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kpeter (Peter Kovacs)
kpeter@inf.elte.hu
Insert citations into the doc (#184) - Add general citations to modules. - Add specific citations for max flow and min cost flow algorithms. - Add citations for the supported LP and MIP solvers. - Extend the main page. - Replace inproceedings entries with the journal versions. - Add a new bibtex entry about network simplex. - Remove unwanted entries.
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\brief Common graph search algorithms.
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This group contains the common graph search algorithms, namely
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\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
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\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
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\ref clrs01algorithms.
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*/
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/**
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@ingroup algs
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\brief Algorithms for finding shortest paths.
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This group contains the algorithms for finding shortest paths in digraphs.
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This group contains the algorithms for finding shortest paths in digraphs
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\ref clrs01algorithms.
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 - \ref Dijkstra algorithm for finding shortest paths from a source node
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   when all arc lengths are non-negative.
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\brief Algorithms for finding minimum cost spanning trees and arborescences.
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This group contains the algorithms for finding minimum cost spanning
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trees and arborescences.
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trees and arborescences \ref clrs01algorithms.
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*/
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/**
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\brief Algorithms for finding maximum flows.
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This group contains the algorithms for finding maximum flows and
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feasible circulations.
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feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
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The \e maximum \e flow \e problem is to find a flow of maximum value between
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a single source and a single target. Formally, there is a \f$G=(V,A)\f$
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\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
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LEMON contains several algorithms for solving maximum flow problems:
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- \ref EdmondsKarp Edmonds-Karp algorithm.
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- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
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- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
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- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
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- \ref EdmondsKarp Edmonds-Karp algorithm
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  \ref edmondskarp72theoretical.
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- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
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  \ref goldberg88newapproach.
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- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
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  \ref dinic70algorithm, \ref sleator83dynamic.
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- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
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  \ref goldberg88newapproach, \ref sleator83dynamic.
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In most cases the \ref Preflow "Preflow" algorithm provides the
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In most cases the \ref Preflow algorithm provides the
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fastest method for computing a maximum flow. All implementations
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also provide functions to query the minimum cut, which is the dual
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problem of maximum flow.
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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. For more information about this problem and its dual
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solution see \ref min_cost_flow "Minimum Cost Flow Problem".
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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.
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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.
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   cost scaling \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.
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 - \ref CancelAndTighten The Cancel and Tighten algorithm.
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 - \ref CycleCanceling Cycle-Canceling algorithms.
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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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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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*/
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/**
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@defgroup lp_group Lp and Mip Solvers
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@defgroup lp_group LP and MIP Solvers
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@ingroup gen_opt_group
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\brief Lp and Mip solver interfaces for LEMON.
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\brief LP and MIP solver interfaces for LEMON.
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This group contains Lp and Mip solver interfaces for LEMON. The
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various LP solvers could be used in the same manner with this
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interface.
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This group contains LP and MIP solver interfaces for LEMON.
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Various LP solvers could be used in the same manner with this
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high-level interface.
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The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
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\ref cplex, \ref soplex.
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*/
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/**
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\section intro Introduction
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\subsection whatis What is LEMON
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LEMON stands for <b>L</b>ibrary for <b>E</b>fficient <b>M</b>odeling
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and <b>O</b>ptimization in <b>N</b>etworks.
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It is a C++ template
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library aimed at combinatorial optimization tasks which
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often involve in working
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with graphs.
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<b>LEMON</b> stands for <i><b>L</b>ibrary for <b>E</b>fficient <b>M</b>odeling
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and <b>O</b>ptimization in <b>N</b>etworks</i>.
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It is a C++ template library providing efficient implementation of common
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data structures and algorithms with focus on combinatorial optimization
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problems in graphs and networks.
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<b>
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LEMON is an <a class="el" href="http://opensource.org/">open&nbsp;source</a>
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\ref license "license terms".
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</b>
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\subsection howtoread How to read the documentation
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The project is maintained by the 
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<a href="http://www.cs.elte.hu/egres/">Egerv&aacute;ry Research Group on
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Combinatorial Optimization</a> \ref egres
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at the Operations Research Department of the
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<a href="http://www.elte.hu/">E&ouml;tv&ouml;s Lor&aacute;nd University,
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Budapest</a>, Hungary.
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LEMON is also a member of the <a href="http://www.coin-or.org/">COIN-OR</a>
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initiative \ref coinor.
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\section howtoread How to Read the Documentation
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If you would like to get to know the library, see
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<a class="el" href="http://lemon.cs.elte.hu/pub/tutorial/">LEMON Tutorial</a>.
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The \e minimum \e cost \e flow \e problem is to find a feasible flow of
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minimum total cost from a set of supply nodes to a set of demand nodes
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in a network with capacity constraints (lower and upper bounds)
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and arc costs.
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and arc costs \ref amo93networkflows.
