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390 |
390 |
391 \brief Algorithms for finding minimum cost flows and circulations. |
391 \brief Algorithms for finding minimum cost flows and circulations. |
392 |
392 |
393 This group contains the algorithms for finding minimum cost flows and |
393 This group contains the algorithms for finding minimum cost flows and |
394 circulations \ref amo93networkflows. For more information about this |
394 circulations \ref amo93networkflows. For more information about this |
395 problem and its dual solution, see \ref min_cost_flow |
395 problem and its dual solution, see: \ref min_cost_flow |
396 "Minimum Cost Flow Problem". |
396 "Minimum Cost Flow Problem". |
397 |
397 |
398 LEMON contains several algorithms for this problem. |
398 LEMON contains several algorithms for this problem. |
399 - \ref NetworkSimplex Primal Network Simplex algorithm with various |
399 - \ref NetworkSimplex Primal Network Simplex algorithm with various |
400 pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. |
400 pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. |
482 |
482 |
483 In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the |
483 In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the |
484 most efficient one, though the best known theoretical bound on its running |
484 most efficient one, though the best known theoretical bound on its running |
485 time is exponential. |
485 time is exponential. |
486 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms |
486 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms |
487 run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is |
487 run in time O(ne) and use space O(n<sup>2</sup>+e). |
488 typically faster due to the applied early termination scheme. |
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489 */ |
488 */ |
490 |
489 |
491 /** |
490 /** |
492 @defgroup matching Matching Algorithms |
491 @defgroup matching Matching Algorithms |
493 @ingroup algs |
492 @ingroup algs |