COIN-OR::LEMON - Graph Library

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    317317
    318318This 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.
     319\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
    321320*/
    322321
     
    326325\brief Algorithms for finding shortest paths.
    327326
    328 This group contains the algorithms for finding shortest paths in digraphs
    329 \ref clrs01algorithms.
     327This group contains the algorithms for finding shortest paths in digraphs.
    330328
    331329 - \ref Dijkstra algorithm for finding shortest paths from a source node
     
    349347
    350348This group contains the algorithms for finding minimum cost spanning
    351 trees and arborescences \ref clrs01algorithms.
     349trees and arborescences.
    352350*/
    353351
     
    358356
    359357This group contains the algorithms for finding maximum flows and
    360 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
     358feasible circulations.
    361359
    362360The \e maximum \e flow \e problem is to find a flow of maximum value between
     
    373371
    374372LEMON 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.
    383 
    384 In most cases the \ref Preflow algorithm provides the
     373- \ref EdmondsKarp Edmonds-Karp algorithm.
     374- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
     375- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
     376- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
     377
     378In most cases the \ref Preflow "Preflow" algorithm provides the
    385379fastest method for computing a maximum flow. All implementations
    386380also provide functions to query the minimum cut, which is the dual
     
    400394
    401395This group contains the algorithms for finding minimum cost flows and
    402 circulations \ref amo93networkflows. For more information about this
    403 problem and its dual solution, see \ref min_cost_flow
    404 "Minimum Cost Flow Problem".
     396circulations. For more information about this problem and its dual
     397solution see \ref min_cost_flow "Minimum Cost Flow Problem".
    405398
    406399LEMON contains several algorithms for this problem.
    407400 - \ref NetworkSimplex Primal Network Simplex algorithm with various
    408    pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
     401   pivot strategies.
    409402 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
    410    cost scaling \ref goldberg90approximation, \ref goldberg97efficient,
    411    \ref bunnagel98efficient.
     403   cost scaling.
    412404 - \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.
     405   capacity scaling.
     406 - \ref CancelAndTighten The Cancel and Tighten algorithm.
     407 - \ref CycleCanceling Cycle-Canceling algorithms.
    418408
    419409In general NetworkSimplex is the most efficient implementation,
     
    451441If you want to find minimum cut just between two distinict nodes,
    452442see the \ref max_flow "maximum flow problem".
    453 */
    454 
    455 /**
    456 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms
    457 @ingroup algs
    458 \brief Algorithms for finding minimum mean cycles.
    459 
    460 This group contains the algorithms for finding minimum mean cycles
    461 \ref clrs01algorithms, \ref amo93networkflows.
    462 
    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.
    467 
    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.
    475 
    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.
    483 
    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.
    490443*/
    491444
     
    582535
    583536/**
    584 @defgroup lp_group LP and MIP Solvers
     537@defgroup lp_group Lp and Mip Solvers
    585538@ingroup gen_opt_group
    586 \brief LP and MIP solver interfaces for LEMON.
    587 
    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.
    591 
    592 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
    593 \ref cplex, \ref soplex.
     539\brief Lp and Mip solver interfaces for LEMON.
     540
     541This group contains Lp and Mip solver interfaces for LEMON. The
     542various LP solvers could be used in the same manner with this
     543interface.
    594544*/
    595545
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