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showpage |
| 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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