r813:25804ef35064
Thu, 12 Nov 2009 23:52:51
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@ingroup algs |
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\brief Algorithms for finding minimum cost flows and circulations. |
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This group contains the algorithms for finding minimum cost flows and |
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circulations \ref amo93networkflows. For more information about this |
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problem and its dual solution, see \ref min_cost_flow |
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"Minimum Cost Flow Problem". |
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LEMON contains several algorithms for this problem. |
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- \ref NetworkSimplex Primal Network Simplex algorithm with various |
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pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. |
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- \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on |
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cost scaling \ref goldberg90approximation, \ref goldberg97efficient, |
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- \ref CostScaling Cost Scaling algorithm based on push/augment and |
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relabel operations \ref goldberg90approximation, \ref goldberg97efficient, |
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\ref bunnagel98efficient. |
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- \ref CapacityScaling Successive Shortest %Path algorithm with optional |
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capacity scaling \ref edmondskarp72theoretical. |
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- \ref CancelAndTighten The Cancel and Tighten algorithm |
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\ref goldberg89cyclecanceling. |
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- \ref CycleCanceling Cycle-Canceling algorithms |
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\ref klein67primal, \ref goldberg89cyclecanceling. |
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- \ref CapacityScaling Capacity Scaling algorithm based on the successive |
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shortest path method \ref edmondskarp72theoretical. |
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- \ref CycleCanceling Cycle-Canceling algorithms, two of which are |
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strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling. |
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In general NetworkSimplex is the most efficient implementation, |
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but in special cases other algorithms could be faster. |
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For example, if the total supply and/or capacities are rather small, |
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CapacityScaling is usually the fastest algorithm (without effective scaling). |
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*/ |
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/** |
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@defgroup min_cut Minimum Cut Algorithms |
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@ingroup algs |
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\brief Algorithms for finding minimum cut in graphs. |
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/// must be \ref RangeMap "RangeMap<int>". |
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typedef BinHeap<Cost, RangeMap<int> > Heap; |
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}; |
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/// \addtogroup min_cost_flow_algs |
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/// @{
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/// \brief Implementation of the Capacity Scaling algorithm for |
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/// finding a \ref min_cost_flow "minimum cost flow". |
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/// |
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/// \ref CapacityScaling implements the capacity scaling version |
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/// of the successive shortest path algorithm for finding a |
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/// \ref min_cost_flow "minimum cost flow" |
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/// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows, |
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/// \ref edmondskarp72theoretical. It is an efficient dual |
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/// solution method. |
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/// |
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/// Most of the parameters of the problem (except for the digraph) |
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/// can be given using separate functions, and the algorithm can be |
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/// executed using the \ref run() function. If some parameters are not |
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/// specified, then default values will be used. |
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/// |
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/// \tparam GR The digraph type the algorithm runs on. |
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/// \tparam V The number type used for flow amounts, capacity bounds |
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/// and supply values in the algorithm. By default it is \c int. |
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/// \tparam C The number type used for costs and potentials in the |
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/// algorithm. By default it is the same as \c V. |
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typedef long LargeCost; |
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#endif |
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}; |
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/// \addtogroup min_cost_flow_algs |
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/// @{
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/// \brief Implementation of the Cost Scaling algorithm for |
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/// finding a \ref min_cost_flow "minimum cost flow". |
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/// |
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/// \ref CostScaling implements a cost scaling algorithm that performs |
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/// push/augment and relabel operations for finding a minimum cost |
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/// flow. It is an efficient primal-dual solution method, which |
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/// push/augment and relabel operations for finding a \ref min_cost_flow |
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/// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation, |
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/// \ref goldberg97efficient, \ref bunnagel98efficient. |
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/// It is a highly efficient primal-dual solution method, which |
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/// can be viewed as the generalization of the \ref Preflow |
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/// "preflow push-relabel" algorithm for the maximum flow problem. |
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/// |
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/// Most of the parameters of the problem (except for the digraph) |
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/// can be given using separate functions, and the algorithm can be |
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/// executed using the \ref run() function. If some parameters are not |
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/// specified, then default values will be used. |
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/// |
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/// \tparam GR The digraph type the algorithm runs on. |
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/// \tparam V The number type used for flow amounts, capacity bounds |
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/// and supply values in the algorithm. By default it is \c int. |
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/// \tparam C The number type used for costs and potentials in the |
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