License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.06111.4
URN: urn:nbn:de:0030-drops-6039
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2006/603/
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Arpe, Jan ; Manthey, Bodo

Approximability of Minimum AND-Circuits

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

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:DagSemProc.06111.4,
  author =	{Arpe, Jan and Manthey, Bodo},
  title =	{{Approximability of Minimum AND-Circuits}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--21},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2006/603},
  URN =		{urn:nbn:de:0030-drops-6039},
  doi =		{10.4230/DagSemProc.06111.4},
  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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