DagSemProc.07212.3.pdf
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A lower bound for the complexity of linear optimization from a quantifier-elimination point of view
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Dagstuhl Seminar Proceedings, Volume 7212
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2007-12-17
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Rafael Grimson. A lower bound for the complexity of linear optimization from a quantifier-elimination point of view. In Constraint Databases, Geometric Elimination and Geographic Information Systems. Dagstuhl Seminar Proceedings, Volume 7212, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.07212.3
https://doi.org/10.4230/DagSemProc.07212.3
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 $Omega(4^{n})$.
Keywords
- Quantifier elimination
- dense representation
- instrinsic
- lower bound
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