Abstract
When an arbitrary equation is inserted into a linear system over the field GF(2) that contains exactly 3 variables from the set of n variables in each equation, the problem of the maximum number of satisfied equations is reoptimized with approximation ratio 3/2. This approximation ratio is a threshold. A similar result holds for systems that contain k variables in each equation when k = O(log n).
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 18–34, May–June 2012.
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Mikhailyuk, V.A. On the approximation ratio threshold for the reoptimization of the maximum number of satisfied equations in linear systems over a finite field. Cybern Syst Anal 48, 335–348 (2012). https://doi.org/10.1007/s10559-012-9413-z
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DOI: https://doi.org/10.1007/s10559-012-9413-z