Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Friday, October 07, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Mitsuo Motoki (Japan Advanced Institute for Science and Technology)

Test Instance Generation for MAX 2SAT

We consider test instance generation problem for MAX 2SAT.

Empirical study is often used to estimate the performance of solvers for combinatorial optimization problems from various points of view. For empirical study, a number of test instances are required. These test instances should have their optimal solution, otherwise it is impossible to estimate how good outputs are obtained. However, it is unlikely to have a polynomial-time (randomized) instance generator that can generate all possible test instances (i.e., all 2CNF formulas) with their optimal solution unless NP = co-NP. Thus we have to waive any of the two options generating all possible instances or generating instance with the optimal solution.

We propose a polynomial-time exact instance generator that can generate a subset of the instances of whole 2CNF formulas with the corresponding optimal solutions. If instances generated are easy, they are not suitable for empirical study. Unfortunately, for any NP-hard optimization problem, there is no polynomial-time exact instance generator such that the problem over the set of instances generated is NP-hard unless NP = co-NP. Thus we analyze how hard it is to recognize our instances. We prove that the set of instances generated is NP complete. We also prove that it is NP-hard to approximately distinguish the instances generated.

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