doc/groups.dox
 author Peter Kovacs Thu, 15 Oct 2009 12:55:41 +0200 changeset 818 8452ca46e29a parent 817 432c54cec63c child 879 25804ef35064 permissions -rw-r--r--
Add citations to the min mean cycle classes (#179, #184)
1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
2  *
3  * This file is a part of LEMON, a generic C++ optimization library.
4  *
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  */
19 namespace lemon {
21 /**
22 @defgroup datas Data Structures
23 This group contains the several data structures implemented in LEMON.
24 */
26 /**
27 @defgroup graphs Graph Structures
28 @ingroup datas
29 \brief Graph structures implemented in LEMON.
31 The implementation of combinatorial algorithms heavily relies on
32 efficient graph implementations. LEMON offers data structures which are
33 planned to be easily used in an experimental phase of implementation studies,
34 and thereafter the program code can be made efficient by small modifications.
36 The most efficient implementation of diverse applications require the
37 usage of different physical graph implementations. These differences
38 appear in the size of graph we require to handle, memory or time usage
39 limitations or in the set of operations through which the graph can be
40 accessed.  LEMON provides several physical graph structures to meet
41 the diverging requirements of the possible users.  In order to save on
42 running time or on memory usage, some structures may fail to provide
43 some graph features like arc/edge or node deletion.
45 Alteration of standard containers need a very limited number of
46 operations, these together satisfy the everyday requirements.
47 In the case of graph structures, different operations are needed which do
48 not alter the physical graph, but gives another view. If some nodes or
49 arcs have to be hidden or the reverse oriented graph have to be used, then
50 this is the case. It also may happen that in a flow implementation
51 the residual graph can be accessed by another algorithm, or a node-set
52 is to be shrunk for another algorithm.
53 LEMON also provides a variety of graphs for these requirements called
55 in conjunction with other graph representations.
57 You are free to use the graph structure that fit your requirements
58 the best, most graph algorithms and auxiliary data structures can be used
59 with any graph structure.
62 */
64 /**
66 @ingroup graphs
67 \brief Adaptor classes for digraphs and graphs
69 This group contains several useful adaptor classes for digraphs and graphs.
71 The main parts of LEMON are the different graph structures, generic
72 graph algorithms, graph concepts, which couple them, and graph
73 adaptors. While the previous notions are more or less clear, the
74 latter one needs further explanation. Graph adaptors are graph classes
75 which serve for considering graph structures in different ways.
77 A short example makes this much clearer.  Suppose that we have an
78 instance \c g of a directed graph type, say ListDigraph and an algorithm
79 \code
80 template <typename Digraph>
81 int algorithm(const Digraph&);
82 \endcode
83 is 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
85 arcs.  In this case, an adaptor class is used, which (according
86 to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87 The adaptor uses the original digraph structure and digraph operations when
88 methods of the reversed oriented graph are called.  This means that the adaptor
89 have minor memory usage, and do not perform sophisticated algorithmic
90 actions.  The purpose of it is to give a tool for the cases when a
91 graph have to be used in a specific alteration.  If this alteration is
92 obtained by a usual construction like filtering the node or the arc set or
93 considering a new orientation, then an adaptor is worthwhile to use.
94 To come back to the reverse oriented graph, in this situation
95 \code
96 template<typename Digraph> class ReverseDigraph;
97 \endcode
98 template class can be used. The code looks as follows
99 \code
100 ListDigraph g;
101 ReverseDigraph<ListDigraph> rg(g);
102 int result = algorithm(rg);
103 \endcode
104 During running the algorithm, the original digraph \c g is untouched.
105 This techniques give rise to an elegant code, and based on stable
106 graph adaptors, complex algorithms can be implemented easily.
108 In flow, circulation and matching problems, the residual
109 graph is of particular importance. Combining an adaptor implementing
110 this with shortest path algorithms or minimum mean cycle algorithms,
111 a range of weighted and cardinality optimization algorithms can be
112 obtained. For other examples, the interested user is referred to the
113 detailed documentation of particular adaptors.
115 The behavior of graph adaptors can be very different. Some of them keep
116 capabilities of the original graph while in other cases this would be
117 meaningless. This means that the concepts that they meet depend
118 on the graph adaptor, and the wrapped graph.
119 For example, if an arc of a reversed digraph is deleted, this is carried
120 out by deleting the corresponding arc of the original digraph, thus the
121 adaptor modifies the original digraph.
