Backport relevant parts of bugfixes [ad22262328b3], [61fdd06833a6] and [4add05447ca0] to branch 1.2 (#623)
1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
3 * This file is a part of LEMON, a generic C++ optimization library.
5 * Copyright (C) 2003-2010
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
22 @defgroup datas Data Structures
23 This group contains the several data structures implemented in LEMON.
27 @defgroup graphs Graph Structures
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
54 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
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.
61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
65 @defgroup graph_adaptors Adaptor Classes for 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
80 template <typename Digraph>
81 int algorithm(const Digraph&);
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
96 template<typename Digraph> class ReverseDigraph;
98 template class can be used. The code looks as follows
101 ReverseDigraph<ListDigraph> rg(g);
102 int result = algorithm(rg);
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
127 ReverseDigraph(Digraph& digraph);
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>.
133 int algorithm1(const ListDigraph& g) {
134 ReverseDigraph<const ListDigraph> rg(g);
135 return algorithm2(rg);
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.
150 <b>See also:</b> \ref map_concepts "Map Concepts".
154 @defgroup graph_maps Graph 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".
166 \defgroup map_adaptors Map Adaptors
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.
173 Most of them are \ref concepts::ReadMap "read-only 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.
183 Color nodeColor(int deg) {
185 return Color(0.5, 0.0, 0.5);
186 } else if (deg == 1) {
187 return Color(1.0, 0.5, 1.0);
189 return Color(0.0, 0.0, 0.0);
193 Digraph::NodeMap<int> degree_map(graph);
195 graphToEps(graph, "graph.eps")
196 .coords(coords).scaleToA4().undirected()
197 .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
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.
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);
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.
229 @defgroup paths Path Structures
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"
245 @defgroup heaps Heap Structures
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
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"
266 @defgroup auxdat Auxiliary Data Structures
268 \brief Auxiliary data structures implemented in LEMON.
270 This group contains some data structures implemented in LEMON in
271 order to make it easier to implement combinatorial algorithms.
275 @defgroup geomdat Geometric Data Structures
277 \brief Geometric data structures implemented in LEMON.
279 This 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
289 @defgroup algs Algorithms
290 \brief This group contains the several algorithms
291 implemented in LEMON.
293 This group contains the several algorithms
294 implemented in LEMON.
298 @defgroup search Graph Search
300 \brief Common graph search algorithms.
302 This group contains the common graph search algorithms, namely
303 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
304 \ref clrs01algorithms.
308 @defgroup shortest_path Shortest Path Algorithms
310 \brief Algorithms for finding shortest paths.
312 This group contains the algorithms for finding shortest paths in digraphs
313 \ref clrs01algorithms.
315 - \ref Dijkstra algorithm for finding shortest paths from a source node
316 when all arc lengths are non-negative.
317 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
318 from a source node when arc lenghts can be either positive or negative,
319 but the digraph should not contain directed cycles with negative total
321 - \ref Suurballe A successive shortest path algorithm for finding
322 arc-disjoint paths between two nodes having minimum total length.
326 @defgroup spantree Minimum Spanning Tree Algorithms
328 \brief Algorithms for finding minimum cost spanning trees and arborescences.
330 This group contains the algorithms for finding minimum cost spanning
331 trees and arborescences \ref clrs01algorithms.
335 @defgroup max_flow Maximum Flow Algorithms
337 \brief Algorithms for finding maximum flows.
339 This group contains the algorithms for finding maximum flows and
340 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
342 The \e maximum \e flow \e problem is to find a flow of maximum value between
343 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
344 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
345 \f$s, t \in V\f$ source and target nodes.
346 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
347 following optimization problem.
349 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
350 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
351 \quad \forall u\in V\setminus\{s,t\} \f]
352 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
354 \ref Preflow is an efficient implementation of Goldberg-Tarjan's
355 preflow push-relabel algorithm \ref goldberg88newapproach for finding
356 maximum flows. It also provides functions to query the minimum cut,
357 which is the dual problem of maximum flow.
359 \ref Circulation is a preflow push-relabel algorithm implemented directly
360 for finding feasible circulations, which is a somewhat different problem,
361 but it is strongly related to maximum flow.
362 For more information, see \ref Circulation.
366 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
369 \brief Algorithms for finding minimum cost flows and circulations.
