# Changes in doc/groups.dox[318:1e2d6ca80793:1023:e0cef67fe565] in lemon

Ignore:
File:
1 edited

### Legend:

Unmodified
 r318 * This file is a part of LEMON, a generic C++ optimization library. * * Copyright (C) 2003-2008 * Copyright (C) 2003-2010 * 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. 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" */ \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 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 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) \ref clrs01algorithms. */ \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 clrs01algorithms. - \ref Dijkstra algorithm for finding shortest paths from a source node when all arc lengths are non-negative. - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths from a source node when arc lenghts can be either positive or negative, 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. */ \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] This group contains the algorithms for finding maximum flows and 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$G=(V,A)\f$ 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] 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 - \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 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 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 \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 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, \ref NetworkSimplex and \ref CostScaling are the most efficient implementations, but the other two algorithms could be faster in special cases. For example, if the total supply and/or capacities are rather small, \ref CapacityScaling is usually the fastest algorithm (without effective scaling). */ \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 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. 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 see the \ref max_flow "maximum flow problem". */ /** @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 turned out 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. */ \brief Algorithms for finding matchings in graphs and bipartite graphs. This group contains algorithm objects and functions to calculate This group contains the algorithms for calculating matchings in graphs and bipartite graphs. The general matching problem is finding a subset of the arcs which does not shares common endpoints. 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 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 \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 a minimum cost spanning tree in a graph. This group describes the algorithms for finding a minimum cost spanning tree in a graph 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. - \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. - \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 Planar 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_algs Approximation Algorithms @ingroup algs \brief Approximation algorithms. This group contains the approximation and heuristic algorithms implemented in LEMON. Maximum Clique Problem - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of Grosso, Locatelli, and Pullan. */ \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 This group contains some general optimization frameworks implemented in LEMON. This group describes some general optimization frameworks 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 describes Lp and Mip solver interfaces for LEMON. The various LP solvers could be used in the same manner with this interface. \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. */ \brief Metaheuristics for LEMON library. This group describes some metaheuristic optimization tools. This group contains 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 graph structures and helper classes used to implement these. This group contains the skeletons and concept checking classes of graph structures. */ \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. */ /** @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 @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 Some utility applications are listed here. The standard compilation procedure (./configure;make) will compile them, as well. */ In order to compile them, use the make demo or the make check commands. */ }