A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
An improved exponential-time algorithm for k-SAT
Journal of the ACM (JACM)
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
A Duality between Clause Width and Clause Density for SAT
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
An algorithm for the SAT problem for formulae of linear length
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Faster exact solving of SAT formulae with a low number of occurrences per variable
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.01 |
In this paper we consider the class of boolean formulas in Conjunctive Normal Form (CNF) where for each variable all but at most d occurrences are either positive or negative. This class is a generalization of the class of CNF formulas with at most d occurrences (positive and negative) of each variable which was studied in [Wahlström, 2005]. Applying complement search [Purdom, 1984], we show that for every d there exists a constant $\gamma_d such that satisfiability of a CNF formula on n variables can be checked in runtime ${\ensuremath{{O}}}(\gamma_d^n)$ if all but at most d occurrences of each variable are either positive or negative. We thoroughly analyze the proposed branching strategy and determine the asymptotic growth constant *** d more precisely. Finally, we show that the trivial ${\ensuremath{{O}}}(2^n)$ barrier of satisfiability checking can be broken even for a more general class of formulas, namely formulas where the positive or negative literals of every variable have what we will call a d---covering . To the best of our knowledge, for the considered classes of formulas there are no previous non-trivial upper bounds on the complexity of satisfiability checking.