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1 | 1 |
SET(PACKAGE_NAME ${PROJECT_NAME}) |
2 | 2 |
SET(PACKAGE_VERSION ${PROJECT_VERSION}) |
3 | 3 |
SET(abs_top_srcdir ${PROJECT_SOURCE_DIR}) |
4 | 4 |
SET(abs_top_builddir ${PROJECT_BINARY_DIR}) |
5 | 5 |
|
6 | 6 |
CONFIGURE_FILE( |
7 | 7 |
${PROJECT_SOURCE_DIR}/doc/Doxyfile.in |
8 | 8 |
${PROJECT_BINARY_DIR}/doc/Doxyfile |
9 | 9 |
@ONLY |
10 | 10 |
) |
11 | 11 |
|
12 | 12 |
IF(DOXYGEN_EXECUTABLE AND PYTHONINTERP_FOUND AND GHOSTSCRIPT_EXECUTABLE) |
13 | 13 |
FILE(MAKE_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/) |
14 | 14 |
SET(GHOSTSCRIPT_OPTIONS -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha) |
15 | 15 |
ADD_CUSTOM_TARGET(html |
16 | 16 |
COMMAND ${CMAKE_COMMAND} -E remove_directory gen-images |
17 | 17 |
COMMAND ${CMAKE_COMMAND} -E make_directory gen-images |
18 | 18 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/bipartite_matching.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_matching.eps |
19 | 19 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/bipartite_partitions.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_partitions.eps |
20 | 20 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/connected_components.eps |
21 | 21 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/edge_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/edge_biconnected_components.eps |
22 | 22 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/grid_graph.png ${CMAKE_CURRENT_SOURCE_DIR}/images/grid_graph.eps |
23 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/matching.png ${CMAKE_CURRENT_SOURCE_DIR}/images/matching.eps |
|
23 | 24 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/node_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/node_biconnected_components.eps |
24 | 25 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_0.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_0.eps |
25 | 26 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_1.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_1.eps |
26 | 27 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_2.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_2.eps |
27 | 28 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_3.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_3.eps |
28 | 29 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/nodeshape_4.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_4.eps |
29 | 30 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/planar.png ${CMAKE_CURRENT_SOURCE_DIR}/images/planar.eps |
30 | 31 |
COMMAND ${GHOSTSCRIPT_EXECUTABLE} ${GHOSTSCRIPT_OPTIONS} -r18 -sOutputFile=gen-images/strongly_connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/strongly_connected_components.eps |
31 | 32 |
COMMAND ${CMAKE_COMMAND} -E remove_directory html |
32 | 33 |
COMMAND ${PYTHON_EXECUTABLE} ${PROJECT_SOURCE_DIR}/scripts/bib2dox.py ${CMAKE_CURRENT_SOURCE_DIR}/references.bib >references.dox |
33 | 34 |
COMMAND ${DOXYGEN_EXECUTABLE} Doxyfile |
34 | 35 |
WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR} |
35 | 36 |
) |
36 | 37 |
|
37 | 38 |
SET_TARGET_PROPERTIES(html PROPERTIES PROJECT_LABEL BUILD_DOC) |
38 | 39 |
|
39 | 40 |
IF(UNIX) |
40 | 41 |
INSTALL( |
41 | 42 |
DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/ |
42 | 43 |