371 This group contains the algorithms for finding minimum cost flows and
372 circulations \ref amo93networkflows. For more information about this
373 problem and its dual solution, see \ref min_cost_flow
374 "Minimum Cost Flow Problem".
376 LEMON contains several algorithms for this problem.
377 - \ref NetworkSimplex Primal Network Simplex algorithm with various
378 pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
379 - \ref CostScaling Cost Scaling algorithm based on push/augment and
380 relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
381 \ref bunnagel98efficient.
382 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
383 shortest path method \ref edmondskarp72theoretical.
384 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
385 strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
387 In general NetworkSimplex is the most efficient implementation,
388 but in special cases other algorithms could be faster.
389 For example, if the total supply and/or capacities are rather small,
390 CapacityScaling is usually the fastest algorithm (without effective scaling).
394 @defgroup min_cut Minimum Cut Algorithms
397 \brief Algorithms for finding minimum cut in graphs.
399 This group contains the algorithms for finding minimum cut in graphs.
401 The \e minimum \e cut \e problem is to find a non-empty and non-complete
402 \f$X\f$ subset of the nodes with minimum overall capacity on
403 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
404 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
405 cut is the \f$X\f$ solution of the next optimization problem:
407 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
408 \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
410 LEMON contains several algorithms related to minimum cut problems:
412 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
414 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
415 all-pairs minimum cut in undirected graphs.
417 If you want to find minimum cut just between two distinict nodes,
418 see the \ref max_flow "maximum flow problem".
422 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms
424 \brief Algorithms for finding minimum mean cycles.
426 This group contains the algorithms for finding minimum mean cycles
427 \ref clrs01algorithms, \ref amo93networkflows.
429 The \e minimum \e mean \e cycle \e problem is to find a directed cycle
430 of minimum mean length (cost) in a digraph.
431 The mean length of a cycle is the average length of its arcs, i.e. the
432 ratio between the total length of the cycle and the number of arcs on it.
434 This problem has an important connection to \e conservative \e length
435 \e functions, too. A length function on the arcs of a digraph is called
436 conservative if and only if there is no directed cycle of negative total
437 length. For an arbitrary length function, the negative of the minimum
438 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
439 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
442 LEMON contains three algorithms for solving the minimum mean cycle problem:
443 - \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
444 \ref dasdan98minmeancycle.
445 - \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
446 version of Karp's algorithm \ref dasdan98minmeancycle.
447 - \ref HowardMmc Howard's policy iteration algorithm
448 \ref dasdan98minmeancycle.
450 In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
451 most efficient one, though the best known theoretical bound on its running
453 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
454 run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
455 typically faster due to the applied early termination scheme.
459 @defgroup matching Matching Algorithms
461 \brief Algorithms for finding matchings in graphs and bipartite graphs.
463 This group contains the algorithms for calculating
464 matchings in graphs and bipartite graphs. The general matching problem is
465 finding a subset of the edges for which each node has at most one incident
468 There are several different algorithms for calculate matchings in
469 graphs. The matching problems in bipartite graphs are generally
470 easier than in general graphs. The goal of the matching optimization
471 can be finding maximum cardinality, maximum weight or minimum cost
472 matching. The search can be constrained to find perfect or
473 maximum cardinality matching.
475 The matching algorithms implemented in LEMON:
476 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
477 maximum cardinality matching in general graphs.
478 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
479 maximum weighted matching in general graphs.
480 - \ref MaxWeightedPerfectMatching
481 Edmond's blossom shrinking algorithm for calculating maximum weighted
482 perfect matching in general graphs.
483 - \ref MaxFractionalMatching Push-relabel algorithm for calculating
484 maximum cardinality fractional matching in general graphs.
485 - \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
486 maximum weighted fractional matching in general graphs.
487 - \ref MaxWeightedPerfectFractionalMatching
488 Augmenting path algorithm for calculating maximum weighted
489 perfect fractional matching in general graphs.
491 \image html matching.png
492 \image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
496 @defgroup graph_properties Connectivity and Other Graph Properties
498 \brief Algorithms for discovering the graph properties
500 This group contains the algorithms for discovering the graph properties
501 like connectivity, bipartiteness, euler property, simplicity etc.
503 \image html connected_components.png
504 \image latex connected_components.eps "Connected components" width=\textwidth
508 @defgroup planar Planarity Embedding and Drawing
510 \brief Algorithms for planarity checking, embedding and drawing
512 This group contains the algorithms for planarity checking,
513 embedding and drawing.
