Approximating maximum satisfiable subsystems of linear equations of bounded width

Authors:
Zeev Nutov;Daniel Reichman
Affiliations:
The Open University of Israel, Israel;The Open University of Israel, Israel
Venue:
Information Processing Letters
Year:
2008

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Abstract

We consider the problem known as MAX-SATISFY: given a system of m linear equations over the rationals, find a maximum set of equations that can be satisfied. Let r be the width of the system, that is, the maximum number of variables in an equation. We give an @W(m^-^1^+^1^/^r)-approximation algorithm for any fixed r. Previously the best approximation ratio for this problem was @W((logm)/m) even for r=2. In addition, we slightly improve the hardness results for MAX-SATISFY.