DESTINATION share/doc/lemon/html |
43 | 44 |
COMPONENT html_documentation |
44 | 45 |
) |
45 | 46 |
ELSEIF(WIN32) |
46 | 47 |
INSTALL( |
47 | 48 |
DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/ |
48 | 49 |
DESTINATION doc |
49 | 50 |
COMPONENT html_documentation |
50 | 51 |
) |
51 | 52 |
ENDIF() |
52 | 53 |
|
53 | 54 |
ENDIF() |
1 | 1 |
EXTRA_DIST += \ |
2 | 2 |
doc/Doxyfile.in \ |
3 | 3 |
doc/DoxygenLayout.xml \ |
4 | 4 |
doc/coding_style.dox \ |
5 | 5 |
doc/dirs.dox \ |
6 | 6 |
doc/groups.dox \ |
7 | 7 |
doc/lgf.dox \ |
8 | 8 |
doc/license.dox \ |
9 | 9 |
doc/mainpage.dox \ |
10 | 10 |
doc/migration.dox \ |
11 | 11 |
doc/min_cost_flow.dox \ |
12 | 12 |
doc/named-param.dox \ |
13 | 13 |
doc/namespaces.dox \ |
14 | 14 |
doc/html \ |
15 | 15 |
doc/CMakeLists.txt |
16 | 16 |
|
17 | 17 |
DOC_EPS_IMAGES18 = \ |
18 | 18 |
grid_graph.eps \ |
19 | 19 |
nodeshape_0.eps \ |
20 | 20 |
nodeshape_1.eps \ |
21 | 21 |
nodeshape_2.eps \ |
22 | 22 |
nodeshape_3.eps \ |
23 | 23 |
nodeshape_4.eps |
24 | 24 |
|
25 | 25 |
DOC_EPS_IMAGES27 = \ |
26 | 26 |
bipartite_matching.eps \ |
27 | 27 |
bipartite_partitions.eps \ |
28 | 28 |
connected_components.eps \ |
29 | 29 |
edge_biconnected_components.eps \ |
30 |
matching.eps \ |
|
30 | 31 |
node_biconnected_components.eps \ |
31 | 32 |
planar.eps \ |
32 | 33 |
strongly_connected_components.eps |
33 | 34 |
|
34 | 35 |
DOC_EPS_IMAGES = \ |
35 | 36 |
$(DOC_EPS_IMAGES18) \ |
36 | 37 |
$(DOC_EPS_IMAGES27) |
37 | 38 |
|
38 | 39 |
DOC_PNG_IMAGES = \ |
39 | 40 |
$(DOC_EPS_IMAGES:%.eps=doc/gen-images/%.png) |
40 | 41 |
|
41 | 42 |
EXTRA_DIST += $(DOC_EPS_IMAGES:%=doc/images/%) |
42 | 43 |
|
43 | 44 |
doc/html: |
44 | 45 |
$(MAKE) $(AM_MAKEFLAGS) html |
45 | 46 |
|
46 | 47 |
GS_COMMAND=gs -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 |
47 | 48 |
|
48 | 49 |
$(DOC_EPS_IMAGES18:%.eps=doc/gen-images/%.png): doc/gen-images/%.png: doc/images/%.eps |
49 | 50 |
-mkdir doc/gen-images |
50 | 51 |
if test ${gs_found} = yes; then \ |
51 | 52 |
$(GS_COMMAND) -sDEVICE=pngalpha -r18 -sOutputFile=$@ $<; \ |
52 | 53 |
else \ |
53 | 54 |
echo; \ |
54 | 55 |
echo "Ghostscript not found."; \ |
55 | 56 |
echo; \ |
56 | 57 |
exit 1; \ |
57 | 58 |
fi |
58 | 59 |
|
59 | 60 |
$(DOC_EPS_IMAGES27:%.eps=doc/gen-images/%.png): doc/gen-images/%.png: doc/images/%.eps |
60 | 61 |
-mkdir doc/gen-images |
61 | 62 |
if test ${gs_found} = yes; then \ |
62 | 63 |
$(GS_COMMAND) -sDEVICE=pngalpha -r27 -sOutputFile=$@ $<; \ |
63 | 64 |
else \ |
64 | 65 |
echo; \ |
65 | 66 |
echo "Ghostscript not found."; \ |
66 | 67 |
echo; \ |
67 | 68 |
exit 1; \ |
68 | 69 |
fi |
69 | 70 |
|
70 | 71 |
references.dox: doc/references.bib |
71 | 72 |
if test ${python_found} = yes; then \ |
72 | 73 |
cd doc; \ |
73 | 74 |
python @abs_top_srcdir@/scripts/bib2dox.py @abs_top_builddir@/$< >$@; \ |
74 | 75 |
cd ..; \ |
75 | 76 |
else \ |
76 | 77 |
echo; \ |
77 | 78 |
echo "Python not found."; \ |
78 | 79 |
echo; \ |
79 | 80 |
exit 1; \ |
80 | 81 |
fi |
81 | 82 |
|
82 | 83 |
html-local: $(DOC_PNG_IMAGES) references.dox |
83 | 84 |
if test ${doxygen_found} = yes; then \ |
84 | 85 |
cd doc; \ |
85 | 86 |
doxygen Doxyfile; \ |
86 | 87 |
cd ..; \ |
87 | 88 |
else \ |
88 | 89 |
echo; \ |
89 | 90 |
echo "Doxygen not found."; \ |
90 | 91 |
echo; \ |
91 | 92 |
exit 1; \ |
92 | 93 |
fi |
93 | 94 |
|
94 | 95 |
