Improved approximation algorithms for minimum AND-circuits problem via k-set cover

Authors:
Hiroki Morizumi
Affiliations:
Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
Venue:
Information Processing Letters
Year:
2011

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Abstract

Arpe and Manthey [J. Arpe, B. Manthey, Approximability of minimum AND-circuits, Algorithmica 53 (3) (2009) 337-357] recently studied the minimum AND-circuit problem, which is a circuit minimization problem, and showed some results including approximation algorithms, APX-hardness and fixed parameter tractability of the problem. In this note, we show that algorithms via the k-set cover problem yield improved approximation ratios for the minimum AND-circuit problem with maximum degree three. In particular, we obtain an approximation ratio of 1.199 for the problem with maximum degree three and unbounded multiplicity.