on Mathematical and Computing Sciences : TR - C 191 title : On Generating Instances for MAX 2 SAT with Optimal Solutions
نویسنده
چکیده
Abstract: A test instance generator (an instance generator for short) for MAX2SAT is a procedure that produces, given a number n of variables, a 2-CNF formula F of n variables (randomly chosen from some reasonably large domain), and simultaneously provides one of the optimal solutions for F . We propose an outline to design an instance generator using an expanding graph of a certain type, called here an “exact 1/2-enlarger”. We first show a simple algorithm for constructing an exact 1/2-enlarger, thereby deriving one concrete polynomialtime instance generator GEN. We also show that an exact 1/2-enlarger can be obtained with high probability from graphs randomly constructed. From this fact, we propose another type of instance generator RGEN; it produces a 2-CNF formula with a solution which is optimal for the formula with high probability. However, RGEN produces less structured formulas and much larger class of formulas than GEN’s. In fact, we prove the NP-hardness of MAX2SAT over the set of 2-CNF formulas produced by RGEN.
منابع مشابه
on Mathematical and Computing Sciences : TR - C 146 title : An Improved Randomized Algorithm for 3 - SAT author :
Schöning [Sch99] proposed a simple yet efficient randomized algorithm for solving the k-SAT problem. His analysis showed that for 3-SAT, finding a satisfying assignment of any satisfiable formula F with n variables can be achieved in poly(n) · (4/3) (= poly(n) · (1.3333)) expected time, which is optimal up to now. In this paper, we improve this expected time bound by using a combination of a de...
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