clean-local: |
95 | 96 |
-rm -rf doc/html |
96 | 97 |
-rm -f doc/doxygen.log |
97 | 98 |
-rm -f $(DOC_PNG_IMAGES) |
98 | 99 |
-rm -rf doc/gen-images |
99 | 100 |
|
100 | 101 |
update-external-tags: |
101 | 102 |
wget -O doc/libstdc++.tag.tmp http://gcc.gnu.org/onlinedocs/libstdc++/latest-doxygen/libstdc++.tag && \ |
102 | 103 |
mv doc/libstdc++.tag.tmp doc/libstdc++.tag || \ |
103 | 104 |
rm doc/libstdc++.tag.tmp |
104 | 105 |
|
105 | 106 |
install-html-local: doc/html |
106 | 107 |
@$(NORMAL_INSTALL) |
107 | 108 |
$(mkinstalldirs) $(DESTDIR)$(htmldir)/html |
108 | 109 |
for p in doc/html/*.{html,css,png,map,gif,tag} ; do \ |
109 | 110 |
f="`echo $$p | sed -e 's|^.*/||'`"; \ |
110 | 111 |
echo " $(INSTALL_DATA) $$p $(DESTDIR)$(htmldir)/html/$$f"; \ |
111 | 112 |
$(INSTALL_DATA) $$p $(DESTDIR)$(htmldir)/html/$$f; \ |
112 | 113 |
done |
113 | 114 |
|
114 | 115 |
uninstall-local: |
115 | 116 |
@$(NORMAL_UNINSTALL) |
116 | 117 |
for p in doc/html/*.{html,css,png,map,gif,tag} ; do \ |
117 | 118 |
f="`echo $$p | sed -e 's|^.*/||'`"; \ |
118 | 119 |
echo " rm -f $(DESTDIR)$(htmldir)/html/$$f"; \ |
119 | 120 |
rm -f $(DESTDIR)$(htmldir)/html/$$f; \ |
120 | 121 |
done |
121 | 122 |
|
122 | 123 |
.PHONY: update-external-tags |
... | ... |
@@ -334,386 +334,386 @@ |
334 | 334 |
from a source node when arc lenghts can be either positive or negative, |
335 | 335 |
but the digraph should not contain directed cycles with negative total |
336 | 336 |
length. |
337 | 337 |
- \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms |
338 | 338 |
for solving the \e all-pairs \e shortest \e paths \e problem when arc |
339 | 339 |
lenghts can be either positive or negative, but the digraph should |
340 | 340 |
not contain directed cycles with negative total length. |
341 | 341 |
- \ref Suurballe A successive shortest path algorithm for finding |
342 | 342 |
arc-disjoint paths between two nodes having minimum total length. |
343 | 343 |
*/ |
344 | 344 |
|
345 | 345 |
/** |
346 | 346 |
@defgroup spantree Minimum Spanning Tree Algorithms |
347 | 347 |
@ingroup algs |
348 | 348 |
\brief Algorithms for finding minimum cost spanning trees and arborescences. |
349 | 349 |
|
350 | 350 |
This group contains the algorithms for finding minimum cost spanning |
351 | 351 |
trees and arborescences \ref clrs01algorithms. |
352 | 352 |
*/ |
353 | 353 |
|
354 | 354 |
/** |
355 | 355 |
@defgroup max_flow Maximum Flow Algorithms |
356 | 356 |
@ingroup algs |
357 | 357 |
\brief Algorithms for finding maximum flows. |
358 | 358 |
|
359 | 359 |
This group contains the algorithms for finding maximum flows and |
360 | 360 |
feasible circulations \ref clrs01algorithms, \ref amo93networkflows. |
361 | 361 |
|
362 | 362 |
The \e maximum \e flow \e problem is to find a flow of maximum value between |
363 | 363 |
a single source and a single target. Formally, there is a \f$G=(V,A)\f$ |
364 | 364 |
digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and |
365 | 365 |
\f$s, t \in V\f$ source and target nodes. |
366 | 366 |
A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the |
367 | 367 |
following optimization problem. |
368 | 368 |
|
369 | 369 |
\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f] |
370 | 370 |
\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu) |
371 | 371 |
\quad \forall u\in V\setminus\{s,t\} \f] |
