COIN-OR::LEMON - Graph Library

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[209]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
[40]2 *
[209]3 * This file is a part of LEMON, a generic C++ optimization library.
[40]4 *
[956]5 * Copyright (C) 2003-2010
[40]6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
[422]19namespace lemon {
22@defgroup datas Data Structures
[606]23This group contains the several data structures implemented in LEMON.
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
[209]31The implementation of combinatorial algorithms heavily relies on
32efficient graph implementations. LEMON offers data structures which are
33planned to be easily used in an experimental phase of implementation studies,
34and thereafter the program code can be made efficient by small modifications.
36The most efficient implementation of diverse applications require the
37usage of different physical graph implementations. These differences
38appear in the size of graph we require to handle, memory or time usage
39limitations or in the set of operations through which the graph can be
40accessed.  LEMON provides several physical graph structures to meet
41the diverging requirements of the possible users.  In order to save on
42running time or on memory usage, some structures may fail to provide
[83]43some graph features like arc/edge or node deletion.
[209]45Alteration of standard containers need a very limited number of
46operations, these together satisfy the everyday requirements.
47In the case of graph structures, different operations are needed which do
48not alter the physical graph, but gives another view. If some nodes or
[83]49arcs have to be hidden or the reverse oriented graph have to be used, then
[209]50this is the case. It also may happen that in a flow implementation
51the residual graph can be accessed by another algorithm, or a node-set
52is to be shrunk for another algorithm.
53LEMON also provides a variety of graphs for these requirements called
54\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
55in conjunction with other graph representations.
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
[314]59with any graph structure.
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
[474]65@defgroup graph_adaptors Adaptor Classes for Graphs
[432]66@ingroup graphs
[474]67\brief Adaptor classes for digraphs and graphs
69This group contains several useful adaptor classes for digraphs and graphs.
71The main parts of LEMON are the different graph structures, generic
[474]72graph algorithms, graph concepts, which couple them, and graph
[432]73adaptors. While the previous notions are more or less clear, the
74latter one needs further explanation. Graph adaptors are graph classes
75which serve for considering graph structures in different ways.
77A short example makes this much clearer.  Suppose that we have an
[474]78instance \c g of a directed graph type, say ListDigraph and an algorithm
80template <typename Digraph>
81int algorithm(const Digraph&);
83is needed to run on the reverse oriented graph.  It may be expensive
84(in time or in memory usage) to copy \c g with the reversed
85arcs.  In this case, an adaptor class is used, which (according
[474]86to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87The adaptor uses the original digraph structure and digraph operations when
88methods of the reversed oriented graph are called.  This means that the adaptor
89have minor memory usage, and do not perform sophisticated algorithmic
[432]90actions.  The purpose of it is to give a tool for the cases when a
91graph have to be used in a specific alteration.  If this alteration is
[474]92obtained by a usual construction like filtering the node or the arc set or
[432]93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
96template<typename Digraph> class ReverseDigraph;
98template class can be used. The code looks as follows
100ListDigraph g;
[474]101ReverseDigraph<ListDigraph> rg(g);
[432]102int result = algorithm(rg);
[474]104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
[432]106graph adaptors, complex algorithms can be implemented easily.
[474]108In flow, circulation and matching problems, the residual
[432]109graph is of particular importance. Combining an adaptor implementing
[474]110this with shortest path algorithms or minimum mean cycle algorithms,
[432]111a range of weighted and cardinality optimization algorithms can be
112obtained. For other examples, the interested user is referred to the
113detailed documentation of particular adaptors.
115The behavior of graph adaptors can be very different. Some of them keep
116capabilities of the original graph while in other cases this would be
[474]117meaningless. This means that the concepts that they meet depend
118on the graph adaptor, and the wrapped graph.
119For example, if an arc of a reversed digraph is deleted, this is carried
120out by deleting the corresponding arc of the original digraph, thus the
121adaptor modifies the original digraph.
