Date of Original Version

9-2005

Type

Article

Abstract or Description

In this paper we show a reduction from the Unique Games problem to the problem of approximating MAX-CUT to within a factor of αGW+ε for all ε > 0; here αGW ≈ .878567 denotes the approximation ratio achieved by the algorithm of Goemans and Williamson in [J. Assoc. Comput. Mach., 42 (1995), pp. 1115–1145]. This implies that if the Unique Games Conjecture of Khot in [Proceedings of the 34th Annual ACM Symposium on Theory of Computing, 2002, pp. 767–775] holds, then the Goemans–Williamson approximation algorithm is optimal. Our result indicates that the geometric nature of the Goemans–Williamson algorithm might be intrinsic to the MAX-CUT problem.

DOI

10.1137/S0097539705447372

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Published In

SIAM Journal of Computing, 37, 1, 319-357.