Approximating Almost All Instances of Max-Cut Within a Ratio Above the H˚astad Threshold ⋆

Abstract

Abstract. We give a deterministic polynomial-time algorithm which for any given average degree d and asymptotically almost all random graphs G in G(n, m = ⌊ d n⌋) outputs a cut of G whose ratio (in cardinality) 2 with the maximum cut is at least 0.952. We remind the reader that it is known that unless P=NP, for no constant ɛ>0isthereaMax-Cut approximation algorithm that for all inputs achieves an approximation ratio of (16/17) + ɛ (16/17 < 0.94118).