122However in case of a residual digraph, this operation has no sense.
124Let us stand one more example here to simplify your work.
[474]125ReverseDigraph has constructor
127ReverseDigraph(Digraph& digraph);
[474]129This means that in a situation, when a <tt>const %ListDigraph&</tt>
[432]130reference to a graph is given, then it have to be instantiated with
[474]131<tt>Digraph=const %ListDigraph</tt>.
133int algorithm1(const ListDigraph& g) {
[474]134  ReverseDigraph<const ListDigraph> rg(g);
[432]135  return algorithm2(rg);
[209]141@defgroup maps Maps
[40]142@ingroup datas
[50]143\brief Map structures implemented in LEMON.
[606]145This group contains the map structures implemented in LEMON.
[314]147LEMON provides several special purpose maps and map adaptors that e.g. combine
[40]148new maps from existing ones.
150<b>See also:</b> \ref map_concepts "Map Concepts".
[209]154@defgroup graph_maps Graph Maps
[40]155@ingroup maps
[83]156\brief Special graph-related maps.
[606]158This group contains maps that are specifically designed to assign
[422]159values to the nodes and arcs/edges of graphs.
161If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
162\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
166\defgroup map_adaptors Map Adaptors
167\ingroup maps
168\brief Tools to create new maps from existing ones
[606]170This group contains map adaptors that are used to create "implicit"
[50]171maps from other maps.
[422]173Most of them are \ref concepts::ReadMap "read-only maps".
[83]174They can make arithmetic and logical operations between one or two maps
175(negation, shifting, addition, multiplication, logical 'and', 'or',
176'not' etc.) or e.g. convert a map to another one of different Value type.
[50]178The typical usage of this classes is passing implicit maps to
[40]179algorithms.  If a function type algorithm is called then the function
180type map adaptors can be used comfortable. For example let's see the
[314]181usage of map adaptors with the \c graphToEps() function.
183  Color nodeColor(int deg) {
184    if (deg >= 2) {
185      return Color(0.5, 0.0, 0.5);
186    } else if (deg == 1) {
187      return Color(1.0, 0.5, 1.0);
188    } else {
189      return Color(0.0, 0.0, 0.0);
190    }
191  }
[83]193  Digraph::NodeMap<int> degree_map(graph);
[314]195  graphToEps(graph, "graph.eps")
[40]196    .coords(coords).scaleToA4().undirected()
[83]197    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
[40]198    .run();
[83]200The \c functorToMap() function makes an \c int to \c Color map from the
[314]201\c nodeColor() function. The \c composeMap() compose the \c degree_map
[83]202and the previously created map. The composed map is a proper function to
203get the color of each node.
205The usage with class type algorithms is little bit harder. In this
206case the function type map adaptors can not be used, because the
[50]207function map adaptors give back temporary objects.
[83]209  Digraph graph;
211  typedef Digraph::ArcMap<double> DoubleArcMap;
212  DoubleArcMap length(graph);
213  DoubleArcMap speed(graph);
215  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
[40]216  TimeMap time(length, speed);
[83]218  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
[40]219, target);
[83]221We have a length map and a maximum speed map on the arcs of a digraph.
222The minimum time to pass the arc can be calculated as the division of
223the two maps which can be done implicitly with the \c DivMap template
[40]224class. We use the implicit minimum time map as the length map of the
225\c Dijkstra algorithm.
229@defgroup paths Path Structures
230@ingroup datas
[318]231\brief %Path structures implemented in LEMON.
[606]233This group contains the path structures implemented in LEMON.
[50]235LEMON provides flexible data structures to work with paths.
236All of them have similar interfaces and they can be copied easily with
237assignment operators and copy constructors. This makes it easy and
[40]238efficient to have e.g. the Dijkstra algorithm to store its result in
239any kind of path structure.
[757]241\sa \ref concepts::Path "Path concept"
245@defgroup heaps Heap Structures
246@ingroup datas
247\brief %Heap structures implemented in LEMON.
