License
when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-12837
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1283/
Grimson, Rafael

A lower bound for the complexity of linear optimization from a quantifier-elimination point of view

pdf-format:
Dokument 1.pdf (168 KB)

Abstract

We discuss the impact of data structures in quantifier elimination. We analyze the arithmetic complexity of the feasibility problem in linear optimization theory as a quantifier-elimination problem. For the case of polyhedra defined by $2n$ halfspaces in $mathbb{R}^n$ we prove that, if dense representation is used to code polynomials, any quantifier-free formula expressing the set of parameters describing nonempty polyhedra has size $Omega(4^{n})$.

BibTeX - Entry

@InProceedings{grimson:DSP:2007:1283,
  author =	{Rafael Grimson},
  title =	{A lower bound for the complexity of linear optimization from a quantifier-elimination point of view},
  booktitle =	{Constraint Databases, Geometric Elimination and Geographic Information Systems},
  year =	{2007},
  editor =	{Bernd Bank and Max J. Egenhofer and Bart Kuijpers},
  number =	{07212},
  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/2007/1283},
  annote =	{Keywords: Quantifier elimination, dense representation, instrinsic, lower bound}
}

Keywords: Quantifier elimination, dense representation, instrinsic, lower bound
Seminar: 07212 - Constraint Databases, Geometric Elimination and Geographic Information Systems
Issue date: 2007
Date of publication: 17.12.2007

DROPS-Home | Fulltext Search | Imprint Published by LZI