372 | 372 |
\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f] |
373 | 373 |
|
374 | 374 |
LEMON contains several algorithms for solving maximum flow problems: |
375 | 375 |
- \ref EdmondsKarp Edmonds-Karp algorithm |
376 | 376 |
\ref edmondskarp72theoretical. |
377 | 377 |
- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm |
378 | 378 |
\ref goldberg88newapproach. |
379 | 379 |
- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees |
380 | 380 |
\ref dinic70algorithm, \ref sleator83dynamic. |
381 | 381 |
- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees |
382 | 382 |
\ref goldberg88newapproach, \ref sleator83dynamic. |
383 | 383 |
|
384 | 384 |
In most cases the \ref Preflow algorithm provides the |
385 | 385 |
fastest method for computing a maximum flow. All implementations |
386 | 386 |
also provide functions to query the minimum cut, which is the dual |
387 | 387 |
problem of maximum flow. |
388 | 388 |
|
389 | 389 |
\ref Circulation is a preflow push-relabel algorithm implemented directly |
390 | 390 |
for finding feasible circulations, which is a somewhat different problem, |
391 | 391 |
but it is strongly related to maximum flow. |
392 | 392 |
For more information, see \ref Circulation. |
393 | 393 |
*/ |
394 | 394 |
|
395 | 395 |
/** |
396 | 396 |
@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms |
397 | 397 |
@ingroup algs |
398 | 398 |
|
399 | 399 |
\brief Algorithms for finding minimum cost flows and circulations. |
400 | 400 |
|
401 | 401 |
This group contains the algorithms for finding minimum cost flows and |
402 | 402 |
circulations \ref amo93networkflows. For more information about this |
403 | 403 |
problem and its dual solution, see \ref min_cost_flow |
404 | 404 |
"Minimum Cost Flow Problem". |
405 | 405 |
|
406 | 406 |
LEMON contains several algorithms for this problem. |
407 | 407 |
- \ref NetworkSimplex Primal Network Simplex algorithm with various |
408 | 408 |
pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. |
409 | 409 |
- \ref CostScaling Cost Scaling algorithm based on push/augment and |
410 | 410 |
relabel operations \ref goldberg90approximation, \ref goldberg97efficient, |
411 | 411 |
\ref bunnagel98efficient. |
412 | 412 |
- \ref CapacityScaling Capacity Scaling algorithm based on the successive |
413 | 413 |
shortest path method \ref edmondskarp72theoretical. |
414 | 414 |
- \ref CycleCanceling Cycle-Canceling algorithms, two of which are |
415 | 415 |
strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling. |
416 | 416 |
|
417 | 417 |
In general NetworkSimplex is the most efficient implementation, |
418 | 418 |
but in special cases other algorithms could be faster. |
419 | 419 |
For example, if the total supply and/or capacities are rather small, |
420 | 420 |
CapacityScaling is usually the fastest algorithm (without effective scaling). |
421 | 421 |
*/ |
422 | 422 |
|
423 | 423 |
/** |
424 | 424 |
@defgroup min_cut Minimum Cut Algorithms |
425 | 425 |
@ingroup algs |
426 | 426 |
|
427 | 427 |
\brief Algorithms for finding minimum cut in graphs. |
428 | 428 |
|
429 | 429 |
This group contains the algorithms for finding minimum cut in graphs. |
430 | 430 |
|
431 | 431 |
The \e minimum \e cut \e problem is to find a non-empty and non-complete |
432 | 432 |