249This group contains the heap structures implemented in LEMON.
251LEMON provides several heap classes. They are efficient implementations
252of the abstract data type \e priority \e queue. They store items with
253specified values called \e priorities in such a way that finding and
254removing the item with minimum priority are efficient.
255The basic operations are adding and erasing items, changing the priority
256of an item, etc.
258Heaps are crucial in several algorithms, such as Dijkstra and Prim.
259The heap implementations have the same interface, thus any of them can be
260used easily in such algorithms.
262\sa \ref concepts::Heap "Heap concept"
[40]266@defgroup auxdat Auxiliary Data Structures
267@ingroup datas
[50]268\brief Auxiliary data structures implemented in LEMON.
[606]270This group contains some data structures implemented in LEMON in
[40]271order to make it easier to implement combinatorial algorithms.
[761]275@defgroup geomdat Geometric Data Structures
276@ingroup auxdat
277\brief Geometric data structures implemented in LEMON.
279This group contains geometric data structures implemented in LEMON.
281 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
282   vector with the usual operations.
283 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
284   rectangular bounding box of a set of \ref lemon::dim2::Point
285   "dim2::Point"'s.
289@defgroup matrices Matrices
290@ingroup auxdat
291\brief Two dimensional data storages implemented in LEMON.
293This group contains two dimensional data storages implemented in LEMON.
[40]297@defgroup algs Algorithms
[606]298\brief This group contains the several algorithms
[40]299implemented in LEMON.
[606]301This group contains the several algorithms
[40]302implemented in LEMON.
306@defgroup search Graph Search
307@ingroup algs
[50]308\brief Common graph search algorithms.
[606]310This group contains the common graph search algorithms, namely
[802]311\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
312\ref clrs01algorithms.
[314]316@defgroup shortest_path Shortest Path Algorithms
[40]317@ingroup algs
[50]318\brief Algorithms for finding shortest paths.
[802]320This group contains the algorithms for finding shortest paths in digraphs
321\ref clrs01algorithms.
323 - \ref Dijkstra algorithm for finding shortest paths from a source node
324   when all arc lengths are non-negative.
325 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
326   from a source node when arc lenghts can be either positive or negative,
327   but the digraph should not contain directed cycles with negative total
328   length.
329 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
330   for solving the \e all-pairs \e shortest \e paths \e problem when arc
331   lenghts can be either positive or negative, but the digraph should
332   not contain directed cycles with negative total length.
333 - \ref Suurballe A successive shortest path algorithm for finding
334   arc-disjoint paths between two nodes having minimum total length.
[761]338@defgroup spantree Minimum Spanning Tree Algorithms
339@ingroup algs
340\brief Algorithms for finding minimum cost spanning trees and arborescences.
342This group contains the algorithms for finding minimum cost spanning
[802]343trees and arborescences \ref clrs01algorithms.
[314]347@defgroup max_flow Maximum Flow Algorithms
[209]348@ingroup algs
[50]349\brief Algorithms for finding maximum flows.
[606]351This group contains the algorithms for finding maximum flows and
[802]352feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
[422]354The \e maximum \e flow \e problem is to find a flow of maximum value between
355a single source and a single target. Formally, there is a \f$G=(V,A)\f$
[656]356digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
[422]357\f$s, t \in V\f$ source and target nodes.
[656]358A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
[422]359following optimization problem.
[656]361\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
362\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
363    \quad \forall u\in V\setminus\{s,t\} \f]
364\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
[50]366LEMON contains several algorithms for solving maximum flow problems:
[802]367- \ref EdmondsKarp Edmonds-Karp algorithm
368  \ref edmondskarp72theoretical.
369- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
370  \ref goldberg88newapproach.
371- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
372  \ref dinic70algorithm, \ref sleator83dynamic.
373- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
374  \ref goldberg88newapproach, \ref sleator83dynamic.
