# Changes in doc/groups.dox[318:1e2d6ca80793:844:c01a98ce01fd] in lemon

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• ## doc/groups.dox

 r318 * This file is a part of LEMON, a generic C++ optimization library. * * Copyright (C) 2003-2008 * Copyright (C) 2003-2009 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport * (Egervary Research Group on Combinatorial Optimization, EGRES). */ namespace lemon { /** @defgroup datas Data Structures This group describes the several data structures implemented in LEMON. This group contains the several data structures implemented in LEMON. */ /** @defgroup semi_adaptors Semi-Adaptor Classes for Graphs @defgroup graph_adaptors 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. \brief Adaptor classes for digraphs and graphs This group contains several useful adaptor classes for digraphs and graphs. The main parts of LEMON are the different graph structures, generic graph algorithms, graph concepts, which couple them, and graph adaptors. While the previous notions are more or less clear, the latter one needs further explanation. Graph adaptors are graph classes which serve for considering graph structures in different ways. A short example makes this much clearer.  Suppose that we have an instance \c g of a directed graph type, say ListDigraph and an algorithm \code template int algorithm(const Digraph&); \endcode is needed to run on the reverse oriented graph.  It may be expensive (in time or in memory usage) to copy \c g with the reversed arcs.  In this case, an adaptor class is used, which (according to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph. The adaptor uses the original digraph structure and digraph operations when methods of the reversed oriented graph are called.  This means that the adaptor have minor memory usage, and do not perform sophisticated algorithmic actions.  The purpose of it is to give a tool for the cases when a graph have to be used in a specific alteration.  If this alteration is obtained by a usual construction like filtering the node or the arc set or considering a new orientation, then an adaptor is worthwhile to use. To come back to the reverse oriented graph, in this situation \code template class ReverseDigraph; \endcode template class can be used. The code looks as follows \code ListDigraph g; ReverseDigraph rg(g); int result = algorithm(rg); \endcode During running the algorithm, the original digraph \c g is untouched. This techniques give rise to an elegant code, and based on stable graph adaptors, complex algorithms can be implemented easily. In flow, circulation and matching problems, the residual graph is of particular importance. Combining an adaptor implementing this with shortest path algorithms or minimum mean cycle algorithms, a range of weighted and cardinality optimization algorithms can be obtained. For other examples, the interested user is referred to the detailed documentation of particular adaptors. The behavior of graph adaptors can be very different. Some of them keep capabilities of the original graph while in other cases this would be meaningless. This means that the concepts that they meet depend on the graph adaptor, and the wrapped graph. For example, if an arc of a reversed digraph is deleted, this is carried out by deleting the corresponding arc of the original digraph, thus the adaptor modifies the original digraph. However in case of a residual digraph, this operation has no sense. Let us stand one more example here to simplify your work. ReverseDigraph has constructor \code ReverseDigraph(Digraph& digraph); \endcode This means that in a situation, when a const %ListDigraph& reference to a graph is given, then it have to be instantiated with Digraph=const %ListDigraph. \code int algorithm1(const ListDigraph& g) { ReverseDigraph rg(g); return algorithm2(rg); } \endcode */ \brief Map structures implemented in LEMON. This group describes the map structures implemented in LEMON. This group contains the map structures implemented in LEMON. LEMON provides several special purpose maps and map adaptors that e.g. combine \brief Special graph-related maps. This group describes maps that are specifically designed to assign values to the nodes and arcs of graphs. This group contains maps that are specifically designed to assign values to the nodes and arcs/edges of graphs. If you are looking for the standard graph maps (\c NodeMap, \c ArcMap, \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts". */ \brief Tools to create new maps from existing ones This group describes map adaptors that are used to create "implicit" This group contains map adaptors that are used to create "implicit" maps from other maps. Most of them are \ref lemon::concepts::ReadMap "read-only maps". Most of them are \ref concepts::ReadMap "read-only maps". They can make arithmetic and logical operations between one or two maps (negation, shifting, addition, multiplication, logical 'and', 'or', /** @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 \brief %Path structures implemented in LEMON. This group describes the path structures implemented in LEMON. This group contains the path structures implemented in LEMON. LEMON provides flexible data structures to work with paths. \brief Auxiliary data structures implemented in LEMON. This group describes some data structures implemented in LEMON in This group contains some data structures implemented in LEMON in order to make it easier to implement combinatorial algorithms. */ /** @defgroup algs Algorithms \brief This group describes the several algorithms \brief This group contains the several algorithms implemented in LEMON. This group describes the several algorithms This group contains the several algorithms implemented in LEMON. */ \brief Common graph search algorithms. This group describes the common graph search algorithms like Breadth-First Search (BFS) and Depth-First Search (DFS). This group contains the common graph search algorithms, namely \e breadth-first \e search (BFS) and \e depth-first \e search (DFS). */ \brief Algorithms for finding shortest paths. This group describes the algorithms for finding shortest paths in graphs. This group contains the algorithms for finding shortest paths in digraphs. - \ref Dijkstra Dijkstra's algorithm for finding shortest paths from a source node when all arc lengths are non-negative. - \ref Suurballe A successive shortest path algorithm for finding arc-disjoint paths between two nodes having minimum total length. */ \brief Algorithms for finding maximum flows. This group describes the algorithms for finding maximum flows and This group contains 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 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$G=(V,A)\f$ digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and \f$s, t \in V\f$ source and target nodes. A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the following optimization problem. \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f] \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu) \quad \forall u\in V\setminus\{s,t\} \f] \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f] \ref Preflow implements the preflow push-relabel algorithm of Goldberg and Tarjan for solving this problem. 