An average case analysis of the branching algorithm for solving κ-satisfiability problems

The k-satisfiability problem is a well known NP-complete problem for k greater than or equal to 3. In this paper, we give an average case analysis of the branching algorithm, proposed by Monien and Speckenmeyer, for solving the k-satisfiability problem. Monien and Speckenmeyer showed that the worst case time complexity of their algorithm is strictly better than 2(n), where n is the number of variables. Based upon the constant degree probabilistic model that given r clause, each clause is randomly chosen from the set of all k-literal clauses over n variables and each clause is chosen independently with others, we can show the Monien and Speckenmeyer's algorithm runs in O(nr) polynomial expected time under the condition that lim(n,r-->infinity) r/n(k-1) --> infinity and k is a constant.