The probabilistic analysis of a greedy satisfiability algorithm

On input a random 3‐CNF formula of clauses‐to‐variables ratio r3 applies repeatedly the following simple heuristic: Set to True a literal that appears in the maximum number of clauses, irrespective of their size and the number of occurrences of the negation of the literal (ties are broken randomly; 1‐clauses when they appear get priority). We prove that for r3 < 3.42 this heuristic succeeds with probability asymptotically bounded away from zero. Previously, heuristics of increasing sophistication were shown to succeed for r3 < 3.26. We improve up to r3 < 3.52 by further exploiting the degree of the negation of the evaluated to True literal. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006