The approximability of non-Boolean satisfiability problems and restricted integer programming

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Abstract

In this paper we present improved approximation algorithms for two classes of maximization problems defined in Barland et al. (J. Comput. System Sci. 57(2) (1998) 144). Our factors of approximation substantially improve the previous known results and are close to the best possible. On the other hand, we show that the approximation results in the framework of Barland et al. hold also in the parallel setting, and thus we have a new common framework for both computational settings. We prove almost tight non-approximability results, thus solving a main open question of Barland et al.

We obtain the results through the constraint satisfaction problem over multi-valued domains, for which we develop approximation algorithms and show non-approximability results. Our parallel approximation algorithms are based on linear programming and random rounding; they are better than previously known sequential algorithms. The non-approximability results are based on new recent progress in the fields of probabilistically checkable proofs and multi-prover one-round proof systems.

Keywords

Parallel approximation algorithms
Non-approximability
Positive linear programming
Randomized rounding
Non-Boolean constraint satisfaction
Maximum capacity representatives

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Preliminary version appeared in Proceedings of 15th Annual Symposium on Theoretical Aspects of Computer Science, STACS’98.

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This research was partially supported by the ALCOM FT Research Project No. IST-1999-14186 and CICYT Project TRACER TIC2002-04498-C05-03.