Approximating maximum satisfiable subsystems of linear equations of bounded width

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 (m-1+1/r)-approximation algorithm for any fixed r. Previously the best approximation ratio for this problem was ((log m)/m) even for r = 2. In addition, we slightly improve the hardness results for MAX-SATISFY. Key words: Linear equations, Satisfiable systems, Approximation algorithms

• Type: Journal
• Year: 2008
• Where: IPL
• Authors: Zeev Nutov, Daniel Reichman
• Keywords: Equations, IPL 2008, Linear, Maximum Number