A new algorithm for MAX-2-SAT

Recently there was a significant progress in proving (exponential- time) worst-case upper bounds for the propositional satisfiability problem (SAT) and related problems. In particular, for MAX-2-SAT Niedermeier and Rossmanith recently presented an algorithm with worstcase upper bound O(K·2^K/2:88…), and the bound O(K·2^K/3:44..) is implicit from the paper by Bansal and Raman (K is the number of clauses). In this paper we improve this bound to p(K)2^K2/4, where K₂ is the number of 2-clauses, and p is a polynomial. In addition, our algorithm and the proof are much simpler than the previous ones. The key ideas are to use the symmetric flow algorithm of Yannakakis and to count only 2-clauses (and not 1-clauses).