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DOI: 10.4230/DagSemProc.07212.3
URN: urn:nbn:de:0030-drops-12837
URL: https://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
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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 |
