# Changes in doc/groups.dox[710:8b0df68370a4:963:3ed8f7c8bed8] in lemon

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 r710 * This file is a part of LEMON, a generic C++ optimization library. * * Copyright (C) 2003-2009 * Copyright (C) 2003-2010 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). /** @defgroup matrices Matrices @ingroup datas \brief Two dimensional data storages implemented in LEMON. This group contains two dimensional data storages implemented in LEMON. */ /** @defgroup paths Path Structures @ingroup datas any kind of path structure. \sa lemon::concepts::Path \sa \ref concepts::Path "Path concept" */ /** @defgroup heaps Heap Structures @ingroup datas \brief %Heap structures implemented in LEMON. This group contains the heap structures implemented in LEMON. LEMON provides several heap classes. They are efficient implementations of the abstract data type \e priority \e queue. They store items with specified values called \e priorities in such a way that finding and removing the item with minimum priority are efficient. The basic operations are adding and erasing items, changing the priority of an item, etc. Heaps are crucial in several algorithms, such as Dijkstra and Prim. The heap implementations have the same interface, thus any of them can be used easily in such algorithms. \sa \ref concepts::Heap "Heap concept" */ /** @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 algs Algorithms \brief This group contains the several 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. */ \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 but the digraph should not contain directed cycles with negative total length. - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms for solving the \e all-pairs \e shortest \e paths \e problem when arc lenghts can be either positive or negative, but the digraph should not contain directed cycles with negative total length. - \ref Suurballe A successive shortest path algorithm for finding arc-disjoint paths between two nodes having minimum total length. /** @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 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 \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. In most cases the \ref Preflow "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. \ref Circulation is a preflow push-relabel algorithm implemented directly \ref Preflow is an efficient implementation of Goldberg-Tarjan's preflow push-relabel algorithm \ref goldberg88newapproach for finding maximum flows. It also provides functions to query the minimum cut, which is the dual problem of maximum flow. \ref Circulation is a preflow push-relabel algorithm implemented directly for finding feasible circulations, which is a somewhat different problem, but it is strongly related to maximum flow. 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. - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on cost scaling. - \ref CapacityScaling Successive Shortest %Path algorithm with optional capacity scaling. - \ref CancelAndTighten The Cancel and Tighten algorithm. - \ref CycleCanceling Cycle-Canceling algorithms. pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. - \ref CostScaling Cost Scaling algorithm based on push/augment and relabel operations \ref goldberg90approximation, \ref goldberg97efficient, \ref bunnagel98efficient. - \ref CapacityScaling Capacity Scaling algorithm based on the successive shortest path method \ref edmondskarp72theoretical. - \ref CycleCanceling Cycle-Canceling algorithms, two of which are strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling. In general NetworkSimplex is the most efficient implementation, \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: - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut in directed graphs. - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for calculating minimum cut in undirected graphs. - \ref GomoryHu "Gomory-Hu tree computation" for calculating all-pairs minimum cut in undirected graphs. /** @defgroup graph_properties Connectivity and Other Graph Properties @ingroup algs \brief Algorithms for discovering the graph properties This group contains the algorithms for discovering the graph properties like connectivity, bipartiteness, euler property, simplicity etc. \image html edge_biconnected_components.png \image latex edge_biconnected_components.eps "bi-edge-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 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 \ref clrs01algorithms, \ref amo93networkflows. 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 KarpMmc Karp's original algorithm \ref amo93networkflows, \ref dasdan98minmeancycle. - \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved version of Karp's algorithm \ref dasdan98minmeancycle. - \ref HowardMmc Howard's policy iteration algorithm \ref dasdan98minmeancycle. In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the most efficient one, though the best known theoretical bound on its running time is exponential. Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" 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. */ The matching algorithms implemented in LEMON: - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm for calculating maximum cardinality matching in bipartite graphs. - \ref PrBipartiteMatching Push-relabel algorithm for calculating maximum cardinality matching in bipartite graphs. - \ref MaxWeightedBipartiteMatching Successive shortest path algorithm for calculating maximum weighted matching and maximum weighted bipartite matching in bipartite graphs. - \ref MinCostMaxBipartiteMatching Successive shortest path algorithm for calculating minimum cost maximum matching in bipartite graphs. - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating maximum cardinality matching in general graphs. Edmond's blossom shrinking algorithm for calculating maximum weighted perfect matching in general graphs. \image html bipartite_matching.png \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth */ /** @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 MaxFractionalMatching Push-relabel algorithm for calculating maximum cardinality fractional matching in general graphs. - \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating maximum weighted fractional matching in general graphs. - \ref MaxWeightedPerfectFractionalMatching Augmenting path algorithm for calculating maximum weighted perfect fractional matching in general graphs. \image html matching.png \image latex matching.eps "Min Cost Perfect Matching" width=\textwidth */ /** @defgroup graph_properties Connectivity and Other Graph Properties @ingroup algs \brief Algorithms for discovering the graph properties 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 */ This group contains some algorithms implemented in LEMON in order to make it easier to implement complex algorithms. */ /** @defgroup approx Approximation Algorithms @ingroup algs \brief Approximation algorithms. This group contains the approximation and heuristic algorithms implemented in LEMON. */ /** @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. This group contains Lp and Mip solver interfaces for LEMON. The various LP solvers could be used in the same manner with this interface. */ /** @defgroup lp_utils Tools for Lp and Mip Solvers @ingroup lp_group \brief Helper tools to the Lp and Mip solvers. This group adds some helper tools to general optimization framework implemented in LEMON. */ /** @defgroup metah Metaheuristics @ingroup gen_opt_group \brief Metaheuristics for LEMON library. This group contains some metaheuristic optimization tools. \brief LP and MIP solver interfaces for LEMON. 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. */ /** @defgroup dimacs_group DIMACS format @defgroup dimacs_group DIMACS Format @ingroup io_group \brief Read and write files in DIMACS format \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. */ /** @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 tools Standalone Utility Applications Some utility applications are listed here. The standard compilation procedure (./configure;make) will compile them, as well. */ }