COIN-OR::LEMON - Graph Library

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2010
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 */
18
19namespace lemon {
20
21/**
22@defgroup datas Data Structures
23This group contains the several data structures implemented in LEMON.
24*/
25
26/**
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
30
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.
35
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
43some graph features like arc/edge or node deletion.
44
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
49arcs have to be hidden or the reverse oriented graph have to be used, then
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.
56
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
59with any graph structure.
60
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
62*/
63
64/**
65@defgroup graph_adaptors Adaptor Classes for Graphs
66@ingroup graphs
67\brief Adaptor classes for digraphs and graphs
68
69This group contains several useful adaptor classes for digraphs and graphs.
70
71The main parts of LEMON are the different graph structures, generic
72graph algorithms, graph concepts, which couple them, and graph
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.
76
77A short example makes this much clearer.  Suppose that we have an
78instance \c g of a directed graph type, say ListDigraph and an algorithm
79\code
80template <typename Digraph>
81int algorithm(const Digraph&);
82\endcode
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
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
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
92obtained by a usual construction like filtering the node or the arc set or
93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
95\code
96template<typename Digraph> class ReverseDigraph;
97\endcode
98template class can be used. The code looks as follows
99\code
100ListDigraph g;
101ReverseDigraph<ListDigraph> rg(g);
102int result = algorithm(rg);
103\endcode
104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
106graph adaptors, complex algorithms can be implemented easily.
107
108In flow, circulation and matching problems, the residual
109graph is of particular importance. Combining an adaptor implementing
110this with shortest path algorithms or minimum mean cycle algorithms,
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.
114
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
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.
123
124Let us stand one more example here to simplify your work.
125ReverseDigraph has constructor
126\code
127ReverseDigraph(Digraph& digraph);
128\endcode
129This means that in a situation, when a <tt>const %ListDigraph&</tt>
130reference to a graph is given, then it have to be instantiated with
131<tt>Digraph=const %ListDigraph</tt>.
132\code
133int algorithm1(const ListDigraph& g) {
134  ReverseDigraph<const ListDigraph> rg(g);
135  return algorithm2(rg);
136}
137\endcode
138*/
139
140/**
141@defgroup maps Maps
142@ingroup datas
143\brief Map structures implemented in LEMON.
144
145This group contains the map structures implemented in LEMON.
146
147LEMON provides several special purpose maps and map adaptors that e.g. combine
148new maps from existing ones.
149
150<b>See also:</b> \ref map_concepts "Map Concepts".
151*/
152
153/**
154@defgroup graph_maps Graph Maps
155@ingroup maps
156\brief Special graph-related maps.
157
158This group contains maps that are specifically designed to assign
159values to the nodes and arcs/edges of graphs.
160
161If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
162\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
163*/
164
165/**
166\defgroup map_adaptors Map Adaptors
167\ingroup maps
168\brief Tools to create new maps from existing ones
169
170This group contains map adaptors that are used to create "implicit"
171maps from other maps.
172
173Most of them are \ref concepts::ReadMap "read-only maps".
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.
177
178The typical usage of this classes is passing implicit maps to
179algorithms.  If a function type algorithm is called then the function
180type map adaptors can be used comfortable. For example let's see the
181usage of map adaptors with the \c graphToEps() function.
182\code
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  }
192
193  Digraph::NodeMap<int> degree_map(graph);
194
195  graphToEps(graph, "graph.eps")
196    .coords(coords).scaleToA4().undirected()
197    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
198    .run();
199\endcode
200The \c functorToMap() function makes an \c int to \c Color map from the
201\c nodeColor() function. The \c composeMap() compose the \c degree_map
202and the previously created map. The composed map is a proper function to
203get the color of each node.
204
205The usage with class type algorithms is little bit harder. In this
206case the function type map adaptors can not be used, because the
207function map adaptors give back temporary objects.
208\code
209  Digraph graph;
210
211  typedef Digraph::ArcMap<double> DoubleArcMap;
212  DoubleArcMap length(graph);
213  DoubleArcMap speed(graph);
214
215  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
216  TimeMap time(length, speed);
217
218  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
219  dijkstra.run(source, target);
220\endcode
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
224class. We use the implicit minimum time map as the length map of the
225\c Dijkstra algorithm.
