Approximating maximum satisfiable subsystems of linear equations of bounded width

Zeev Nutov; Daniel Reichman

doi:10.1016/j.ipl.2007.11.011

Approximating maximum satisfiable subsystems of linear equations of bounded width

Zeev Nutov
, Daniel Reichman

Computer Science

Research output: Contribution to journal › Article › peer-review

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 Ω (m^{- 1 + 1 / r})-approximation algorithm for any fixed r. Previously the best approximation ratio for this problem was Ω ((log m) / m) even for r = 2. In addition, we slightly improve the hardness results for MAX - SATISFY.

Original language	English
Pages (from-to)	203-207
Number of pages	5
Journal	Information Processing Letters
Volume	106
Issue number	5
DOIs	https://doi.org/10.1016/j.ipl.2007.11.011
State	Published - 31 May 2008

Keywords

Approximation algorithms
Linear equations
Satisfiable systems

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10.1016/j.ipl.2007.11.011

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AB - 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 Ω (m- 1 + 1 / r)-approximation algorithm for any fixed r. Previously the best approximation ratio for this problem was Ω ((log m) / m) even for r = 2. In addition, we slightly improve the hardness results for MAX - SATISFY.

KW - Approximation algorithms

KW - Linear equations

KW - Satisfiable systems

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Approximating maximum satisfiable subsystems of linear equations of bounded width

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