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Sequential and parallel algorithms for minimum flows. (English) Zbl 1139.90335
Summary: First, we present two classes of sequential algorithms for minimum flow problem: decreasing path algorithms and preflow algorithms. Then we describe another approach of the minimum flow problem, that consists of applying any maximum flow algorithm in a modified network. In section 5 we present several parallel preflow algorithms that solve the minimum flow problem. Finally, we present an application of the minimum flow problem.
MSC:
90B10Network models, deterministic (optimization)
05C85Graph algorithms (graph theory)
68R10Graph theory in connection with computer science (including graph drawing)
90C35Programming involving graphs or networks
References:
[1]R. Ahuja, T. Magnanti and J. Orlin,Network Flows. Theory, al gorithms and applications, Prentice Hall, Inc, Englewood Cliffs, NJ, 1993.
[2]R. Ahuja, T. Magnanti and J. Orlin,Some Recent Advances in Network Flows, SIAM Review33 (1990), 175–219. · Zbl 0732.90028 · doi:10.1137/1033048
[3]R. Ahuja and J. Orlin,A Fast and Simple Algorithm for the Maximum Flow Problem, Operation Research37 (1988), 748–759. · Zbl 0691.90024 · doi:10.1287/opre.37.5.748
[4]R. Ahuja, J. Orlin and R. Tarjan,Improved Time Bounds for the Maximum Flow Problem. SIAM Journal of Computing18 (1988), 939–954. · Zbl 0675.90029 · doi:10.1137/0218065
[5]A. V. Goldberg,Processor-efficient implementation of a maxim um flow algorithm, Information Processing Letters38 (1991), 179–185. · Zbl 0754.90024 · doi:10.1016/0020-0190(91)90097-2
[6]A. V. Goldberg,A New Max-Flow Algorithm, MIT, Cambridge, 1985.
[7]A. V. Goldberg and R. E. Tarjan,A New Approach to the Maximum Flow Problem, Journal of ACM35 (1988), 921–940. · Zbl 0661.90031 · doi:10.1145/48014.61051
[8]A. V. Goldberg and R. E. Tarjan,A Parallel Algorithm for Fin ding a Blocking Flow in an Acyclic Network, Information Processing Letters31 (1989), 265–271. · Zbl 0688.68034 · doi:10.1016/0020-0190(89)90084-7
[9]A. V. Karzanov,Determining the Maximum Flow in a Network by the Method of Preflows, Soviet. Math. Dokl.15 (1974), 434–437.
[10]Y. Shiloach and U. Vishkin,An O (n 2 logn)parallel max-flow algorithm, J. Algorithms3 (1982) 128–146. · Zbl 0483.90044 · doi:10.1016/0196-6774(82)90013-X