Tight bound on Johnson's algorithm for maximum satisfiability

Abstract

We present new techniques that give a more thorough analysis on Johnson's classical algorithm for the Maximum Satisfiability problem. In contrast to the common belief for two decades that Johnson's Algorithm has performance ratio 1/2 , we show that the performance ratio is 2/3 and that this bound is tight. Moreover, we show that simple generalizations of Johnson's algorithm do not improve the performance ratio bound 2/3.