226*/
227
228/**
229@defgroup paths Path Structures
230@ingroup datas
231\brief %Path structures implemented in LEMON.
232
233This group contains the path structures implemented in LEMON.
234
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
238efficient to have e.g. the Dijkstra algorithm to store its result in
239any kind of path structure.
240
241\sa \ref concepts::Path "Path concept"
242*/
243
244/**
245@defgroup heaps Heap Structures
246@ingroup datas
247\brief %Heap structures implemented in LEMON.
248
249This group contains the heap structures implemented in LEMON.
250
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.
257
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.
261
262\sa \ref concepts::Heap "Heap concept"
263*/
264
265/**
266@defgroup auxdat Auxiliary Data Structures
267@ingroup datas
268\brief Auxiliary data structures implemented in LEMON.
269
270This group contains some data structures implemented in LEMON in
271order to make it easier to implement combinatorial algorithms.
272*/
273
274/**
275@defgroup geomdat Geometric Data Structures
276@ingroup auxdat
277\brief Geometric data structures implemented in LEMON.
278
279This group contains geometric data structures implemented in LEMON.
280
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.
286*/
287
288/**
289@defgroup matrices Matrices
290@ingroup auxdat
291\brief Two dimensional data storages implemented in LEMON.
292
293This group contains two dimensional data storages implemented in LEMON.
294*/
295
296/**
297@defgroup algs Algorithms
298\brief This group contains the several algorithms
299implemented in LEMON.
300
301This group contains the several algorithms
302implemented in LEMON.
303*/
304
305/**
306@defgroup search Graph Search
307@ingroup algs
308\brief Common graph search algorithms.
309
310This group contains the common graph search algorithms, namely
311\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
312\ref clrs01algorithms.
313*/
314
315/**
316@defgroup shortest_path Shortest Path Algorithms
317@ingroup algs
318\brief Algorithms for finding shortest paths.
319
320This group contains the algorithms for finding shortest paths in digraphs
321\ref clrs01algorithms.
322
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.
335*/
336
337/**
338@defgroup spantree Minimum Spanning Tree Algorithms
339@ingroup algs
340\brief Algorithms for finding minimum cost spanning trees and arborescences.
341
342This group contains the algorithms for finding minimum cost spanning
343trees and arborescences \ref clrs01algorithms.
344*/
345
346/**
347@defgroup max_flow Maximum Flow Algorithms
348@ingroup algs
349\brief Algorithms for finding maximum flows.
350
351This group contains the algorithms for finding maximum flows and
352feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
353
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$G=(V,A)\f$
356digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
357\f$s, t \in V\f$ source and target nodes.
358A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
359following optimization problem.
360
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]
365
366LEMON contains several algorithms for solving maximum flow problems:
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.
375
376In most cases the \ref Preflow algorithm provides the
377fastest method for computing a maximum flow. All implementations
378also provide functions to query the minimum cut, which is the dual
379problem of maximum flow.
380
381\ref Circulation is a preflow push-relabel algorithm implemented directly
382for finding feasible circulations, which is a somewhat different problem,
383but it is strongly related to maximum flow.
384For more information, see \ref Circulation.
385*/
386
387/**
388@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
389@ingroup algs
390
391\brief Algorithms for finding minimum cost flows and circulations.
392
393This group contains the algorithms for finding minimum cost flows and
394circulations \ref amo93networkflows. For more information about this
395problem and its dual solution, see \ref min_cost_flow
396"Minimum Cost Flow Problem".
397
398LEMON contains several algorithms for this problem.
399 - \ref NetworkSimplex Primal Network Simplex algorithm with various
400   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
401 - \ref CostScaling Cost Scaling algorithm based on push/augment and
402   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
403   \ref bunnagel98efficient.
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.
408
409In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
410implementations.
411\ref NetworkSimplex is usually the fastest on relatively small graphs (up to
412several thousands of nodes) and on dense graphs, while \ref CostScaling is
413typically more efficient on large graphs (e.g. hundreds of thousands of
414nodes or above), especially if they are sparse.
