# Changes in doc/groups.dox[789:8e68671af789:818:8452ca46e29a] in lemon

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 r789 This group contains the common graph search algorithms, namely \e breadth-first \e search (BFS) and \e depth-first \e search (DFS). \e breadth-first \e search (BFS) and \e depth-first \e search (DFS) \ref clrs01algorithms. */ \brief Algorithms for finding shortest paths. This group contains the algorithms for finding shortest paths in digraphs. This group contains the algorithms for finding shortest paths in digraphs \ref clrs01algorithms. - \ref Dijkstra algorithm for finding shortest paths from a source node This group contains the algorithms for finding minimum cost spanning trees and arborescences. trees and arborescences \ref clrs01algorithms. */ This group contains the algorithms for finding maximum flows and feasible circulations. feasible circulations \ref clrs01algorithms, \ref amo93networkflows. The \e maximum \e flow \e problem is to find a flow of maximum value between LEMON contains several algorithms for solving maximum flow problems: - \ref EdmondsKarp Edmonds-Karp algorithm. - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm. - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees. - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees. In most cases the \ref Preflow "Preflow" algorithm provides the - \ref EdmondsKarp Edmonds-Karp algorithm \ref edmondskarp72theoretical. - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm \ref goldberg88newapproach. - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees \ref dinic70algorithm, \ref sleator83dynamic. - \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees \ref goldberg88newapproach, \ref sleator83dynamic. In most cases the \ref Preflow algorithm provides the fastest method for computing a maximum flow. All implementations also provide functions to query the minimum cut, which is the dual This group contains the algorithms for finding minimum cost flows and circulations. For more information about this problem and its dual solution see \ref min_cost_flow "Minimum Cost Flow Problem". circulations \ref amo93networkflows. For more information about this problem and its dual solution, see \ref min_cost_flow "Minimum Cost Flow Problem". LEMON contains several algorithms for this problem. - \ref NetworkSimplex Primal Network Simplex algorithm with various pivot strategies. pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on cost scaling. cost scaling \ref goldberg90approximation, \ref goldberg97efficient, \ref bunnagel98efficient. - \ref CapacityScaling Successive Shortest %Path algorithm with optional capacity scaling. - \ref CancelAndTighten The Cancel and Tighten algorithm. - \ref CycleCanceling Cycle-Canceling algorithms. capacity scaling \ref edmondskarp72theoretical. - \ref CancelAndTighten The Cancel and Tighten algorithm \ref goldberg89cyclecanceling. - \ref CycleCanceling Cycle-Canceling algorithms \ref klein67primal, \ref goldberg89cyclecanceling. In general NetworkSimplex is the most efficient implementation, If you want to find minimum cut just between two distinict nodes, see the \ref max_flow "maximum flow problem". */ /** @defgroup min_mean_cycle Minimum Mean Cycle Algorithms @ingroup algs \brief Algorithms for finding minimum mean cycles. This group contains the algorithms for finding minimum mean cycles \ref clrs01algorithms, \ref amo93networkflows. The \e minimum \e mean \e cycle \e problem is to find a directed cycle of minimum mean length (cost) in a digraph. The mean length of a cycle is the average length of its arcs, i.e. the ratio between the total length of the cycle and the number of arcs on it. This problem has an important connection to \e conservative \e length \e functions, too. A length function on the arcs of a digraph is called conservative if and only if there is no directed cycle of negative total length. For an arbitrary length function, the negative of the minimum cycle mean is the smallest \f$\epsilon\f$ value so that increasing the arc lengths uniformly by \f$\epsilon\f$ results in a conservative length function. LEMON contains three algorithms for solving the minimum mean cycle problem: - \ref Karp "Karp"'s original algorithm \ref amo93networkflows, \ref dasdan98minmeancycle. - \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved version of Karp's algorithm \ref dasdan98minmeancycle. - \ref Howard "Howard"'s policy iteration algorithm \ref dasdan98minmeancycle. In practice, the Howard algorithm proved to be by far the most efficient one, though the best known theoretical bound on its running time is exponential. Both Karp and HartmannOrlin algorithms run in time O(ne) and use space O(n2+e), but the latter one is typically faster due to the applied early termination scheme. */ /** @defgroup lp_group Lp and Mip Solvers @defgroup lp_group LP and MIP Solvers @ingroup gen_opt_group \brief Lp and Mip solver interfaces for LEMON. This group contains Lp and Mip solver interfaces for LEMON. The various LP solvers could be used in the same manner with this interface. \brief LP and MIP solver interfaces for LEMON. This group contains LP and MIP solver interfaces for LEMON. Various LP solvers could be used in the same manner with this high-level interface. The currently supported solvers are \ref glpk, \ref clp, \ref cbc, \ref cplex, \ref soplex. */