122 However in case of a residual digraph, this operation has no sense.
124 Let us stand one more example here to simplify your work.
125 ReverseDigraph has constructor
126 \code
127 ReverseDigraph(Digraph& digraph);
128 \endcode
129 This means that in a situation, when a <tt>const %ListDigraph&</tt>
130 reference to a graph is given, then it have to be instantiated with
131 <tt>Digraph=const %ListDigraph</tt>.
132 \code
133 int algorithm1(const ListDigraph& g) {
134   ReverseDigraph<const ListDigraph> rg(g);
135   return algorithm2(rg);
136 }
137 \endcode
138 */
140 /**
141 @defgroup maps Maps
142 @ingroup datas
143 \brief Map structures implemented in LEMON.
145 This group contains the map structures implemented in LEMON.
147 LEMON provides several special purpose maps and map adaptors that e.g. combine
148 new maps from existing ones.
151 */
153 /**
154 @defgroup graph_maps Graph Maps
155 @ingroup maps
156 \brief Special graph-related maps.
158 This group contains maps that are specifically designed to assign
159 values to the nodes and arcs/edges of graphs.
161 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
162 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
163 */
165 /**
167 \ingroup maps
168 \brief Tools to create new maps from existing ones
170 This group contains map adaptors that are used to create "implicit"
171 maps from other maps.
174 They 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.
178 The typical usage of this classes is passing implicit maps to
179 algorithms.  If a function type algorithm is called then the function
180 type map adaptors can be used comfortable. For example let's see the
181 usage 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   }
193   Digraph::NodeMap<int> degree_map(graph);
195   graphToEps(graph, "graph.eps")
196     .coords(coords).scaleToA4().undirected()
197     .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
198     .run();
199 \endcode
200 The \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
202 and the previously created map. The composed map is a proper function to
203 get the color of each node.
205 The usage with class type algorithms is little bit harder. In this
206 case the function type map adaptors can not be used, because the
207 function map adaptors give back temporary objects.
208 \code
209   Digraph graph;
211   typedef Digraph::ArcMap<double> DoubleArcMap;
212   DoubleArcMap length(graph);
213   DoubleArcMap speed(graph);
215   typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
216   TimeMap time(length, speed);
218   Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
219   dijkstra.run(source, target);
220 \endcode
221 We have a length map and a maximum speed map on the arcs of a digraph.
222 The minimum time to pass the arc can be calculated as the division of
223 the two maps which can be done implicitly with the \c DivMap template
224 class. We use the implicit minimum time map as the length map of the
225 \c Dijkstra algorithm.
226 */
228 /**
229 @defgroup paths Path Structures
230 @ingroup datas
231 \brief %Path structures implemented in LEMON.
233 This group contains the path structures implemented in LEMON.
235 LEMON provides flexible data structures to work with paths.
236 All of them have similar interfaces and they can be copied easily with
237 assignment operators and copy constructors. This makes it easy and
238 efficient to have e.g. the Dijkstra algorithm to store its result in
239 any kind of path structure.
241 \sa \ref concepts::Path "Path concept"
242 */
244 /**
245 @defgroup heaps Heap Structures
246 @ingroup datas
247 \brief %Heap structures implemented in LEMON.
249 This group contains the heap structures implemented in LEMON.
251 LEMON provides several heap classes. They are efficient implementations
252 of the abstract data type \e priority \e queue. They store items with
253 specified values called \e priorities in such a way that finding and
254 removing the item with minimum priority are efficient.
255 The basic operations are adding and erasing items, changing the priority
256 of an item, etc.
258 Heaps are crucial in several algorithms, such as Dijkstra and Prim.
259 The heap implementations have the same interface, thus any of them can be
260 used easily in such algorithms.
262 \sa \ref concepts::Heap "Heap concept"
263 */
265 /**
266 @defgroup matrices Matrices
267 @ingroup datas
268 \brief Two dimensional data storages implemented in LEMON.
270 This group contains two dimensional data storages implemented in LEMON.
271 */
273 /**
274 @defgroup auxdat Auxiliary Data Structures
275 @ingroup datas
276 \brief Auxiliary data structures implemented in LEMON.
278 This group contains some data structures implemented in LEMON in
279 order to make it easier to implement combinatorial algorithms.
280 */
282 /**
283 @defgroup geomdat Geometric Data Structures
284 @ingroup auxdat
285 \brief Geometric data structures implemented in LEMON.
287 This group contains geometric data structures implemented in LEMON.
289  - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
290    vector with the usual operations.
291  - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
292    rectangular bounding box of a set of \ref lemon::dim2::Point
293    "dim2::Point"'s.
294 */
296 /**
297 @defgroup matrices Matrices
298 @ingroup auxdat
299 \brief Two dimensional data storages implemented in LEMON.
