Probabilistic Analysis of Two Heuristics for the 3-Satisfiability Problem

Abstract

An algorithm for the 3-Satisfiability problem is presented and a probabilistic analysis is performed. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm assigns values to variables appearing in a given instance of 3-Satisfiability, one at a time, using the unit clause heuristic and a maximum occurring literal selection heuristic; at each step a variable is chosen randomly from a subset of variables which is usually large. The algorithm runs in polynomial time and it is shown that the algorithm finds a solution to a random instance of 3-Satisfiability with probability bounded from below by a constant greater than zero for a range of parameter values. The heuristics studied here can be used to select variables in a Backtrack algorithm for 3-Satisfiability. Experiments have shown that for about the same range of parameters as above the Backtrack algorithm using the heuristics finds a solution in polynomial average time.