415However, other algorithms could be faster in special cases.
416For example, if the total supply and/or capacities are rather small,
417\ref CapacityScaling is usually the fastest algorithm (without effective scaling).
418
419These classes are intended to be used with integer-valued input data
420(capacities, supply values, and costs), except for \ref CapacityScaling,
421which is capable of handling real-valued arc costs (other numerical
422data are required to be integer).
423*/
424
425/**
426@defgroup min_cut Minimum Cut Algorithms
427@ingroup algs
428
429\brief Algorithms for finding minimum cut in graphs.
430
431This group contains the algorithms for finding minimum cut in graphs.
432
433The \e minimum \e cut \e problem is to find a non-empty and non-complete
434\f$X\f$ subset of the nodes with minimum overall capacity on
435outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
436\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
437cut is the \f$X\f$ solution of the next optimization problem:
438
439\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
440    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
441
442LEMON contains several algorithms related to minimum cut problems:
443
444- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
445  in directed graphs.
446- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
447  calculating minimum cut in undirected graphs.
448- \ref GomoryHu "Gomory-Hu tree computation" for calculating
449  all-pairs minimum cut in undirected graphs.
450
451If you want to find minimum cut just between two distinict nodes,
452see the \ref max_flow "maximum flow problem".
453*/
454
455/**
456@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
457@ingroup algs
458\brief Algorithms for finding minimum mean cycles.
459
460This group contains the algorithms for finding minimum mean cycles
461\ref amo93networkflows, \ref karp78characterization.
462
463The \e minimum \e mean \e cycle \e problem is to find a directed cycle
464of minimum mean length (cost) in a digraph.
465The mean length of a cycle is the average length of its arcs, i.e. the
466ratio between the total length of the cycle and the number of arcs on it.
467
468This problem has an important connection to \e conservative \e length
469\e functions, too. A length function on the arcs of a digraph is called
470conservative if and only if there is no directed cycle of negative total
471length. For an arbitrary length function, the negative of the minimum
472cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
473arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
474function.
475
476LEMON contains three algorithms for solving the minimum mean cycle problem:
477- \ref KarpMmc Karp's original algorithm \ref karp78characterization.
478- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
479  version of Karp's algorithm \ref hartmann93finding.
480- \ref HowardMmc Howard's policy iteration algorithm
481  \ref dasdan98minmeancycle, \ref dasdan04experimental.
482
483In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
484most efficient one, though the best known theoretical bound on its running
485time is exponential.
486Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
487run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
488typically faster due to the applied early termination scheme.
489*/
490
491/**
492@defgroup matching Matching Algorithms
493@ingroup algs
494\brief Algorithms for finding matchings in graphs and bipartite graphs.
495
496This group contains the algorithms for calculating
497matchings in graphs and bipartite graphs. The general matching problem is
498finding a subset of the edges for which each node has at most one incident
499edge.
500
501There are several different algorithms for calculate matchings in
502graphs.  The matching problems in bipartite graphs are generally
503easier than in general graphs. The goal of the matching optimization
504can be finding maximum cardinality, maximum weight or minimum cost
505matching. The search can be constrained to find perfect or
506maximum cardinality matching.
507
508The matching algorithms implemented in LEMON:
509- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
510  for calculating maximum cardinality matching in bipartite graphs.
511- \ref PrBipartiteMatching Push-relabel algorithm
512  for calculating maximum cardinality matching in bipartite graphs.
513- \ref MaxWeightedBipartiteMatching
514  Successive shortest path algorithm for calculating maximum weighted
515  matching and maximum weighted bipartite matching in bipartite graphs.
516- \ref MinCostMaxBipartiteMatching
517  Successive shortest path algorithm for calculating minimum cost maximum
518  matching in bipartite graphs.
519- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
520  maximum cardinality matching in general graphs.
521- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
522  maximum weighted matching in general graphs.
523- \ref MaxWeightedPerfectMatching
524  Edmond's blossom shrinking algorithm for calculating maximum weighted
525  perfect matching in general graphs.