[802]376In most cases the \ref Preflow algorithm provides the
[422]377fastest method for computing a maximum flow. All implementations
[698]378also provide functions to query the minimum cut, which is the dual
379problem of maximum flow.
[948]381\ref Circulation is a preflow push-relabel algorithm implemented directly
[698]382for finding feasible circulations, which is a somewhat different problem,
383but it is strongly related to maximum flow.
384For more information, see \ref Circulation.
[710]388@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
[40]389@ingroup algs
[50]391\brief Algorithms for finding minimum cost flows and circulations.
[656]393This group contains the algorithms for finding minimum cost flows and
[802]394circulations \ref amo93networkflows. For more information about this
395problem and its dual solution, see \ref min_cost_flow
396"Minimum Cost Flow Problem".
[710]398LEMON contains several algorithms for this problem.
[656]399 - \ref NetworkSimplex Primal Network Simplex algorithm with various
[802]400   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
[879]401 - \ref CostScaling Cost Scaling algorithm based on push/augment and
402   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
[802]403   \ref bunnagel98efficient.
[879]404 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
405   shortest path method \ref edmondskarp72theoretical.
406 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
407   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
[1023]409In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
410implementations, but the other two algorithms could be faster in special cases.
[656]411For example, if the total supply and/or capacities are rather small,
[1023]412\ref CapacityScaling is usually the fastest algorithm (without effective scaling).
[314]416@defgroup min_cut Minimum Cut Algorithms
[209]417@ingroup algs
[50]419\brief Algorithms for finding minimum cut in graphs.
[606]421This group contains the algorithms for finding minimum cut in graphs.
[422]423The \e minimum \e cut \e problem is to find a non-empty and non-complete
424\f$X\f$ subset of the nodes with minimum overall capacity on
425outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
426\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
[50]427cut is the \f$X\f$ solution of the next optimization problem:
[210]429\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
[760]430    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
[50]432LEMON contains several algorithms related to minimum cut problems:
[422]434- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
435  in directed graphs.
436- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
437  calculating minimum cut in undirected graphs.
[606]438- \ref GomoryHu "Gomory-Hu tree computation" for calculating
[422]439  all-pairs minimum cut in undirected graphs.
441If you want to find minimum cut just between two distinict nodes,
[422]442see the \ref max_flow "maximum flow problem".
[815]446@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
[40]447@ingroup algs
[815]448\brief Algorithms for finding minimum mean cycles.
[818]450This group contains the algorithms for finding minimum mean cycles
451\ref clrs01algorithms, \ref amo93networkflows.
[815]453The \e minimum \e mean \e cycle \e problem is to find a directed cycle
454of minimum mean length (cost) in a digraph.
455The mean length of a cycle is the average length of its arcs, i.e. the
456ratio between the total length of the cycle and the number of arcs on it.
[815]458This problem has an important connection to \e conservative \e length
459\e functions, too. A length function on the arcs of a digraph is called
460conservative if and only if there is no directed cycle of negative total
461length. For an arbitrary length function, the negative of the minimum
462cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
463arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
[815]466LEMON contains three algorithms for solving the minimum mean cycle problem:
[959]467- \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
[818]468  \ref dasdan98minmeancycle.
[959]469- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
[818]470  version of Karp's algorithm \ref dasdan98minmeancycle.
[959]471- \ref HowardMmc Howard's policy iteration algorithm
[818]472  \ref dasdan98minmeancycle.
[1023]474In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
[959]475most efficient one, though the best known theoretical bound on its running
476time is exponential.
477Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
478run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
479typically faster due to the applied early termination scheme.
[314]483@defgroup matching Matching Algorithms
[40]484@ingroup algs
[50]485\brief Algorithms for finding matchings in graphs and bipartite graphs.