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Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{R}\f$,
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\f$upper: A\rightarrow\mathbf{R}\cup\{+\infty\}\f$ denote the lower and
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%%%%% Maximum flow algorithms %%%%%
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@inproceedings{goldberg86newapproach,
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@article{edmondskarp72theoretical,
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  author =       {Jack Edmonds and Richard M. Karp},
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  title =        {Theoretical improvements in algorithmic efficiency
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                  for network flow problems},
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  journal =      {Journal of the ACM},
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  year =         1972,
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  volume =       19,
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  number =       2,
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  pages =        {248-264}
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}
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@article{goldberg88newapproach,
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  author =       {Andrew V. Goldberg and Robert E. Tarjan},
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  title =        {A new approach to the maximum flow problem},
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  booktitle =    {STOC '86: Proceedings of the Eighteenth Annual ACM
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                  Symposium on Theory of Computing},
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  year =         1986,
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  publisher =    {ACM Press},
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  address =      {New York, NY},
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  pages =        {136-146}
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  journal =      {Journal of the ACM},
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  year =         1988,
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  volume =       35,
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  number =       4,
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  pages =        {921-940}
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}
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@article{dinic70algorithm,
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  pages =        {205-220}
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}
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@inproceedings{goldberg88cyclecanceling,
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@article{goldberg89cyclecanceling,
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  author =       {Andrew V. Goldberg and Robert E. Tarjan},
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  title =        {Finding minimum-cost circulations by canceling
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                  negative cycles},
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  booktitle =    {STOC '88: Proceedings of the Twentieth Annual ACM
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                  Symposium on Theory of Computing},
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  year =         1988,
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  publisher =    {ACM Press},
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  address =      {New York, NY},
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  pages =        {388-397}
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  journal =      {Journal of the ACM},
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  year =         1989,
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  volume =       36,
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  number =       4,
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  pages =        {873-886}
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}
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@article{edmondskarp72theoretical,
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  author =       {Jack Edmonds and Richard M. Karp},
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  title =        {Theoretical improvements in algorithmic efficiency
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                  for network flow problems},
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  journal =      {Journal of the ACM},
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  year =         1972,
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  volume =       19,
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  number =       2,
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  pages =        {248-264}
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}
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@inproceedings{goldberg87approximation,
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  author =       {Andrew V. Goldberg and Robert E. Tarjan},
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  title =        {Solving minimum-cost flow problems by successive
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                  approximation},
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  booktitle =    {STOC '87: Proceedings of the Nineteenth Annual ACM
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                  Symposium on Theory of Computing},
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  year =         1987,
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  publisher =    {ACM Press},
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  address =      {New York, NY},
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  pages =        {7-18}
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}
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@article{goldberg90finding,
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@article{goldberg90approximation,
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  author =       {Andrew V. Goldberg and Robert E. Tarjan},
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  title =        {Finding Minimum-Cost Circulations by Successive
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                  Approximation},
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  pages =        {157-174}
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}
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@book{dantzig63linearprog,
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  author =       {George B. Dantzig},
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  title =        {Linear Programming and Extensions},
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  publisher =    {Princeton University Press},
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  year =         1963
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}
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@mastersthesis{kellyoneill91netsimplex,
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  author =       {Damian J. Kelly and Garrett M. O'Neill},
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  title =        {The Minimum Cost Flow Problem and The Network
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  year =         1991,
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  month =        sep,
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}
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@techreport{lobel96networksimplex,
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  author =       {Andreas L{\"o}bel},
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  title =        {Solving large-scale real-world minimum-cost flow
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                  problems by a network simplex method},
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  institution =  {Konrad-Zuse-Zentrum fur Informationstechnik Berlin
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                  ({ZIB})},
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  address =      {Berlin, Germany},
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  year =         1996,
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  number =       {SC 96-7}
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}
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@article{frangioni06computational,
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  author =       {Antonio Frangioni and Antonio Manca},
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  title =        {A Computational Study of Cost Reoptimization for
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                  Min-Cost Flow Problems},
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  journal =      {INFORMS Journal On Computing},
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  year =         2006,
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  volume =       18,
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  number =       1,
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  pages =        {61-70}
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}
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  /// for finding a \ref min_cost_flow "minimum cost flow".
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  ///
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  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
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  /// for finding a \ref min_cost_flow "minimum cost flow".
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  /// for finding a \ref min_cost_flow "minimum cost flow"
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  /// \ref amo93networkflows, \ref dantzig63linearprog,
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  /// \ref kellyoneill91netsimplex.
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  /// This algorithm is a specialized version of the linear programming
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  /// simplex method directly for the minimum cost flow problem.
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  /// It is one of the most efficient solution methods.
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  ///
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  /// This class provides an implementation of Goldberg-Tarjan's \e preflow
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  /// \e push-relabel algorithm producing a \ref max_flow
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  /// "flow of maximum value" in a digraph.
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  /// "flow of maximum value" in a digraph \ref clrs01algorithms,
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  /// \ref amo93networkflows, \ref goldberg88newapproach.
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  /// The preflow algorithms are the fastest known maximum
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  /// flow algorithms. The current implementation uses a mixture of the
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  /// \e "highest label" and the \e "bound decrease" heuristics.
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