301 This group contains two dimensional data storages implemented in LEMON.
302 */
304 /**
305 @defgroup algs Algorithms
306 \brief This group contains the several algorithms
307 implemented in LEMON.
309 This group contains the several algorithms
310 implemented in LEMON.
311 */
313 /**
314 @defgroup search Graph Search
315 @ingroup algs
316 \brief Common graph search algorithms.
318 This group contains the common graph search algorithms, namely
319 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
320 \ref clrs01algorithms.
321 */
323 /**
324 @defgroup shortest_path Shortest Path Algorithms
325 @ingroup algs
326 \brief Algorithms for finding shortest paths.
328 This group contains the algorithms for finding shortest paths in digraphs
329 \ref clrs01algorithms.
331  - \ref Dijkstra algorithm for finding shortest paths from a source node
332    when all arc lengths are non-negative.
333  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
334    from a source node when arc lenghts can be either positive or negative,
335    but the digraph should not contain directed cycles with negative total
336    length.
337  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
338    for solving the \e all-pairs \e shortest \e paths \e problem when arc
339    lenghts can be either positive or negative, but the digraph should
340    not contain directed cycles with negative total length.
341  - \ref Suurballe A successive shortest path algorithm for finding
342    arc-disjoint paths between two nodes having minimum total length.
343 */
345 /**
346 @defgroup spantree Minimum Spanning Tree Algorithms
347 @ingroup algs
348 \brief Algorithms for finding minimum cost spanning trees and arborescences.
350 This group contains the algorithms for finding minimum cost spanning
351 trees and arborescences \ref clrs01algorithms.
352 */
354 /**
355 @defgroup max_flow Maximum Flow Algorithms
356 @ingroup algs
357 \brief Algorithms for finding maximum flows.
359 This group contains the algorithms for finding maximum flows and
360 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
362 The \e maximum \e flow \e problem is to find a flow of maximum value between
363 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
364 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
365 \f$s, t \in V\f$ source and target nodes.
366 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
367 following optimization problem.
369 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
370 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
371     \quad \forall u\in V\setminus\{s,t\} \f]
372 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
374 LEMON contains several algorithms for solving maximum flow problems:
375 - \ref EdmondsKarp Edmonds-Karp algorithm
376   \ref edmondskarp72theoretical.
377 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
378   \ref goldberg88newapproach.
379 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
380   \ref dinic70algorithm, \ref sleator83dynamic.
381 - \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
382   \ref goldberg88newapproach, \ref sleator83dynamic.
384 In most cases the \ref Preflow algorithm provides the
385 fastest method for computing a maximum flow. All implementations
386 also provide functions to query the minimum cut, which is the dual
387 problem of maximum flow.
389 \ref Circulation is a preflow push-relabel algorithm implemented directly
390 for finding feasible circulations, which is a somewhat different problem,
391 but it is strongly related to maximum flow.
393 */
395 /**
396 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
397 @ingroup algs
399 \brief Algorithms for finding minimum cost flows and circulations.
401 This group contains the algorithms for finding minimum cost flows and
403 problem and its dual solution, see \ref min_cost_flow
404 "Minimum Cost Flow Problem".
406 LEMON contains several algorithms for this problem.
407  - \ref NetworkSimplex Primal Network Simplex algorithm with various
408    pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
409  - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
410    cost scaling \ref goldberg90approximation, \ref goldberg97efficient,
411    \ref bunnagel98efficient.
412  - \ref CapacityScaling Successive Shortest %Path algorithm with optional
413    capacity scaling \ref edmondskarp72theoretical.
414  - \ref CancelAndTighten The Cancel and Tighten algorithm
415    \ref goldberg89cyclecanceling.
416  - \ref CycleCanceling Cycle-Canceling algorithms
417    \ref klein67primal, \ref goldberg89cyclecanceling.
419 In general NetworkSimplex is the most efficient implementation,
420 but in special cases other algorithms could be faster.
421 For example, if the total supply and/or capacities are rather small,
422 CapacityScaling is usually the fastest algorithm (without effective scaling).
423 */
425 /**
426 @defgroup min_cut Minimum Cut Algorithms
427 @ingroup algs
429 \brief Algorithms for finding minimum cut in graphs.
431 This group contains the algorithms for finding minimum cut in graphs.
433 The \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
435 outgoing 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
437 cut is the \f$X\f$ solution of the next optimization problem:
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]
442 LEMON contains several algorithms related to minimum cut problems:
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.
451 If you want to find minimum cut just between two distinict nodes,
452 see the \ref max_flow "maximum flow problem".
453 */
455 /**
456 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms
457 @ingroup algs
458 \brief Algorithms for finding minimum mean cycles.
