Min-max graph partitioning and small set expansion

Nikhil Bansal*, Uriel Feige, Robert Krauthgamer, Konstantin Makarychev, Viswanath Nagarajan, Joseph Naor, Roy Schwartz

*Corresponding author for this work

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

32 Scopus citations

Abstract

We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are: (i) the k parts need to be of equal size, and (ii) the parts must separate a set of k given terminals. We consider a common generalization of these two problems, and design for it an O(√log n log k)-approximation algorithm. This improves over an O(log 2 n) approximation for the second version due to Svitkina and Tardos, and roughly O(k log n) approximation for the first version that follows from other previous work. We also give an improved O(1)-approximation algorithm for graphs that exclude any fixed minor. Our algorithm uses a new procedure for solving the Small Set Expansion problem. In this problem, we are given a graph G and the goal is to find a non-empty set S ⊆ V of size |S| ≤ ρn with minimum edge-expansion. We give an O(√log n log (1/ρ)) bicriteria approximation algorithm for the general case of Small Set Expansion and O(1) approximation algorithm for graphs that exclude any fixed minor.

Original languageEnglish (US)
Title of host publicationProceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Pages17-26
Number of pages10
DOIs
StatePublished - Dec 1 2011
Event2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States
Duration: Oct 22 2011Oct 25 2011

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Other

Other2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
CountryUnited States
CityPalm Springs, CA
Period10/22/1110/25/11

ASJC Scopus subject areas

  • Computer Science(all)

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