[637]487This group contains the algorithms for calculating
[40]488matchings in graphs and bipartite graphs. The general matching problem is
[637]489finding a subset of the edges for which each node has at most one incident
[40]492There are several different algorithms for calculate matchings in
493graphs.  The matching problems in bipartite graphs are generally
494easier than in general graphs. The goal of the matching optimization
[422]495can be finding maximum cardinality, maximum weight or minimum cost
[40]496matching. The search can be constrained to find perfect or
497maximum cardinality matching.
[422]499The matching algorithms implemented in LEMON:
500- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
501  for calculating maximum cardinality matching in bipartite graphs.
502- \ref PrBipartiteMatching Push-relabel algorithm
503  for calculating maximum cardinality matching in bipartite graphs.
504- \ref MaxWeightedBipartiteMatching
505  Successive shortest path algorithm for calculating maximum weighted
506  matching and maximum weighted bipartite matching in bipartite graphs.
507- \ref MinCostMaxBipartiteMatching
508  Successive shortest path algorithm for calculating minimum cost maximum
509  matching in bipartite graphs.
510- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
511  maximum cardinality matching in general graphs.
512- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
513  maximum weighted matching in general graphs.
514- \ref MaxWeightedPerfectMatching
515  Edmond's blossom shrinking algorithm for calculating maximum weighted
516  perfect matching in general graphs.
[948]517- \ref MaxFractionalMatching Push-relabel algorithm for calculating
518  maximum cardinality fractional matching in general graphs.
519- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
520  maximum weighted fractional matching in general graphs.
521- \ref MaxWeightedPerfectFractionalMatching
522  Augmenting path algorithm for calculating maximum weighted
523  perfect fractional matching in general graphs.
[943]525\image html matching.png
[952]526\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
[761]530@defgroup graph_properties Connectivity and Other Graph Properties
[40]531@ingroup algs
[761]532\brief Algorithms for discovering the graph properties
[761]534This group contains the algorithms for discovering the graph properties
535like connectivity, bipartiteness, euler property, simplicity etc.
537\image html connected_components.png
538\image latex connected_components.eps "Connected components" width=\textwidth
[1023]542@defgroup planar Planar Embedding and Drawing
[761]543@ingroup algs
544\brief Algorithms for planarity checking, embedding and drawing
546This group contains the algorithms for planarity checking,
547embedding and drawing.
549\image html planar.png
550\image latex planar.eps "Plane graph" width=\textwidth
[999]554@defgroup approx_algs Approximation Algorithms
[761]555@ingroup algs
556\brief Approximation algorithms.
558This group contains the approximation and heuristic algorithms
559implemented in LEMON.
561<b>Maximum Clique Problem</b>
562  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
563    Grosso, Locatelli, and Pullan.
[314]567@defgroup auxalg Auxiliary Algorithms
[40]568@ingroup algs
[50]569\brief Auxiliary algorithms implemented in LEMON.
[606]571This group contains some algorithms implemented in LEMON
[50]572in order to make it easier to implement complex algorithms.
576@defgroup gen_opt_group General Optimization Tools
[606]577\brief This group contains some general optimization frameworks
[40]578implemented in LEMON.
[606]580This group contains some general optimization frameworks
[40]581implemented in LEMON.
[802]585@defgroup lp_group LP and MIP Solvers
[40]586@ingroup gen_opt_group
[802]587\brief LP and MIP solver interfaces for LEMON.
[802]589This group contains LP and MIP solver interfaces for LEMON.
590Various LP solvers could be used in the same manner with this
591high-level interface.
593The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
594\ref cplex, \ref soplex.
[314]598@defgroup lp_utils Tools for Lp and Mip Solvers
[40]599@ingroup lp_group
[50]600\brief Helper tools to the Lp and Mip solvers.
602This group adds some helper tools to general optimization framework
603implemented in LEMON.
607@defgroup metah Metaheuristics
608@ingroup gen_opt_group
609\brief Metaheuristics for LEMON library.
[606]611This group contains some metaheuristic optimization tools.
[209]615@defgroup utils Tools and Utilities
[50]616\brief Tools and utilities for programming in LEMON
[50]618Tools and utilities for programming in LEMON.
