A (log n)Ω(1) integrality gap for the sparsest cut SDP

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

Abstract

We show that the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem with general demands has integrality gap (log n)Ω(1). This is achieved by exhibiting n-point metric spaces of negative type whose L1 distortion is (log n)Ω(1). Our result is based on quantitative bounds on the rate of degeneration of Lipschitz maps from the Heisenberg group to L1 when restricted to cosets of the center.

Original languageEnglish (US)
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Pages555-564
Number of pages10
DOIs
StatePublished - Dec 1 2009
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: Oct 25 2009Oct 27 2009

Publication series

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

Other

Other50th Annual Symposium on Foundations of Computer Science, FOCS 2009
CountryUnited States
CityAtlanta, GA
Period10/25/0910/27/09

Keywords

  • Heisenberg group
  • Integrality gap
  • Metric embeddings
  • Semidefinite programming
  • Sparsest cut problem

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Cheeger, J., Kleiner, B., & Naor, A. (2009). A (log n)Ω(1) integrality gap for the sparsest cut SDP. In Proceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009 (pp. 555-564). [5438599] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2009.47