diff -r 58c330ad0b5c -r 6be1f9bd2ac0 doc/groups.dox --- a/doc/groups.dox Sun Oct 04 10:15:32 2009 +0200 +++ b/doc/groups.dox Wed Dec 09 11:14:06 2009 +0100 @@ -280,6 +280,28 @@ */ /** +@defgroup geomdat Geometric Data Structures +@ingroup auxdat +\brief Geometric data structures implemented in LEMON. + +This group contains geometric data structures implemented in LEMON. + + - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional + vector with the usual operations. + - \ref lemon::dim2::Box "dim2::Box" can be used to determine the + rectangular bounding box of a set of \ref lemon::dim2::Point + "dim2::Point"'s. +*/ + +/** +@defgroup matrices Matrices +@ingroup auxdat +\brief Two dimensional data storages implemented in LEMON. + +This group contains two dimensional data storages implemented in LEMON. +*/ + +/** @defgroup algs Algorithms \brief This group contains the several algorithms implemented in LEMON. @@ -294,7 +316,8 @@ \brief Common graph search algorithms. This group contains the common graph search algorithms, namely -\e breadth-first \e search (BFS) and \e depth-first \e search (DFS). +\e breadth-first \e search (BFS) and \e depth-first \e search (DFS) +\ref clrs01algorithms. */ /** @@ -302,7 +325,8 @@ @ingroup algs \brief Algorithms for finding shortest paths. -This group contains the algorithms for finding shortest paths in digraphs. +This group contains the algorithms for finding shortest paths in digraphs +\ref clrs01algorithms. - \ref Dijkstra algorithm for finding shortest paths from a source node when all arc lengths are non-negative. @@ -319,12 +343,21 @@ */ /** +@defgroup spantree Minimum Spanning Tree Algorithms +@ingroup algs +\brief Algorithms for finding minimum cost spanning trees and arborescences. + +This group contains the algorithms for finding minimum cost spanning +trees and arborescences \ref clrs01algorithms. +*/ + +/** @defgroup max_flow Maximum Flow Algorithms @ingroup algs \brief Algorithms for finding maximum flows. This group contains the algorithms for finding maximum flows and -feasible circulations. +feasible circulations \ref clrs01algorithms, \ref amo93networkflows. The \e maximum \e flow \e problem is to find a flow of maximum value between a single source and a single target. Formally, there is a \f$G=(V,A)\f$ @@ -339,12 +372,16 @@ \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f] LEMON contains several algorithms for solving maximum flow problems: -- \ref EdmondsKarp Edmonds-Karp algorithm. -- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm. -- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees. -- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees. +- \ref EdmondsKarp Edmonds-Karp algorithm + \ref edmondskarp72theoretical. +- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm + \ref goldberg88newapproach. +- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees + \ref dinic70algorithm, \ref sleator83dynamic. +- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees + \ref goldberg88newapproach, \ref sleator83dynamic. -In most cases the \ref Preflow "Preflow" algorithm provides the +In most cases the \ref Preflow algorithm provides the fastest method for computing a maximum flow. All implementations also provide functions to query the minimum cut, which is the dual problem of maximum flow. @@ -362,18 +399,22 @@ \brief Algorithms for finding minimum cost flows and circulations. This group contains the algorithms for finding minimum cost flows and -circulations. For more information about this problem and its dual -solution see \ref min_cost_flow "Minimum Cost Flow Problem". +circulations \ref amo93networkflows. For more information about this +problem and its dual solution, see \ref min_cost_flow +"Minimum Cost Flow Problem". LEMON contains several algorithms for this problem. - \ref NetworkSimplex Primal Network Simplex algorithm with various - pivot strategies. + pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on - cost scaling. + cost scaling \ref goldberg90approximation, \ref goldberg97efficient, + \ref bunnagel98efficient. - \ref CapacityScaling Successive Shortest %Path algorithm with optional - capacity scaling. - - \ref CancelAndTighten The Cancel and Tighten algorithm. - - \ref CycleCanceling Cycle-Canceling algorithms. + capacity scaling \ref edmondskarp72theoretical. + - \ref CancelAndTighten The Cancel and Tighten algorithm + \ref goldberg89cyclecanceling. + - \ref CycleCanceling Cycle-Canceling algorithms + \ref klein67primal, \ref goldberg89cyclecanceling. In general NetworkSimplex is the most efficient implementation, but in special cases other algorithms could be faster. @@ -396,7 +437,7 @@ cut is the \f$X\f$ solution of the next optimization problem: \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} - \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f] + \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f] LEMON