A node-capacitated okamura-seymour theorem

James R. Lee, Manor Mendel, Mohamad Moharrami

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal " ε > 0, if the node cut conditions are satisfied, then one can simultaneously route an " ε- fraction of all the demands. This answers an open question of Chekuri and Kawarabayashi. More generally, we show that this holds in the setting of multi-commodity polymatroid networks introduced by Chekuri, et. al. Our approach employs a new type of random metric embedding in order to round the convex programs corresponding to these more general flow problems.

Original languageEnglish
Title of host publicationSTOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing
Number of pages10
StatePublished - 2013
Event45th Annual ACM Symposium on Theory of Computing, STOC 2013 - Palo Alto, CA, United States
Duration: 1 Jun 20134 Jun 2013

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference45th Annual ACM Symposium on Theory of Computing, STOC 2013
Country/TerritoryUnited States
CityPalo Alto, CA


  • Metric embeddings
  • Multi-commodity flows


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