Improved approximations for max set splitting and max NAE SAT

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Abstract

We present a 0.7499-approximation algorithm for Max Set Splitting in this paper. The previously best known result for this problem is a 0.7240-approximation by Andersson and Engebretsen (Inform. Process. Lett. 65 (1998) 305), which is based on a semidefinite programming (SDP) relaxation. Our improvement is resulted from a strengthened SDP relaxation, an improved rounding method, and a tighter analysis compared with that in Andersson and Engebretsen (1998).

Keywords

Max-Set-Splitting
Max NAE SAT
Approximation algorithm
Semidefinite programming relaxation

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This research was supported in part by NSF grants DMI-9908077 and DMS-9703490.

1

This work was done while the author was visiting Fudan University, Shanghai, PR China.

2

This work was done while the author was visiting Computational Optimization Laboratory, Department of Management Sciences, University of Iowa. The author is supported by in part by NSFC grants 10226017 and 10201011.