contains several algorithms related to minimum cut problems: @@ -412,27 +453,40 @@ */ /** -@defgroup graph_properties Connectivity and Other Graph Properties +@defgroup min_mean_cycle Minimum Mean Cycle Algorithms @ingroup algs -\brief Algorithms for discovering the graph properties +\brief Algorithms for finding minimum mean cycles. -This group contains the algorithms for discovering the graph properties -like connectivity, bipartiteness, euler property, simplicity etc. +This group contains the algorithms for finding minimum mean cycles +\ref clrs01algorithms, \ref amo93networkflows. -\image html edge_biconnected_components.png -\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth -*/ +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. -/** -@defgroup planar Planarity Embedding and Drawing -@ingroup algs -\brief Algorithms for planarity checking, embedding and drawing +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. -This group contains the algorithms for planarity checking, -embedding and drawing. +LEMON contains three algorithms for solving the minimum mean cycle problem: +- \ref Karp "Karp"'s original algorithm \ref amo93networkflows, + \ref dasdan98minmeancycle. +- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved + version of Karp's algorithm \ref dasdan98minmeancycle. +- \ref Howard "Howard"'s policy iteration algorithm + \ref dasdan98minmeancycle. -\image html planar.png -\image latex planar.eps "Plane graph" width=\textwidth +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(n2+e), but the latter one is typically faster due to the +applied early termination scheme. */ /** @@ -476,12 +530,36 @@ */ /** -@defgroup spantree Minimum Spanning Tree Algorithms +@defgroup graph_properties Connectivity and Other Graph Properties @ingroup algs -\brief Algorithms for finding minimum cost spanning trees and arborescences. +\brief Algorithms for discovering the graph properties -This group contains the algorithms for finding minimum cost spanning -trees and arborescences. +This group contains the algorithms for discovering the graph properties +like connectivity, bipartiteness, euler property, simplicity etc. + +\image html connected_components.png +\image latex connected_components.eps "Connected components" width=\textwidth +*/ + +/** +@defgroup planar Planarity Embedding and Drawing +@ingroup algs +\brief Algorithms for planarity checking, embedding and drawing + +This group contains the algorithms for planarity checking, +embedding and drawing. + +\image html planar.png +\image latex planar.eps "Plane graph" width=\textwidth +*/ + +/** +@defgroup approx Approximation Algorithms +@ingroup algs +\brief Approximation algorithms. + +This group contains the approximation and heuristic algorithms +implemented in LEMON. */ /** @@ -494,15 +572,6 @@ */ /** -@defgroup approx Approximation Algorithms -@ingroup algs -\brief Approximation algorithms. - -This group contains the approximation and heuristic algorithms -implemented in LEMON. -*/ - -/** @defgroup gen_opt_group General Optimization Tools \brief This group contains some general optimization frameworks implemented in LEMON. @@ -512,13 +581,16 @@ */ /** -@defgroup lp_group Lp and Mip Solvers +@defgroup lp_group LP and MIP Solvers @ingroup gen_opt_group -\brief Lp and Mip solver interfaces for LEMON. +\brief LP and MIP solver interfaces for LEMON. -This group contains Lp and Mip solver interfaces for LEMON. The -various LP solvers could be used in the same manner with this -interface. +This group contains LP and MIP solver interfaces for LEMON. +Various LP solvers could be used in the same manner with this +high-level interface. + +The currently supported solvers are \ref glpk, \ref clp, \ref cbc, +\ref cplex, \ref soplex. */ /** @@ -608,7 +680,7 @@ */ /** -@defgroup dimacs_group DIMACS format +@defgroup dimacs_group DIMACS Format @ingroup io_group \brief Read and write files in DIMACS format @@ -657,8 +729,8 @@ @ingroup concept \brief Skeleton and concept checking classes for graph structures -This group contains the skeletons and concept checking classes of LEMON's -graph structures and helper classes used to implement these. +This group contains the skeletons and concept checking classes of +graph structures. */ /** @@ -670,6 +742,15 @@ */ /** +@defgroup tools Standalone Utility Applications + +Some utility applications are listed here. + +The standard compilation procedure (./configure;make) will compile +them, as well. +*/ + +/** \anchor demoprograms @defgroup demos Demo Programs @@ -681,13 +762,4 @@ make check commands. */ -/** -@defgroup tools Standalone Utility Applications - -Some utility applications are listed here. - -The standard compilation procedure (./configure;make) will compile -them, as well. -*/ - }