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Strongly Polynomial Parallel Maximum Flow Revisited

Authors Adam Karczmarz , Paweł Pilarski

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Subject Classification

ACM Subject Classification
  • Theory of computation → Network flows
  • Theory of computation → Shared memory algorithms
Keywords
  • maximum flow
  • parallel algorithm
  • work-depth tradeoff
  • strongly polynomial

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Abstract

We study the maximum flow problem in directed networks with real capacities in the parallel setting. For a network with n vertices and m arcs, we show that a randomized parallel implementation of a variant of the strongly polynomial max-flow algorithm of Dadush, Orlin, Sidford, and Végh [Dadush et al., 2026] runs in Õ(mn) work and Õ(m) depth. This improves upon the previously described tradeoffs between work and depth for strongly polynomial parallel maximum flow algorithms: earlier Õ(n³)-work algorithms have Õ(n²) depth [Goldberg and Tarjan, 1988; Shiloach and Vishkin, 1982], while the known Õ(m)-depth approach uses Õ(mn³) work [Orlin, 1993].

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Adam Karczmarz and Paweł Pilarski. Strongly Polynomial Parallel Maximum Flow Revisited. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 147:1-147:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.147

Author Details

Adam Karczmarz
  • University of Warsaw, Poland
Paweł Pilarski
  • University of Warsaw, Poland

Funding

Supported by the National Science Centre (NCN) grant no. 2022/47/D/ST6/02184.

Acknowledgements

We thank the anonymous ESA reviewers for their helpful comments.

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