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Arpe, Jan ; Manthey, Bodo

Approximability of Minimum AND-Circuits

06111.ArpeJan.Paper.603.pdf (0.3 MB)


Given a set of monomials, the {sc 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 $mathsf{P} = mathsf{NP}$, 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 {sc Minimum AND-Circuit} problem and several problems from different areas.

BibTeX - Entry

  author =	{Jan Arpe and Bodo Manthey},
  title =	{Approximability of Minimum AND-Circuits},
  booktitle =	{Complexity of Boolean Functions},
  year =	{2006},
  editor =	{Matthias Krause and Pavel Pudl{\'a}k and R{\"u}diger Reischuk and Dieter van Melkebeek},
  number =	{06111},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Optimization problems, approximability, automated circuit design}

Keywords: Optimization problems, approximability, automated circuit design
Collection: 06111 - Complexity of Boolean Functions
Issue Date: 2006
Date of publication: 09.10.2006

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