New approximation algorithms for MAX 2SAT and MAX DICUT

We propose a 0.935-approximation algorithm for MAX 2SAT and a 0.863-approximation algorithm for MAX DICUT. The approximation ratios improve upon the recent results of Zwick, which are equal to 0.93109 and 0.8596434254 respectively. Also proposed are derandomized versions of the same approximation ratios. We note that these approximation ratios are obtained by numerical computation rather than theoretical proof. The algorithms are based on the SDP relaxation proposed by Goemans and Williamson but do not use the ‘rotation’ technique proposed by Feige and Goemans. The improvements in the approximation ratios are obtained by the technique of ‘hyperplane separation with skewed distribution function on the sphere.’