460 This group contains the algorithms for finding minimum mean cycles
461 \ref clrs01algorithms, \ref amo93networkflows.
463 The \e minimum \e mean \e cycle \e problem is to find a directed cycle
464 of minimum mean length (cost) in a digraph.
465 The mean length of a cycle is the average length of its arcs, i.e. the
466 ratio between the total length of the cycle and the number of arcs on it.
468 This 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
470 conservative if and only if there is no directed cycle of negative total
471 length. For an arbitrary length function, the negative of the minimum
472 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
473 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
474 function.
476 LEMON contains three algorithms for solving the minimum mean cycle problem:
477 - \ref Karp "Karp"'s original algorithm \ref amo93networkflows,
478   \ref dasdan98minmeancycle.
479 - \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
480   version of Karp's algorithm \ref dasdan98minmeancycle.
481 - \ref Howard "Howard"'s policy iteration algorithm
482   \ref dasdan98minmeancycle.
484 In practice, the Howard algorithm proved to be by far the most efficient
485 one, though the best known theoretical bound on its running time is
486 exponential.
487 Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
488 O(n<sup>2</sup>+e), but the latter one is typically faster due to the
489 applied early termination scheme.
490 */
492 /**
493 @defgroup matching Matching Algorithms
494 @ingroup algs
495 \brief Algorithms for finding matchings in graphs and bipartite graphs.
497 This group contains the algorithms for calculating
498 matchings in graphs and bipartite graphs. The general matching problem is
499 finding a subset of the edges for which each node has at most one incident
500 edge.
502 There are several different algorithms for calculate matchings in
503 graphs.  The matching problems in bipartite graphs are generally
504 easier than in general graphs. The goal of the matching optimization
505 can be finding maximum cardinality, maximum weight or minimum cost
506 matching. The search can be constrained to find perfect or
507 maximum cardinality matching.
509 The matching algorithms implemented in LEMON:
510 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
511   for calculating maximum cardinality matching in bipartite graphs.
512 - \ref PrBipartiteMatching Push-relabel algorithm
513   for calculating maximum cardinality matching in bipartite graphs.
514 - \ref MaxWeightedBipartiteMatching
515   Successive shortest path algorithm for calculating maximum weighted
516   matching and maximum weighted bipartite matching in bipartite graphs.
517 - \ref MinCostMaxBipartiteMatching
518   Successive shortest path algorithm for calculating minimum cost maximum
519   matching in bipartite graphs.
520 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
521   maximum cardinality matching in general graphs.
522 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
523   maximum weighted matching in general graphs.
524 - \ref MaxWeightedPerfectMatching
525   Edmond's blossom shrinking algorithm for calculating maximum weighted
526   perfect matching in general graphs.
528 \image html bipartite_matching.png
529 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
530 */
532 /**
533 @defgroup graph_properties Connectivity and Other Graph Properties
534 @ingroup algs
535 \brief Algorithms for discovering the graph properties
537 This group contains the algorithms for discovering the graph properties
538 like connectivity, bipartiteness, euler property, simplicity etc.
540 \image html connected_components.png
541 \image latex connected_components.eps "Connected components" width=\textwidth
542 */
544 /**
545 @defgroup planar Planarity Embedding and Drawing
546 @ingroup algs
547 \brief Algorithms for planarity checking, embedding and drawing
549 This group contains the algorithms for planarity checking,
550 embedding and drawing.
552 \image html planar.png
553 \image latex planar.eps "Plane graph" width=\textwidth
554 */
556 /**
557 @defgroup approx Approximation Algorithms
558 @ingroup algs
559 \brief Approximation algorithms.
561 This group contains the approximation and heuristic algorithms
562 implemented in LEMON.
563 */
565 /**
566 @defgroup auxalg Auxiliary Algorithms
567 @ingroup algs
568 \brief Auxiliary algorithms implemented in LEMON.
570 This group contains some algorithms implemented in LEMON
571 in order to make it easier to implement complex algorithms.
572 */
574 /**
575 @defgroup gen_opt_group General Optimization Tools
576 \brief This group contains some general optimization frameworks
577 implemented in LEMON.
579 This group contains some general optimization frameworks
580 implemented in LEMON.
581 */
583 /**
584 @defgroup lp_group LP and MIP Solvers
585 @ingroup gen_opt_group
586 \brief LP and MIP solver interfaces for LEMON.
588 This group contains LP and MIP solver interfaces for LEMON.
589 Various LP solvers could be used in the same manner with this
590 high-level interface.
592 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
593 \ref cplex, \ref soplex.
