# Changeset 327:12626fc94ccf in lemon for doc/groups.dox

Ignore:
Timestamp:
10/09/08 15:37:44 (11 years ago)
Branch:
1.0
Parents:
326:de38fca76780 (diff), 315:c175e387da19 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.
Phase:
public
Message:

Merge from trunk

Files:
2 edited

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Unmodified
 r314 some graph features like arc/edge or node deletion. Alteration of standard containers need a very limited number of operations, these together satisfy the everyday requirements. In the case of graph structures, different operations are needed which do not alter the physical graph, but gives another view. If some nodes or arcs have to be hidden or the reverse oriented graph have to be used, then this is the case. It also may happen that in a flow implementation the residual graph can be accessed by another algorithm, or a node-set is to be shrunk for another algorithm. LEMON also provides a variety of graphs for these requirements called \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only in conjunction with other graph representations. You are free to use the graph structure that fit your requirements the best, most graph algorithms and auxiliary data structures can be used See also: \ref graph_concepts "Graph Structure Concepts". */ /** @defgroup semi_adaptors Semi-Adaptor Classes for Graphs @ingroup graphs \brief Graph types between real graphs and graph adaptors. This group describes some graph types between real graphs and graph adaptors. These classes wrap graphs to give new functionality as the adaptors do it. On the other hand they are not light-weight structures as the adaptors. */ /** @defgroup matrices Matrices @ingroup datas \brief Two dimensional data storages implemented in LEMON. This group describes two dimensional data storages implemented in LEMON. */ /** @defgroup paths Path Structures @ingroup datas /** @defgroup max_flow Maximum Flow Algorithms @ingroup algs \brief Algorithms for finding maximum flows. This group describes the algorithms for finding maximum flows and feasible circulations. The maximum flow problem is to find a flow between a single source and a single target that is maximum. Formally, there is a \f$G=(V,A)\f$ directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function and given \f$s, t \in V\f$ source and target node. The maximum flow is the \f$f_a\f$ solution of the next optimization problem: \f[ 0 \le f_a \le c_a \f] \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv} \qquad \forall u \in V \setminus \{s,t\}\f] \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f] LEMON contains several algorithms for solving maximum flow problems: - \ref lemon::EdmondsKarp "Edmonds-Karp" - \ref lemon::Preflow "Goldberg's Preflow algorithm" - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees" - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees" In most cases the \ref lemon::Preflow "Preflow" algorithm provides the fastest method to compute the maximum flow. All impelementations provides functions to query the minimum cut, which is the dual linear programming problem of the maximum flow. */ /** @defgroup min_cost_flow Minimum Cost Flow Algorithms @ingroup algs \brief Algorithms for finding minimum cost flows and circulations. This group describes the algorithms for finding minimum cost flows and circulations. */ /** @defgroup min_cut Minimum Cut Algorithms @ingroup algs \brief Algorithms for finding minimum cut in graphs. This group describes the algorithms for finding minimum cut in graphs. The minimum cut problem is to find a non-empty and non-complete \f$X\f$ subset of the vertices with minimum overall capacity on outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum 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}c_{uv}\f] LEMON contains several algorithms related to minimum cut problems: - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut in directed graphs - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to calculate minimum cut in undirected graphs - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all pairs minimum cut in undirected graphs If you want to find minimum cut just between two distinict nodes, please see the \ref max_flow "Maximum Flow page". */ /** @defgroup graph_prop Connectivity and Other Graph Properties @ingroup algs \brief Algorithms for discovering the graph properties This group describes 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 describes the algorithms for planarity checking, embedding and drawing. \image html planar.png \image latex planar.eps "Plane graph" width=\textwidth */ /** @defgroup matching Matching Algorithms @ingroup algs \brief Algorithms for finding matchings in graphs and bipartite graphs. This group contains algorithm objects and functions to calculate matchings in graphs and bipartite graphs. The general matching problem is finding a subset of the arcs which does not shares common endpoints. There are several different algorithms for calculate matchings in graphs.  The matching problems in bipartite graphs are generally easier than in general graphs. The goal of the matching optimization can be the finding maximum cardinality, maximum weight or minimum cost matching. The search can be constrained to find perfect or maximum cardinality matching. LEMON contains the next algorithms: - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp augmenting path algorithm for calculate maximum cardinality matching in bipartite graphs - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel algorithm for calculate maximum cardinality matching in bipartite graphs - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching" Successive shortest path algorithm for calculate maximum weighted matching and maximum weighted bipartite matching in bipartite graph - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching" Successive shortest path algorithm for calculate minimum cost maximum matching in bipartite graph - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm for calculate maximum cardinality matching in general graph - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom shrinking algorithm for calculate maximum weighted matching in general graph - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching" Edmond's blossom shrinking algorithm for calculate maximum weighted perfect matching in general graph \image html bipartite_matching.png \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth */ /** @defgroup spantree Minimum Spanning Tree Algorithms @ingroup algs */ /** @defgroup auxalg Auxiliary Algorithms @ingroup algs \brief Auxiliary algorithms implemented in LEMON. This group describes 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 describes the approximation and heuristic algorithms implemented in LEMON. */ /** @defgroup gen_opt_group General Optimization Tools \brief This group describes some general optimization frameworks implemented in LEMON. This group describes some general optimization frameworks implemented in LEMON. */ /** @defgroup lp_group Lp and Mip Solvers @ingroup gen_opt_group \brief Lp and Mip solver interfaces for LEMON. This group describes 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 describes some metaheuristic optimization tools. */ /** @defgroup utils Tools and Utilities This group describes the tools for importing and exporting graphs and graph related data. Now it supports the \ref lgf-format "LEMON Graph Format", the \c DIMACS format and the encapsulated and graph related data. Now it supports the LEMON format and the encapsulated postscript (EPS) format. postscript (EPS) format. */ */ /** @defgroup map_concepts Map Concepts @ingroup concept \brief Skeleton and concept checking classes for maps This group describes the skeletons and concept checking classes of maps. */ /** \anchor demoprograms build the library. */ /** @defgroup tools Standalone utility applications Some utility applications are listed here. The standard compilation procedure (./configure;make) will compile them, as well. */