Approximability of Minimum AND-Circuits

Jan Arpe, Bodo Manthey


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.

Original languageEnglish
Title of host publicationSWAT 2006: Algorithm Theory – SWAT 2006
Number of pages12
Volume4059 LNCS
PublisherSpringer Verlag
Publication date01.01.2006
ISBN (Print)978-3-540-35753-7
ISBN (Electronic)978-3-540-35755-1
Publication statusPublished - 01.01.2006
Event10th Scandinavian Workshop on Algorithm Theory - Riga, Latvia
Duration: 06.07.200608.07.2006
Conference number: 67922


Dive into the research topics of 'Approximability of Minimum AND-Circuits'. Together they form a unique fingerprint.

Cite this