526- \ref MaxFractionalMatching Push-relabel algorithm for calculating
527  maximum cardinality fractional matching in general graphs.
528- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
529  maximum weighted fractional matching in general graphs.
530- \ref MaxWeightedPerfectFractionalMatching
531  Augmenting path algorithm for calculating maximum weighted
532  perfect fractional matching in general graphs.
533
534\image html matching.png
535\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
536*/
537
538/**
539@defgroup graph_properties Connectivity and Other Graph Properties
540@ingroup algs
541\brief Algorithms for discovering the graph properties
542
543This group contains the algorithms for discovering the graph properties
544like connectivity, bipartiteness, euler property, simplicity etc.
545
546\image html connected_components.png
547\image latex connected_components.eps "Connected components" width=\textwidth
548*/
549
550/**
551@defgroup planar Planar Embedding and Drawing
552@ingroup algs
553\brief Algorithms for planarity checking, embedding and drawing
554
555This group contains the algorithms for planarity checking,
556embedding and drawing.
557
558\image html planar.png
559\image latex planar.eps "Plane graph" width=\textwidth
560*/
561 
562/**
563@defgroup tsp Traveling Salesman Problem
564@ingroup algs
565\brief Algorithms for the symmetric traveling salesman problem
566
567This group contains basic heuristic algorithms for the the symmetric
568\e traveling \e salesman \e problem (TSP).
569Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
570the problem is to find a shortest possible tour that visits each node exactly
571once (i.e. the minimum cost Hamiltonian cycle).
572
573These TSP algorithms are intended to be used with a \e metric \e cost
574\e function, i.e. the edge costs should satisfy the triangle inequality.
575Otherwise the algorithms could yield worse results.
576
577LEMON provides five well-known heuristics for solving symmetric TSP:
578 - \ref NearestNeighborTsp Neareast neighbor algorithm
579 - \ref GreedyTsp Greedy algorithm
580 - \ref InsertionTsp Insertion heuristic (with four selection methods)
581 - \ref ChristofidesTsp Christofides algorithm
582 - \ref Opt2Tsp 2-opt algorithm
583
584\ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
585solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
586
587\ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
588approximation factor: 3/2.
589
590\ref Opt2Tsp usually provides the best results in practice, but
591it is the slowest method. It can also be used to improve given tours,
592for example, the results of other algorithms.
593
594\image html tsp.png
595\image latex tsp.eps "Traveling salesman problem" width=\textwidth
596*/
597
598/**
599@defgroup approx_algs Approximation Algorithms
600@ingroup algs
601\brief Approximation algorithms.
602
603This group contains the approximation and heuristic algorithms
604implemented in LEMON.
605
606<b>Maximum Clique Problem</b>
607  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
608    Grosso, Locatelli, and Pullan.
609*/
610
611/**
612@defgroup auxalg Auxiliary Algorithms
613@ingroup algs
614\brief Auxiliary algorithms implemented in LEMON.
615
616This group contains some algorithms implemented in LEMON
617in order to make it easier to implement complex algorithms.
618*/
619
620/**
621@defgroup gen_opt_group General Optimization Tools
622\brief This group contains some general optimization frameworks
623implemented in LEMON.
624
625This group contains some general optimization frameworks
626implemented in LEMON.
627*/
628
629/**
630@defgroup lp_group LP and MIP Solvers
631@ingroup gen_opt_group
632\brief LP and MIP solver interfaces for LEMON.
633
634This group contains LP and MIP solver interfaces for LEMON.
635Various LP solvers could be used in the same manner with this
636high-level interface.
637
638The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
639\ref cplex, \ref soplex.
640*/
641
642/**
643@defgroup lp_utils Tools for Lp and Mip Solvers
644@ingroup lp_group
645\brief Helper tools to the Lp and Mip solvers.
646
647This group adds some helper tools to general optimization framework
648implemented in LEMON.
649*/
650
651/**
652@defgroup metah Metaheuristics
653@ingroup gen_opt_group
654\brief Metaheuristics for LEMON library.
655
656This group contains some metaheuristic optimization tools.
657*/
658
659/**
660@defgroup utils Tools and Utilities
661\brief Tools and utilities for programming in LEMON
662
663Tools and utilities for programming in LEMON.