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. For more information, see \ref Circulation. */ /** @defgroup min_cost_flow_algs 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. 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". \ref NetworkSimplex is an efficient implementation of the primal Network Simplex algorithm for finding minimum cost flows. It also provides dual solution (node potentials), if an optimal flow is found. */ \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 This group contains the algorithms for finding minimum cut in graphs. The \e minimum \e cut \e problem is to find a non-empty and non-complete \f$X\f$ subset of the nodes with minimum overall capacity on outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ 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] \sum_{uv\in A, u\in X, v\not\in X}cap(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 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut in directed graphs. - \ref GomoryHu "Gomory-Hu tree computation" for calculating 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 see the \ref max_flow "maximum flow problem". */ /** @defgroup graph_properties Connectivity and Other Graph Properties @ingroup algs \brief Algorithms for discovering the graph properties This group describes the algorithms for discovering the graph properties This group contains the algorithms for discovering the graph properties like connectivity, bipartiteness, euler property, simplicity etc. /** @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. This group contains the algorithms for calculating matchings in graphs. The general matching problem is finding a subset of the edges for which each node has at most one incident edge. 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 graphs. The goal of the matching optimization can be 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 The matching algorithms implemented in LEMON: - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating maximum cardinality matching in general graphs. - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating maximum weighted matching in general graphs. - \ref MaxWeightedPerfectMatching Edmond's blossom shrinking algorithm for calculating maximum weighted perfect matching in general graphs. \image html bipartite_matching.png @defgroup spantree Minimum Spanning Tree Algorithms @ingroup algs \brief Algorithms for finding a minimum cost spanning tree in a graph. This group describes the algorithms for finding a minimum cost spanning tree in a graph \brief Algorithms for finding minimum cost spanning trees and arborescences. This group contains the algorithms for finding minimum cost spanning trees and arborescences. */ \brief Auxiliary algorithms implemented in LEMON. This group describes some algorithms implemented in LEMON 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 describes the approximation and heuristic algorithms @defgroup gen_opt_group General Optimization Tools \brief This group contains some general optimization frameworks 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 This group contains some general optimization frameworks implemented in LEMON. */ \brief Lp and Mip solver interfaces for LEMON. This group describes Lp and Mip solver interfaces for LEMON. The 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 describes some metaheuristic optimization tools. */ \brief Simple basic graph utilities. This group describes some simple basic graph utilities. This group contains some simple basic graph utilities. */ \brief Tools for development, debugging and testing. This group describes several useful tools for development, This group contains several useful tools for development, debugging and testing. */ \brief Simple tools for measuring the performance of algorithms. This group describes simple tools for measuring the performance This group contains simple tools for measuring the performance of algorithms. */ \brief Exceptions defined in LEMON. This group describes the exceptions defined in LEMON. This group contains the exceptions defined in LEMON. */ \brief Graph Input-Output methods This group describes the tools for importing and exporting graphs This group contains 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 /** @defgroup lemon_io LEMON Input-Output @defgroup lemon_io LEMON Graph Format @ingroup io_group \brief Reading and writing LEMON Graph Format. This group describes methods for reading and writing This group contains methods for reading and writing \ref lgf-format "LEMON Graph Format". */ \brief General \c EPS drawer and graph exporter This group describes general \c EPS drawing methods and special This group contains general \c EPS drawing methods and special graph exporting tools. */ /** @defgroup dimacs_group DIMACS format @ingroup io_group \brief Read and write files in DIMACS format Tools to read a digraph from or write it to a file in DIMACS format data. */ /** @defgroup nauty_group NAUTY Format @ingroup io_group \brief Read \e Nauty format Tool to read graphs from \e Nauty format data. */ \brief Skeleton classes and concept checking classes This group describes the data/algorithm skeletons and concept checking This group contains the data/algorithm skeletons and concept checking classes implemented in LEMON. \brief Skeleton and concept checking classes for graph structures This group describes the skeletons and concept checking classes of LEMON's This group contains the skeletons and concept checking classes of LEMON's graph structures and helper classes used to implement these. */ \brief Skeleton and concept checking classes for maps This group describes the skeletons and concept checking classes of maps. This group contains the skeletons and concept checking classes of maps. */ \anchor demoprograms @defgroup demos Demo programs @defgroup demos Demo Programs Some demo programs are listed here. Their full source codes can be found in the \c demo subdirectory of the source tree. It order to compile them, use --enable-demo configure option when build the library. */ /** @defgroup tools Standalone utility applications In order to compile them, use the make demo or the make check commands. */ /** @defgroup tools Standalone Utility Applications Some utility applications are listed here. */ }
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