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

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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:DagSemProc.07212.3,
  author =	{Grimson, Rafael},
  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},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7212},
  editor =	{Bernd Bank and Max J. Egenhofer and Bart Kuijpers},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2007/1283},
  URN =		{urn:nbn:de:0030-drops-12837},
  doi =		{10.4230/DagSemProc.07212.3},
  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


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