515 \image html planar.png
516 \image latex planar.eps "Plane graph" width=\textwidth
520 @defgroup auxalg Auxiliary Algorithms
522 \brief Auxiliary algorithms implemented in LEMON.
524 This group contains some algorithms implemented in LEMON
525 in order to make it easier to implement complex algorithms.
529 @defgroup gen_opt_group General Optimization Tools
530 \brief This group contains some general optimization frameworks
531 implemented in LEMON.
533 This group contains some general optimization frameworks
534 implemented in LEMON.
538 @defgroup lp_group LP and MIP Solvers
539 @ingroup gen_opt_group
540 \brief LP and MIP solver interfaces for LEMON.
542 This group contains LP and MIP solver interfaces for LEMON.
543 Various LP solvers could be used in the same manner with this
544 high-level interface.
546 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
547 \ref cplex, \ref soplex.
551 @defgroup utils Tools and Utilities
552 \brief Tools and utilities for programming in LEMON
554 Tools and utilities for programming in LEMON.
558 @defgroup gutils Basic Graph Utilities
560 \brief Simple basic graph utilities.
562 This group contains some simple basic graph utilities.
566 @defgroup misc Miscellaneous Tools
568 \brief Tools for development, debugging and testing.
570 This group contains several useful tools for development,
571 debugging and testing.
575 @defgroup timecount Time Measuring and Counting
577 \brief Simple tools for measuring the performance of algorithms.
579 This group contains simple tools for measuring the performance
584 @defgroup exceptions Exceptions
586 \brief Exceptions defined in LEMON.
588 This group contains the exceptions defined in LEMON.
592 @defgroup io_group Input-Output
593 \brief Graph Input-Output methods
595 This group contains the tools for importing and exporting graphs
596 and graph related data. Now it supports the \ref lgf-format
597 "LEMON Graph Format", the \c DIMACS format and the encapsulated
598 postscript (EPS) format.
602 @defgroup lemon_io LEMON Graph Format
604 \brief Reading and writing LEMON Graph Format.
606 This group contains methods for reading and writing
607 \ref lgf-format "LEMON Graph Format".
611 @defgroup eps_io Postscript Exporting
613 \brief General \c EPS drawer and graph exporter
615 This group contains general \c EPS drawing methods and special
616 graph exporting tools.
620 @defgroup dimacs_group DIMACS Format
622 \brief Read and write files in DIMACS format
624 Tools to read a digraph from or write it to a file in DIMACS format data.
628 @defgroup nauty_group NAUTY Format
630 \brief Read \e Nauty format
632 Tool to read graphs from \e Nauty format data.
636 @defgroup concept Concepts
637 \brief Skeleton classes and concept checking classes
639 This group contains the data/algorithm skeletons and concept checking
640 classes implemented in LEMON.
642 The purpose of the classes in this group is fourfold.
644 - These classes contain the documentations of the %concepts. In order
645 to avoid document multiplications, an implementation of a concept
646 simply refers to the corresponding concept class.
648 - These classes declare every functions, <tt>typedef</tt>s etc. an
649 implementation of the %concepts should provide, however completely
650 without implementations and real data structures behind the
651 interface. On the other hand they should provide nothing else. All
652 the algorithms working on a data structure meeting a certain concept
653 should compile with these classes. (Though it will not run properly,
654 of course.) In this way it is easily to check if an algorithm
655 doesn't use any extra feature of a certain implementation.
657 - The concept descriptor classes also provide a <em>checker class</em>
658 that makes it possible to check whether a certain implementation of a
659 concept indeed provides all the required features.
661 - Finally, They can serve as a skeleton of a new implementation of a concept.
665 @defgroup graph_concepts Graph Structure Concepts
667 \brief Skeleton and concept checking classes for graph structures
669 This group contains the skeletons and concept checking classes of
674 @defgroup map_concepts Map Concepts
676 \brief Skeleton and concept checking classes for maps
678 This group contains the skeletons and concept checking classes of maps.
682 @defgroup tools Standalone Utility Applications
684 Some utility applications are listed here.
686 The standard compilation procedure (<tt>./configure;make</tt>) will compile
693 @defgroup demos Demo Programs
695 Some demo programs are listed here. Their full source codes can be found in
696 the \c demo subdirectory of the source tree.
698 In order to compile them, use the <tt>make demo</tt> or the
699 <tt>make check</tt> commands.