A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems

We present a simple probabilistic algorithm for solving kSAT, and more generally, for solving constraint satisfaction problems (CSP). The algorithm follows a simple localsearch paradigm (cf. [9]): randomly guess an initial assignment and then, guided by those clauses (constraints) that are not satisfied, by successively choosing a random literal from such a clause and flipping the corresponding bit, try to find a satisfying assignment. If no satisfying assignment is found after O(n) steps, start over again. Our analysis shows that for any satisfiable k-CNF formula with n variables this process has to be repeated only t times, on the average, to find a satisfying assignment, where t is within a polynomial factor of (2(1 - 1/k))n . This is the fastest (and also the simplest) algorithm for 3-SAT known up to date. We consider also the more general case of a CSP with n variables, each variable taking at most d values, and constraints of order l, and analyze the complexity of the correspond...

• Type: Conference
• Year: 1999
• Where: FOCS
• Authors: Uwe Schöning
• Keywords: Constraint Satisfaction Problems, FOCS 1999, Satisfying Assignment, Simple Probabilistic Algorithm, Theoretical Computer Science