License
when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-6039
URL: http://drops.dagstuhl.de/opus/volltexte/2006/603/

Arpe, Jan ; Manthey, Bodo

Approximability of Minimum AND-Circuits

pdf-format:
Dokument 1.pdf (331 KB)


Abstract

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

@InProceedings{arpe_et_al:DSP:2006:603,
  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 =		{http://drops.dagstuhl.de/opus/volltexte/2006/603},
  annote =	{Keywords: Optimization problems, approximability, automated circuit design}
}

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


DROPS-Home | Fulltext Search | Imprint Published by LZI