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TR00-019 | 20th March 2000 00:00
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#### Worst-case time bounds for MAX-k-SAT w.r.t. the number of variables using local search

**Abstract:**
During the past three years there was an explosion of algorithms

solving MAX-SAT and MAX-2-SAT in worst-case time of the order

c^K, where c<2 is a constant, and K is the number of clauses

in the input formula. Such bounds w.r.t. the number of variables

instead of the number of clauses are not known.

Also, it was proved that approximate solutions for these problems

(even beyond inapproximability ratios) can be obtained faster

than exact solutions. However, the corresponding exponents still

depended on the number of clauses in the input formula.

In this paper we give a randomized (1-\epsilon)-approximation

algorithm for MAX-k-SAT. This algorithm runs in time of the order

c_{k,\epsilon}^N, where N is the number of variables,

and c_{k,\epsilon}<2 is a constant depending on k and \epsilon.