Techniques from combinatorial approximation algorithms yield efficient algorithms for random [formula omitted]-SAT

Abstract

We apply techniques from the theory of approximation algorithms to the problem of deciding whether a random k-SAT formula is satisfiable. Let Formn,k,m denote a random k-SAT instance with n variables and m clauses. Using known approximation algorithms for MAX CUT or MIN BISECTION, we show how to certify that Formn,4,m is unsatisfiable efficiently, provided that m⩾Cn2 for a sufficiently large constant C>0. In addition, we present an algorithm based on the Lovász ϑ function that decides within polynomial expected time whether Formn,k,m is satisfiable, provided that k is even and m⩾C·4knk/2. Finally, we present an algorithm that approximates random MAX 2-SAT on input Formn,2,m within a factor of 1-O(n/m)1/2 in expected polynomial time, for m⩾Cn.