\f$X\f$ subset of the nodes with minimum overall capacity on |
433 | 433 |
outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a |
434 | 434 |
\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum |
435 | 435 |
cut is the \f$X\f$ solution of the next optimization problem: |
436 | 436 |
|
437 | 437 |
\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} |
438 | 438 |
\sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f] |
439 | 439 |
|
440 | 440 |
LEMON contains several algorithms related to minimum cut problems: |
441 | 441 |
|
442 | 442 |
- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut |
443 | 443 |
in directed graphs. |
444 | 444 |
- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for |
445 | 445 |
calculating minimum cut in undirected graphs. |
446 | 446 |
- \ref GomoryHu "Gomory-Hu tree computation" for calculating |
447 | 447 |
all-pairs minimum cut in undirected graphs. |
448 | 448 |
|
449 | 449 |
If you want to find minimum cut just between two distinict nodes, |
450 | 450 |
see the \ref max_flow "maximum flow problem". |
451 | 451 |
*/ |
452 | 452 |
|
453 | 453 |
/** |
454 | 454 |
@defgroup min_mean_cycle Minimum Mean Cycle Algorithms |
455 | 455 |
@ingroup algs |
456 | 456 |
\brief Algorithms for finding minimum mean cycles. |
457 | 457 |
|
458 | 458 |
This group contains the algorithms for finding minimum mean cycles |
459 | 459 |
\ref clrs01algorithms, \ref amo93networkflows. |
460 | 460 |
|
461 | 461 |
The \e minimum \e mean \e cycle \e problem is to find a directed cycle |
462 | 462 |
of minimum mean length (cost) in a digraph. |
463 | 463 |
The mean length of a cycle is the average length of its arcs, i.e. the |
464 | 464 |
ratio between the total length of the cycle and the number of arcs on it. |
465 | 465 |
|
466 | 466 |
This problem has an important connection to \e conservative \e length |
467 | 467 |
\e functions, too. A length function on the arcs of a digraph is called |
468 | 468 |
conservative if and only if there is no directed cycle of negative total |
469 | 469 |
length. For an arbitrary length function, the negative of the minimum |
470 | 470 |
cycle mean is the smallest \f$\epsilon\f$ value so that increasing the |
471 | 471 |
arc lengths uniformly by \f$\epsilon\f$ results in a conservative length |
472 | 472 |
function. |
473 | 473 |
|
474 | 474 |
LEMON contains three algorithms for solving the minimum mean cycle problem: |
475 | 475 |
- \ref Karp "Karp"'s original algorithm \ref amo93networkflows, |
476 | 476 |
\ref dasdan98minmeancycle. |
477 | 477 |
- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved |
478 | 478 |
version of Karp's algorithm \ref dasdan98minmeancycle. |
479 | 479 |
- \ref Howard "Howard"'s policy iteration algorithm |
480 | 480 |
\ref dasdan98minmeancycle. |
481 | 481 |
|
482 | 482 |
In practice, the Howard algorithm proved to be by far the most efficient |
483 | 483 |
one, though the best known theoretical bound on its running time is |
484 | 484 |
exponential. |
485 | 485 |
Both Karp and HartmannOrlin algorithms run in time O(ne) and use space |
486 | 486 |
O(n<sup>2</sup>+e), but the latter one is typically faster due to the |
487 | 487 |
applied early termination scheme. |
488 | 488 |
*/ |
489 | 489 |
|
490 | 490 |
/** |
491 | 491 |
@defgroup matching Matching Algorithms |
492 | 492 |
@ingroup algs |
