On the hardness and easiness of random 4-SAT formulas

Abstract

Assuming random 3-SAT formulas are hard to refute, Feige showed approximation hardness results, among others for the max bipartite clique. We extend this result in that we show that approximating max bipartite clique is hard under the weaker assumption, that random 4-SAT formulas are hard to refute. On the positive side we present an efficient algorithm which finds a hidden solution in an otherwise random not-all-equal 4-SAT instance. This extends analogous results on not-allequal 3-SAT and classical 3-SAT. The common principle underlying our results is to obtain efficiently information about discrepancy (expansion) properties of graphs naturally associated to 4-SAT instances. In case of 4-SAT (or fc-SAT in general) the relationship between the structure of these graphs and that of the instance itself is weaker than in case of 3-SAT. This causes problems whose solution is the technical core of this paper. © Springer-Verlag 2004.