Constructing worst case instances for semidefinite programming based approximation algorithms

Noga Alon, Benny Sudakov, Uri Zwick

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

1 Scopus citations

Abstract

Semidefinite programming based approximation algorithms, such as the Goemans and Williamson approximation algorithm for the MAX CUT problem, are usually shown to have certain performance guarantees using local ratio techniques. Are the bounds obtained in this way tight? This problem was considered before by Karloff and by Alon and Sudakov. Here we further extend their results and show, for the first time, that the local analyses of the Goemans and Williamson MAX CUT algorithm, as well as its extension by Zwick, are tight for every possible relative size of the maximum cut. We also obtain similar results for several related problems. Our approach is quite general and could possibly be applied to some additional problems and algorithms.

Original languageEnglish (US)
Title of host publicationProceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages92-100
Number of pages9
StatePublished - Dec 1 2001
Externally publishedYes
Event2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States
Duration: Apr 30 2001May 1 2001

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other2001 Operating Section Proceedings, American Gas Association
CountryUnited States
CityDallas, TX
Period4/30/015/1/01

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Keywords

  • Algorithms
  • Performance
  • Theory
  • Verification

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  • Cite this

    Alon, N., Sudakov, B., & Zwick, U. (2001). Constructing worst case instances for semidefinite programming based approximation algorithms. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 92-100). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).