493 | 493 |
\brief Algorithms for finding matchings in graphs and bipartite graphs. |
494 | 494 |
|
495 | 495 |
This group contains the algorithms for calculating |
496 | 496 |
matchings in graphs and bipartite graphs. The general matching problem is |
497 | 497 |
finding a subset of the edges for which each node has at most one incident |
498 | 498 |
edge. |
499 | 499 |
|
500 | 500 |
There are several different algorithms for calculate matchings in |
501 | 501 |
graphs. The matching problems in bipartite graphs are generally |
502 | 502 |
easier than in general graphs. The goal of the matching optimization |
503 | 503 |
can be finding maximum cardinality, maximum weight or minimum cost |
504 | 504 |
matching. The search can be constrained to find perfect or |
505 | 505 |
maximum cardinality matching. |
506 | 506 |
|
507 | 507 |
The matching algorithms implemented in LEMON: |
508 | 508 |
- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm |
509 | 509 |
for calculating maximum cardinality matching in bipartite graphs. |
510 | 510 |
- \ref PrBipartiteMatching Push-relabel algorithm |
511 | 511 |
for calculating maximum cardinality matching in bipartite graphs. |
512 | 512 |
- \ref MaxWeightedBipartiteMatching |
513 | 513 |
Successive shortest path algorithm for calculating maximum weighted |
514 | 514 |
matching and maximum weighted bipartite matching in bipartite graphs. |
515 | 515 |
- \ref MinCostMaxBipartiteMatching |
516 | 516 |
Successive shortest path algorithm for calculating minimum cost maximum |
517 | 517 |
matching in bipartite graphs. |
518 | 518 |
- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating |
519 | 519 |
maximum cardinality matching in general graphs. |
520 | 520 |
- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating |
521 | 521 |
maximum weighted matching in general graphs. |
522 | 522 |
- \ref MaxWeightedPerfectMatching |
523 | 523 |
Edmond's blossom shrinking algorithm for calculating maximum weighted |
524 | 524 |
perfect matching in general graphs. |
525 | 525 |
|
526 |
\image html bipartite_matching.png |
|
527 |
\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth |
|
526 |
\image html matching.png |
|
527 |
\image latex matching.eps "Bipartite Matching" width=\textwidth |
|
528 | 528 |
*/ |
529 | 529 |
|
530 | 530 |
/** |
531 | 531 |
@defgroup graph_properties Connectivity and Other Graph Properties |
532 | 532 |
@ingroup algs |
533 | 533 |
\brief Algorithms for discovering the graph properties |
534 | 534 |
|
535 | 535 |
This group contains the algorithms for discovering the graph properties |
536 | 536 |
like connectivity, bipartiteness, euler property, simplicity etc. |
537 | 537 |
|
538 | 538 |
\image html connected_components.png |
539 | 539 |
\image latex connected_components.eps "Connected components" width=\textwidth |
540 | 540 |
*/ |
541 | 541 |
|
542 | 542 |
/** |
543 | 543 |
@defgroup planar Planarity Embedding and Drawing |
544 | 544 |
@ingroup algs |
545 | 545 |
\brief Algorithms for planarity checking, embedding and drawing |
546 | 546 |
|
547 | 547 |
This group contains the algorithms for planarity checking, |
548 | 548 |
embedding and drawing. |
549 | 549 |
|
550 | 550 |
\image html planar.png |
551 | 551 |
\image latex planar.eps "Plane graph" width=\textwidth |
552 | 552 |
*/ |
553 | 553 |
|
