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On dual minimum cost flow algorithms

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  • Jens Vygen

Abstract

We describe a new dual algorithm for the minimum cost flow problem. It can be regarded as a variation of the best known strongly polynomial minimum cost flow algorithm, due to Orlin. Indeed we obtain the same running time of O(m log m(m+n log n)), where n and m denote the number of vertices and the number of edges. However, in contrast to Orlin's algorithm we work directly with the capacitated network (rather than transforming it to a transshipment problem). Thus our algorithm is applicable to more general problems (like submodular flow) and is likely to be more efficient in practice. Our algorithm can be interpreted as a cut cancelling algorithm, improving the best known strongly polynomial bound for this important class of algorithms by a factor of m. On the other hand, our algorithm can be considered as a variant of the dual network simplex algorithm. Although dual network simplex algorithms are reportedly quite efficient in practice, the best worst-case running time known so far exceeds the running time of our algorithm by a factor of n. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Jens Vygen, 2002. "On dual minimum cost flow algorithms," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(1), pages 101-126, August.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:1:p:101-126
    DOI: 10.1007/s001860200202
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    Cited by:

    1. Reinhard Bürgy & Heinz Gröflin, 2016. "The blocking job shop with rail-bound transportation," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 152-181, January.
    2. Dorit S. Hochbaum, 2008. "The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem," Operations Research, INFORMS, vol. 56(4), pages 992-1009, August.
    3. Roghayeh Etemad & Behrooz Alizadeh, 2018. "Reverse selective obnoxious center location problems on tree graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 431-450, June.
    4. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    5. Ioannis Panageas & Thorben Trobst & Vijay V. Vazirani, 2021. "Time-Efficient Algorithms for Nash-Bargaining-Based Matching Market Models," Papers 2106.02024, arXiv.org, revised Nov 2024.

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