Skip to main content
Log in

On dual minimum cost flow algorithms

  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vygen, J. On dual minimum cost flow algorithms. Mathematical Methods of OR 56, 101–126 (2002). https://doi.org/10.1007/s001860200202

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001860200202

Navigation