622@defgroup gutils Basic Graph Utilities
623@ingroup utils
[50]624\brief Simple basic graph utilities.
[606]626This group contains some simple basic graph utilities.
630@defgroup misc Miscellaneous Tools
631@ingroup utils
[50]632\brief Tools for development, debugging and testing.
[606]634This group contains several useful tools for development,
[40]635debugging and testing.
[314]639@defgroup timecount Time Measuring and Counting
[40]640@ingroup misc
[50]641\brief Simple tools for measuring the performance of algorithms.
[606]643This group contains simple tools for measuring the performance
[40]644of algorithms.
648@defgroup exceptions Exceptions
649@ingroup utils
[50]650\brief Exceptions defined in LEMON.
[606]652This group contains the exceptions defined in LEMON.
656@defgroup io_group Input-Output
[50]657\brief Graph Input-Output methods
[606]659This group contains the tools for importing and exporting graphs
[314]660and graph related data. Now it supports the \ref lgf-format
661"LEMON Graph Format", the \c DIMACS format and the encapsulated
662postscript (EPS) format.
[363]666@defgroup lemon_io LEMON Graph Format
[40]667@ingroup io_group
[314]668\brief Reading and writing LEMON Graph Format.
[606]670This group contains methods for reading and writing
[236]671\ref lgf-format "LEMON Graph Format".
[314]675@defgroup eps_io Postscript Exporting
[40]676@ingroup io_group
677\brief General \c EPS drawer and graph exporter
[606]679This group contains general \c EPS drawing methods and special
[209]680graph exporting tools.
[761]684@defgroup dimacs_group DIMACS Format
[403]685@ingroup io_group
686\brief Read and write files in DIMACS format
688Tools to read a digraph from or write it to a file in DIMACS format data.
[363]692@defgroup nauty_group NAUTY Format
693@ingroup io_group
694\brief Read \e Nauty format
[363]696Tool to read graphs from \e Nauty format data.
[40]700@defgroup concept Concepts
701\brief Skeleton classes and concept checking classes
[606]703This group contains the data/algorithm skeletons and concept checking
[40]704classes implemented in LEMON.
706The purpose of the classes in this group is fourfold.
[318]708- These classes contain the documentations of the %concepts. In order
[40]709  to avoid document multiplications, an implementation of a concept
710  simply refers to the corresponding concept class.
712- These classes declare every functions, <tt>typedef</tt>s etc. an
[318]713  implementation of the %concepts should provide, however completely
[40]714  without implementations and real data structures behind the
715  interface. On the other hand they should provide nothing else. All
716  the algorithms working on a data structure meeting a certain concept
717  should compile with these classes. (Though it will not run properly,
718  of course.) In this way it is easily to check if an algorithm
719  doesn't use any extra feature of a certain implementation.
721- The concept descriptor classes also provide a <em>checker class</em>
[50]722  that makes it possible to check whether a certain implementation of a
[40]723  concept indeed provides all the required features.
725- Finally, They can serve as a skeleton of a new implementation of a concept.
729@defgroup graph_concepts Graph Structure Concepts
730@ingroup concept
731\brief Skeleton and concept checking classes for graph structures
[782]733This group contains the skeletons and concept checking classes of
734graph structures.
738@defgroup map_concepts Map Concepts
739@ingroup concept
740\brief Skeleton and concept checking classes for maps
[606]742This group contains the skeletons and concept checking classes of maps.
[761]746@defgroup tools Standalone Utility Applications
748Some utility applications are listed here.
750The standard compilation procedure (<tt>./configure;make</tt>) will compile
751them, as well.
[40]755\anchor demoprograms
[422]757@defgroup demos Demo Programs
759Some demo programs are listed here. Their full source codes can be found in
760the \c demo subdirectory of the source tree.
[611]762In order to compile them, use the <tt>make demo</tt> or the
763<tt>make check</tt> commands.
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