A Probabilistic Algorithm for k -SAT Based on Limited Local Search and Restart |
| |
Authors: | Sch?ning |
| |
Affiliation: | (1) Abteilung Theoretische Informatik, Universit?t Ulm, James-Franck-Ring, D-89069 Ulm, Germany. schoenin@informatik.uni-ulm.de., DE |
| |
Abstract: | Abstract. A simple probabilistic algorithm for solving the NP-complete problem k -SAT is reconsidered. This algorithm follows a well-known local-search paradigm: randomly guess an initial assignment and
then, guided by those clauses that are not satisfied, by successively choosing a random literal from such a clause and changing
the corresponding truth value, try to find a satisfying assignment. Papadimitriou 11] introduced this random approach and
applied it to the case of 2-SAT, obtaining an expected O(n
2
) time bound. The novelty here is to restart the algorithm after 3n unsuccessful steps of local search. The analysis shows that for any satisfiable k -CNF formula with n variables the expected number of repetitions until a satisfying assignment is found this way is (2⋅ (k-1)/ k)
n
. Thus, for 3-SAT the algorithm presented here has a complexity which is within a polynomial factor of (\frac 4 3 )
n
. This is the fastest and also the simplest among those algorithms known up to date for 3-SAT achieving an o(2
n
) time bound. Also, the analysis is quite simple compared with other such algorithms considered before. |
| |
Keywords: | , Satisfiability problem, NP-completeness, |
本文献已被 SpringerLink 等数据库收录! |
|