On the hardness and easiness of random 4-SAT formulas

Authors:
Andreas Goerdt;André Lanka
Affiliations:
Fakultät für Informatik, Technische Universität Chemnitz, Chemnitz, Germany;Fakultät für Informatik, Technische Universität Chemnitz, Chemnitz, Germany
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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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-all-equal 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 k-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.