## The Probabilistic Analysis of a Greedy Satisfiability Algorithm (2002)

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### BibTeX

@MISC{Kaporis02theprobabilistic,

author = {Alexis C. Kaporis and Lefteris M. Kirousis and Efthimios G. Lalas},

title = {The Probabilistic Analysis of a Greedy Satisfiability Algorithm},

year = {2002}

}

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### Abstract

Consider the following simple, greedy Davis-Putnam algorithm applied to a random 3CNF formula of fixed density (clauses to variables ratio): Arbitrarily select and set to True a literal that appears in as many clauses as possible, irrespective of their size (and irrespective of the number of occurrences of the negation of the literal). Delete these clauses from the formula, and also delete the negation of this literal from any clauses it appears. Repeat. If however unit clauses ever appear, then first repeatedly and in any order set the literals in them to True and delete and shrink clauses accordingly, until no unit clause remains. Also if at any step an empty clause appears, then do not backtrack, but just terminate the algorithm and report failure. A slight modification of this algorithm is probabilistically analyzed in this paper (rigorously). It is proved that for random formulas of n variables and density up to 3.42, it succeeds in producing a satisfying truth assignment with bounded away from zero probability, as n approaches infinity. Therefore the satisfiability threshold is at least 3.42.