\ref dasdan98minmeancycle. |
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- \ref |
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- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved |
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version of Karp's algorithm \ref dasdan98minmeancycle. |
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- \ref |
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- \ref HowardMmc Howard's policy iteration algorithm |
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\ref dasdan98minmeancycle. |
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In practice, the Howard algorithm proved to be by far the most efficient |
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one, though the best known theoretical bound on its running time is |
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exponential. |
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Both Karp and HartmannOrlin algorithms run in time O(ne) and use space |
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O(n<sup>2</sup>+e), but the latter one is typically faster due to the |
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applied early termination scheme. |
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In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the |
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most efficient one, though the best known theoretical bound on its running |
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time is exponential. |
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Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms |
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run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is |
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typically faster due to the applied early termination scheme. |
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*/ |
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/** |
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@defgroup matching Matching Algorithms |
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@ingroup algs |
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\brief Algorithms for finding matchings in graphs and bipartite graphs. |
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///\file |
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///\brief A tool to parse command line arguments. |
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namespace lemon {
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///Exception used by ArgParser |
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///Exception used by ArgParser. |
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/// |
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class ArgParserException : public Exception {
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public: |
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/// Reasons for failure |
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/// Reasons for failure. |
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/// |
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enum Reason {
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HELP, /// <tt>--help</tt> option was given |
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UNKNOWN_OPT, /// Unknown option was given |
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HELP, ///< <tt>--help</tt> option was given. |
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UNKNOWN_OPT, ///< Unknown option was given. |
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INVALID_OPT ///< Invalid combination of options. |
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}; |
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private: |
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Reason _reason; |
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public: |
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/// \brief Default traits class of HartmannOrlinMmc class. |
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/// |
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/// Default traits class of HartmannOrlinMmc class. |
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/// \tparam GR The type of the digraph. |
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/// \tparam CM The type of the cost map. |
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/// It must conform to the \ref concepts:: |
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/// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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#ifdef DOXYGEN |
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template <typename GR, typename CM> |
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#else |
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template <typename GR, typename CM, |
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bool integer = std::numeric_limits<typename CM::Value>::is_integer> |
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#endif |
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/// \brief Implementation of the Hartmann-Orlin algorithm for finding |
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/// a minimum mean cycle. |
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/// |
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/// This class implements the Hartmann-Orlin algorithm for finding |
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/// a directed cycle of minimum mean cost in a digraph |
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/// \ref amo93networkflows, \ref dasdan98minmeancycle. |
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/// It is an improved version of \ref |
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/// It is an improved version of \ref KarpMmc "Karp"'s original algorithm, |
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/// it applies an efficient early termination scheme. |
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/// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
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/// |
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/// \tparam GR The type of the digraph the algorithm runs on. |
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/// \tparam CM The type of the cost map. The default |
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/// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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