Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

Da Chuan Xu, Shu Zhong Zhang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we consider a class of quadratic maximization problems. For a subclass of the problems, we show that the SDP relaxation approach yields an approximation solution with the worst-case performance ratio at least α = 0.87856 ⋯. In fact, the estimated worst-case performance ratio is dependent on the data of the problem with α being a uniform lower bound. In light of this new bound, we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α + δ d if every weight is strictly positive, where δ d > 0 is a constant depending on the problem dimension and data.

Original languageEnglish (US)
Pages (from-to)1583-1596
Number of pages14
JournalScience in China, Series A: Mathematics
Volume50
Issue number11
DOIs
StatePublished - Nov 2007

Bibliographical note

Funding Information:
Received April 4, 2006; accepted March 14, 2007; published online July 31, 2007 DOI: 10.1007/s11425-007-0080-x † Corresponding author This work was supported by the National Natural Science Foundation of China (Grant No. 10401038) and Startup Grant for Doctoral Research of Beijing University of Technology and Hong Kong RGC Earmarked Grant CUHK4242/04E

Keywords

  • Approximation algorithm
  • Max-cut problem
  • Performance ratio
  • Quadratic maximization
  • Semidefinite programming relaxation

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