594 */
596 /**
597 @defgroup lp_utils Tools for Lp and Mip Solvers
598 @ingroup lp_group
599 \brief Helper tools to the Lp and Mip solvers.
601 This group adds some helper tools to general optimization framework
602 implemented in LEMON.
603 */
605 /**
606 @defgroup metah Metaheuristics
607 @ingroup gen_opt_group
608 \brief Metaheuristics for LEMON library.
610 This group contains some metaheuristic optimization tools.
611 */
613 /**
614 @defgroup utils Tools and Utilities
615 \brief Tools and utilities for programming in LEMON
617 Tools and utilities for programming in LEMON.
618 */
620 /**
621 @defgroup gutils Basic Graph Utilities
622 @ingroup utils
623 \brief Simple basic graph utilities.
625 This group contains some simple basic graph utilities.
626 */
628 /**
629 @defgroup misc Miscellaneous Tools
630 @ingroup utils
631 \brief Tools for development, debugging and testing.
633 This group contains several useful tools for development,
634 debugging and testing.
635 */
637 /**
638 @defgroup timecount Time Measuring and Counting
639 @ingroup misc
640 \brief Simple tools for measuring the performance of algorithms.
642 This group contains simple tools for measuring the performance
643 of algorithms.
644 */
646 /**
647 @defgroup exceptions Exceptions
648 @ingroup utils
649 \brief Exceptions defined in LEMON.
651 This group contains the exceptions defined in LEMON.
652 */
654 /**
655 @defgroup io_group Input-Output
656 \brief Graph Input-Output methods
658 This group contains the tools for importing and exporting graphs
659 and graph related data. Now it supports the \ref lgf-format
660 "LEMON Graph Format", the \c DIMACS format and the encapsulated
661 postscript (EPS) format.
662 */
664 /**
665 @defgroup lemon_io LEMON Graph Format
666 @ingroup io_group
667 \brief Reading and writing LEMON Graph Format.
669 This group contains methods for reading and writing
670 \ref lgf-format "LEMON Graph Format".
671 */
673 /**
674 @defgroup eps_io Postscript Exporting
675 @ingroup io_group
676 \brief General \c EPS drawer and graph exporter
678 This group contains general \c EPS drawing methods and special
679 graph exporting tools.
680 */
682 /**
683 @defgroup dimacs_group DIMACS Format
684 @ingroup io_group
685 \brief Read and write files in DIMACS format
687 Tools to read a digraph from or write it to a file in DIMACS format data.
688 */
690 /**
691 @defgroup nauty_group NAUTY Format
692 @ingroup io_group
693 \brief Read \e Nauty format
695 Tool to read graphs from \e Nauty format data.
696 */
698 /**
699 @defgroup concept Concepts
700 \brief Skeleton classes and concept checking classes
702 This group contains the data/algorithm skeletons and concept checking
703 classes implemented in LEMON.
705 The purpose of the classes in this group is fourfold.
707 - These classes contain the documentations of the %concepts. In order
708   to avoid document multiplications, an implementation of a concept
709   simply refers to the corresponding concept class.
711 - These classes declare every functions, <tt>typedef</tt>s etc. an
712   implementation of the %concepts should provide, however completely
713   without implementations and real data structures behind the
714   interface. On the other hand they should provide nothing else. All
715   the algorithms working on a data structure meeting a certain concept
716   should compile with these classes. (Though it will not run properly,
717   of course.) In this way it is easily to check if an algorithm
718   doesn't use any extra feature of a certain implementation.
720 - The concept descriptor classes also provide a <em>checker class</em>
721   that makes it possible to check whether a certain implementation of a
722   concept indeed provides all the required features.
724 - Finally, They can serve as a skeleton of a new implementation of a concept.
725 */
727 /**
728 @defgroup graph_concepts Graph Structure Concepts
729 @ingroup concept
730 \brief Skeleton and concept checking classes for graph structures
732 This group contains the skeletons and concept checking classes of
733 graph structures.
734 */
736 /**
737 @defgroup map_concepts Map Concepts
738 @ingroup concept
739 \brief Skeleton and concept checking classes for maps
741 This group contains the skeletons and concept checking classes of maps.
742 */
744 /**
745 @defgroup tools Standalone Utility Applications
747 Some utility applications are listed here.
749 The standard compilation procedure (<tt>./configure;make</tt>) will compile
750 them, as well.
751 */
753 /**
754 \anchor demoprograms
756 @defgroup demos Demo Programs
758 Some demo programs are listed here. Their full source codes can be found in
759 the \c demo subdirectory of the source tree.
761 In order to compile them, use the <tt>make demo</tt> or the
762 <tt>make check</tt> commands.
763 */
765 }