We examine probabilistic greedy heuristics for maximization and minimization versions of the satisfiability problem. Like deterministic greedy algorithms, these heuristics construct a truth assignment one variable at a time. Unlike them, they set a variable true or false using a probabilistic mechanism, the probabilities of a true assignment depending on the incremental number of clauses satisfied if a variable is set true. We discuss alternative probabilistic functions, and characterize the expected performance of the simplest of these rules relative to optimal solutions. We discuss the advantages of probabilistic algorithms in general, and the probabilistic algorithms we analyze in particular.
Handbook of Approximation Algorithms and Metaheuristics, edited by
Chapman & Hall/CRC, 2007.