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

Arpe and Manthey [Algorithmica’09] recently studied the minimum ANDcircuit 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.