Approximation algorithms and hardness of the k-route cut problem

Julia Chuzhoy, Yury Makarychev, Aravindan Vijayaraghavan, Yuan Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the k-route cut problem: given an undirected edge-weighted graph G = (V, E), a collection {(s 1, t 1), (s 2, t 2), . . . , (s r, t r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset E′ of edges to remove, such that the connectivity of every pair (s i, t i) falls below k. Specifically, in the edge-connectivity version, EC-kRC, the requirement is that there are at most (k - 1) edge-disjoint paths connecting s i to t i in G\E′, while in the vertex-connectivity version, VC-kRC, the same requirement is for vertex-disjoint paths. Prior to our work, poly-logarithmic approximation algorithms have been known for the special case where k ≤ 3, but no non-trivial approximation algorithms were known for any value k > 3, except in the single-source setting. We show an O(k log 3/2 r)-approximation algorithm for EC-kRC with uniform edge weights, and several polylogarithmic bi-criteria approximation algorithms for EC-kRC and VC-kRC, where the connectivity requirement k is violated by a constant factor. We complement these upper bounds by proving that VC-kRC is hard to approximate to within a factor of k ε for some fixed ε > 0. We then turn to study a simpler version of VC-kRC, where only one source-sink pair is present. We give a simple bi-criteria approximation algorithm for this case, and show evidence that even this restricted version of the problem may be hard to approximate. For example, we prove that the single source-sink pair version of VC-kRC has no constant-factor approximation, assuming Feige's Random κ-AND assumption.

Original languageEnglish (US)
Title of host publicationProceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
PublisherAssociation for Computing Machinery
Pages780-799
Number of pages20
ISBN (Print)9781611972108
DOIs
StatePublished - Apr 30 2012
Externally publishedYes
Event23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 - Kyoto, Japan
Duration: Jan 17 2012Jan 19 2012

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
CountryJapan
CityKyoto
Period1/17/121/19/12

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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  • Cite this

    Chuzhoy, J., Makarychev, Y., Vijayaraghavan, A., & Zhou, Y. (2012). Approximation algorithms and hardness of the k-route cut problem. In Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 (pp. 780-799). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973099.63