2026-07-23T15:08:03Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24380 2025-12-12T15:01:15Z ddc:004 open_access

Improved Lower Bounds on Multiflow-Multicut Gaps Kalantarzadeh, Sina Kumar, Nikhil Approximation Algorithms Randomized Algorithms Linear Programming Graph Algorithms Scheduling Multicut Multiflow 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sina Kalantarzadeh and Nikhil Kumar 2025 Is Part Of LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2025.14 urn:nbn:de:0030-drops-243803 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.14 eng https://creativecommons.org/licenses/by/4.0/legalcode