554 | 554 |
/** |
555 | 555 |
@defgroup approx Approximation Algorithms |
556 | 556 |
@ingroup algs |
557 | 557 |
\brief Approximation algorithms. |
558 | 558 |
|
559 | 559 |
This group contains the approximation and heuristic algorithms |
560 | 560 |
implemented in LEMON. |
561 | 561 |
*/ |
562 | 562 |
|
563 | 563 |
/** |
564 | 564 |
@defgroup auxalg Auxiliary Algorithms |
565 | 565 |
@ingroup algs |
566 | 566 |
\brief Auxiliary algorithms implemented in LEMON. |
567 | 567 |
|
568 | 568 |
This group contains some algorithms implemented in LEMON |
569 | 569 |
in order to make it easier to implement complex algorithms. |
570 | 570 |
*/ |
571 | 571 |
|
572 | 572 |
/** |
573 | 573 |
@defgroup gen_opt_group General Optimization Tools |
574 | 574 |
\brief This group contains some general optimization frameworks |
575 | 575 |
implemented in LEMON. |
576 | 576 |
|
577 | 577 |
This group contains some general optimization frameworks |
578 | 578 |
implemented in LEMON. |
579 | 579 |
*/ |
580 | 580 |
|
581 | 581 |
/** |
582 | 582 |
@defgroup lp_group LP and MIP Solvers |
583 | 583 |
@ingroup gen_opt_group |
584 | 584 |
\brief LP and MIP solver interfaces for LEMON. |
585 | 585 |
|
586 | 586 |
This group contains LP and MIP solver interfaces for LEMON. |
587 | 587 |
Various LP solvers could be used in the same manner with this |
588 | 588 |
high-level interface. |
589 | 589 |
|
590 | 590 |
The currently supported solvers are \ref glpk, \ref clp, \ref cbc, |
591 | 591 |
\ref cplex, \ref soplex. |
592 | 592 |
*/ |
593 | 593 |
|
594 | 594 |
/** |
595 | 595 |
@defgroup lp_utils Tools for Lp and Mip Solvers |
596 | 596 |
@ingroup lp_group |
597 | 597 |
\brief Helper tools to the Lp and Mip solvers. |
598 | 598 |
|
599 | 599 |
This group adds some helper tools to general optimization framework |
600 | 600 |
implemented in LEMON. |
601 | 601 |
*/ |
602 | 602 |
|
603 | 603 |
/** |
604 | 604 |
@defgroup metah Metaheuristics |
605 | 605 |
@ingroup gen_opt_group |
606 | 606 |
\brief Metaheuristics for LEMON library. |
607 | 607 |
|
608 | 608 |
This group contains some metaheuristic optimization tools. |
609 | 609 |
*/ |
610 | 610 |
|
611 | 611 |
/** |
612 | 612 |
@defgroup utils Tools and Utilities |
613 | 613 |
\brief Tools and utilities for programming in LEMON |
614 | 614 |
|
615 | 615 |
Tools and utilities for programming in LEMON. |
616 | 616 |
*/ |
617 | 617 |
|
618 | 618 |
/** |
619 | 619 |
@defgroup gutils Basic Graph Utilities |
620 | 620 |
@ingroup utils |
621 | 621 |
\brief Simple basic graph utilities. |
622 | 622 |
|
623 | 623 |
This group contains some simple basic graph utilities. |
624 | 624 |
*/ |
625 | 625 |
|
626 | 626 |
/** |
627 | 627 |
@defgroup misc Miscellaneous Tools |
628 | 628 |
@ingroup utils |
629 | 629 |
\brief Tools for development, debugging and testing. |
630 | 630 |
|
631 | 631 |
This group contains several useful tools for development, |
632 | 632 |
debugging and testing. |
633 | 633 |
*/ |
634 | 634 |
|
635 | 635 |
/** |
636 | 636 |
@defgroup timecount Time Measuring and Counting |
637 | 637 |
@ingroup misc |
638 | 638 |
\brief Simple tools for measuring the performance of algorithms. |
639 | 639 |
|
640 | 640 |
This group contains simple tools for measuring the performance |
641 | 641 |
of algorithms. |
642 | 642 |
*/ |
643 | 643 |
|
644 | 644 |
/** |
