Exact Algorithms for k SAT Based on Local Search

Years and Authors of Summarized Original Work

• 1999; Schöning

Problem Definition

The CNF satisfiability problem is to determine, given a CNF formula F with n variables, whether or not there exists a satisfying assignment for F. If each clause of F contains at most k literals, then F is called a k-CNF formula and the problem is called k-SAT, which is one of the most fundamental NP-complete problems. The trivial algorithm is to search 2ⁿ 0/1-assignments for the n variables. But since [6], several algorithms which run significantly faster than this O(2ⁿ) bound have been developed. As a simple exercise, consider the following straightforward algorithm for 3-SAT, which gives us an upper bound of 1. 913ⁿ: choose an arbitrary clause in F, say, $(x_{1} \vee \overline{x_{2}} \vee x_{3})$. Then generate seven new formulas by substituting to these x₁, x₂, and x₃ all the possible values except (x₁, x₂, x₃) = (0, 1, 0) which obviously unsatisfies F. Now one can check the satisfiability of these...