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Improved Lower Bounds on Multiflow-Multicut Gaps

Authors Sina Kalantarzadeh , Nikhil Kumar

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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Mathematics of computing → Approximation algorithms
Keywords
  • Approximation Algorithms
  • Randomized Algorithms
  • Linear Programming
  • Graph Algorithms
  • Scheduling
  • Multicut
  • Multiflow

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Abstract

Given a set of source-sink pairs, the maximum multiflow problem asks for the maximum total amount of flow that can be feasibly routed between them. The minimum multicut, a dual problem to multiflow, seeks the minimum-cost set of edges whose removal disconnects all the source-sink pairs. It is easy to see that the value of the minimum multicut is at least that of the maximum multiflow, and their ratio is called the multiflow-multicut gap. The classical max-flow min-cut theorem states that when there is only one source-sink pair, the gap is exactly one. However, in general, it is well known that this gap can be arbitrarily large. In this paper, we study this gap for classes of planar graphs and establish improved lower bound results. In particular, we show that this gap is at least 20/9 for the class of planar graphs, improving upon the decades-old lower bound of 2. More importantly, we develop new techniques for proving such a lower bound, which may be useful in other settings as well.

Cite As Get BibTex

Sina Kalantarzadeh and Nikhil Kumar. Improved Lower Bounds on Multiflow-Multicut Gaps. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.14

Author Details

Sina Kalantarzadeh
  • University of Waterloo, Canada
Nikhil Kumar
  • University of Waterloo, Canada

Acknowledgements

We would like to thank Joseph Cheriyan for many helpful discussions throughout the course of this project.

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