Revision #1 Authors: Jan Arpe, Bodo Manthey

Accepted on: 20th May 2006 00:00

Downloads: 2049

Keywords:

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.

TR06-045 Authors: Jan Arpe, Bodo Manthey

Publication: 31st March 2006 02:09

Downloads: 2047

Keywords:

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.