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.

• Type: Journal
• Year: 2006
• Where: RSA
• Authors: Alexis C. Kaporis, Lefteris M. Kirousis, Efthimios G. Lalas
• Keywords: Clauses-to-variables Ratio, Heuristics, Random 3-CNF Formula, RSA 2006