Approximability of Minimum AND-Circuits

Complexity of Boolean Functions

计算机科学;物理学;物理学

Jan Arpe∗ ; 1 Bodo Manthey† ; 2 ; 2 Universita¨t des Saarlandes Informatik Postfach 151150 66041 Saarbru¨cken ; Germany

Others  :  http://drops.dagstuhl.de/opus/volltexte/2006/603/pdf/06111.ArpeJan.Paper.603.pdf
PID  :  6446

学科分类：计算机科学（综合）

来源: CEUR

【 摘 要 】

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-