The Parameterized Complexity of k-Flip Local Search for SAT and MAX SAT

Stefan Szeider

Discrete Optimization, vol. 8, pp. 139-145, 2011.

Preliminary version appeared in the proceedings of SAT 2009, Lecture Notes in Computer Science, vol. 5584, pp. 276-283, Springer, 2009.


SAT and MAX SAT are among the most prominent problems for which local search algorithms have been successfully applied. A fundamental task for such an algorithm is k-flip local search, to increase the number of clauses satisfied by a given truth assignment by flipping the truth values of at most k variables. For a total number of n variables the size of the search space is of order nk and grows quickly in k; hence most practical algorithms use 1-flip local search only.

In this paper we investigate the worst-case complexity of k-flip local search, considering k as a parameter: is it possible to search significantly faster than the trivial nk bound? In addition to the unbounded case we consider instances with a bounded number of literals per clause or where each variable occurs in a bounded number of clauses. We also consider the related problem that asks whether we can satisfy all clauses by flipping at most k variables.

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