645 | 645 |
@defgroup exceptions Exceptions |
646 | 646 |
@ingroup utils |
647 | 647 |
\brief Exceptions defined in LEMON. |
648 | 648 |
|
649 | 649 |
This group contains the exceptions defined in LEMON. |
650 | 650 |
*/ |
651 | 651 |
|
652 | 652 |
/** |
653 | 653 |
@defgroup io_group Input-Output |
654 | 654 |
\brief Graph Input-Output methods |
655 | 655 |
|
656 | 656 |
This group contains the tools for importing and exporting graphs |
657 | 657 |
and graph related data. Now it supports the \ref lgf-format |
658 | 658 |
"LEMON Graph Format", the \c DIMACS format and the encapsulated |
659 | 659 |
postscript (EPS) format. |
660 | 660 |
*/ |
661 | 661 |
|
662 | 662 |
/** |
663 | 663 |
@defgroup lemon_io LEMON Graph Format |
664 | 664 |
@ingroup io_group |
665 | 665 |
\brief Reading and writing LEMON Graph Format. |
666 | 666 |
|
667 | 667 |
This group contains methods for reading and writing |
668 | 668 |
\ref lgf-format "LEMON Graph Format". |
669 | 669 |
*/ |
670 | 670 |
|
671 | 671 |
/** |
672 | 672 |
@defgroup eps_io Postscript Exporting |
673 | 673 |
@ingroup io_group |
674 | 674 |
\brief General \c EPS drawer and graph exporter |
675 | 675 |
|
676 | 676 |
This group contains general \c EPS drawing methods and special |
677 | 677 |
graph exporting tools. |
678 | 678 |
*/ |
679 | 679 |
|
680 | 680 |
/** |
681 | 681 |
@defgroup dimacs_group DIMACS Format |
682 | 682 |
@ingroup io_group |
683 | 683 |
\brief Read and write files in DIMACS format |
684 | 684 |
|
685 | 685 |
Tools to read a digraph from or write it to a file in DIMACS format data. |
686 | 686 |
*/ |
687 | 687 |
|
688 | 688 |
/** |
689 | 689 |
@defgroup nauty_group NAUTY Format |
690 | 690 |
@ingroup io_group |
691 | 691 |
\brief Read \e Nauty format |
692 | 692 |
|
693 | 693 |
Tool to read graphs from \e Nauty format data. |
694 | 694 |
*/ |
695 | 695 |
|
696 | 696 |
/** |
697 | 697 |
@defgroup concept Concepts |
698 | 698 |
\brief Skeleton classes and concept checking classes |
699 | 699 |
|
700 | 700 |
This group contains the data/algorithm skeletons and concept checking |
701 | 701 |
classes implemented in LEMON. |
702 | 702 |
|
703 | 703 |
The purpose of the classes in this group is fourfold. |
704 | 704 |
|
705 | 705 |
- These classes contain the documentations of the %concepts. In order |
706 | 706 |
to avoid document multiplications, an implementation of a concept |
707 | 707 |
simply refers to the corresponding concept class. |
708 | 708 |
|
709 | 709 |
- These classes declare every functions, <tt>typedef</tt>s etc. an |
710 | 710 |
implementation of the %concepts should provide, however completely |
711 | 711 |
without implementations and real data structures behind the |
712 | 712 |
interface. On the other hand they should provide nothing else. All |
713 | 713 |
the algorithms working on a data structure meeting a certain concept |
714 | 714 |
should compile with these classes. (Though it will not run properly, |
715 | 715 |
of course.) In this way it is easily to check if an algorithm |
716 | 716 |
doesn't use any extra feature of a certain implementation. |
717 | 717 |
|
718 | 718 |
- The concept descriptor classes also provide a <em>checker class</em> |
719 | 719 |
that makes it possible to check whether a certain implementation of a |
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