664*/
665
666/**
667@defgroup gutils Basic Graph Utilities
668@ingroup utils
669\brief Simple basic graph utilities.
670
671This group contains some simple basic graph utilities.
672*/
673
674/**
675@defgroup misc Miscellaneous Tools
676@ingroup utils
677\brief Tools for development, debugging and testing.
678
679This group contains several useful tools for development,
680debugging and testing.
681*/
682
683/**
684@defgroup timecount Time Measuring and Counting
685@ingroup misc
686\brief Simple tools for measuring the performance of algorithms.
687
688This group contains simple tools for measuring the performance
689of algorithms.
690*/
691
692/**
693@defgroup exceptions Exceptions
694@ingroup utils
695\brief Exceptions defined in LEMON.
696
697This group contains the exceptions defined in LEMON.
698*/
699
700/**
701@defgroup io_group Input-Output
702\brief Graph Input-Output methods
703
704This group contains the tools for importing and exporting graphs
705and graph related data. Now it supports the \ref lgf-format
706"LEMON Graph Format", the \c DIMACS format and the encapsulated
707postscript (EPS) format.
708*/
709
710/**
711@defgroup lemon_io LEMON Graph Format
712@ingroup io_group
713\brief Reading and writing LEMON Graph Format.
714
715This group contains methods for reading and writing
716\ref lgf-format "LEMON Graph Format".
717*/
718
719/**
720@defgroup eps_io Postscript Exporting
721@ingroup io_group
722\brief General \c EPS drawer and graph exporter
723
724This group contains general \c EPS drawing methods and special
725graph exporting tools.
726*/
727
728/**
729@defgroup dimacs_group DIMACS Format
730@ingroup io_group
731\brief Read and write files in DIMACS format
732
733Tools to read a digraph from or write it to a file in DIMACS format data.
734*/
735
736/**
737@defgroup nauty_group NAUTY Format
738@ingroup io_group
739\brief Read \e Nauty format
740
741Tool to read graphs from \e Nauty format data.
742*/
743
744/**
745@defgroup concept Concepts
746\brief Skeleton classes and concept checking classes
747
748This group contains the data/algorithm skeletons and concept checking
749classes implemented in LEMON.
750
751The purpose of the classes in this group is fourfold.
752
753- These classes contain the documentations of the %concepts. In order
754  to avoid document multiplications, an implementation of a concept
755  simply refers to the corresponding concept class.
756
757- These classes declare every functions, <tt>typedef</tt>s etc. an
758  implementation of the %concepts should provide, however completely
759  without implementations and real data structures behind the
760  interface. On the other hand they should provide nothing else. All
761  the algorithms working on a data structure meeting a certain concept
762  should compile with these classes. (Though it will not run properly,
763  of course.) In this way it is easily to check if an algorithm
764  doesn't use any extra feature of a certain implementation.
765
766- The concept descriptor classes also provide a <em>checker class</em>
767  that makes it possible to check whether a certain implementation of a
768  concept indeed provides all the required features.
769
770- Finally, They can serve as a skeleton of a new implementation of a concept.
771*/
772
773/**
774@defgroup graph_concepts Graph Structure Concepts
775@ingroup concept
776\brief Skeleton and concept checking classes for graph structures
777
778This group contains the skeletons and concept checking classes of
779graph structures.
780*/
781
782/**
783@defgroup map_concepts Map Concepts
784@ingroup concept
785\brief Skeleton and concept checking classes for maps
786
787This group contains the skeletons and concept checking classes of maps.
788*/
789
790/**
791@defgroup tools Standalone Utility Applications
792
793Some utility applications are listed here.
794
795The standard compilation procedure (<tt>./configure;make</tt>) will compile
796them, as well.
797*/
798
799/**
800\anchor demoprograms
801
802@defgroup demos Demo Programs
803
804Some demo programs are listed here. Their full source codes can be found in
805the \c demo subdirectory of the source tree.
806
807In order to compile them, use the <tt>make demo</tt> or the
808<tt>make check</tt> commands.
809*/
810
811}
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