Abstract
Given a set of monomials, the Minimum-AND-Circuit problem asks for a circuit that computes these monomials using AND-gates of fan-in two and being of minimum size. We prove that the problem is not polynomial time approximable within a factor of less than 1.0051 unless P = NP, even if the monomials are restricted to be of degree at most three. For the latter case, we devise several efficient approximation algorithms, yielding an approximation ratio of 1.278. For the general problem, we achieve an approximation ratio of d–3/2, where d is the degree of the largest monomial. In addition, we prove that the problem is fixed parameter tractable with the number of monomials as parameter. Finally, we reveal connections between the Minimum AND-Circuit problem and several problems from different areas.
A full version of this work with all proofs is available as Report 06-045 of the Electronic Colloquium on Computational Complexity (ECCC).
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Arpe, J., Manthey, B. (2006). Approximability of Minimum AND-Circuits. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_28
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DOI: https://doi.org/10.1007/11785293_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35753-7
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