Abstract:
We analyze the arithmetic complexity of the linear programming feasibility problem over the reals. For the case of polyhedra defined by 2 n half-spaces in Rn we prove that the set I(2 n, n), of parameters describing nonempty polyhedra, has an exponential number of limiting hypersurfaces. From this geometric result we obtain, as a corollary, the existence of a constant c > 1 such that, if dense or sparse representation is used to code polynomials, the length of any quantifier-free formula expressing the set I(2 n, n) is bounded from below by Ω (cn). Other related complexity results are stated; in particular, a lower bound for algebraic computation trees based on the notion of limiting hypersurface is presented. © 2008 Elsevier Inc. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | Some lower bounds for the complexity of the linear programming feasibility problem over the reals |
Autor: | Grimson, R.; Kuijpers, B. |
Filiación: | Theoretical Computer Science Group, Hasselt University, Transnational University of Limburg, Belgium Departamento de Matemática, Universidad de Buenos Aires, Argentina
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Palabras clave: | Algebraic complexity; Elimination theory; Limiting hypersurface; Linear programming; Lower bounds; Algebra; Geometry; Linear programming; Algebraic complexity; Algebraic computations; Arithmetic complexity; Elimination theory; Feasibility problem; Limiting hypersurface; Lower bounds; Sparse representation; C (programming language) |
Año: | 2009
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Volumen: | 25
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Número: | 1
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Página de inicio: | 25
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Página de fin: | 37
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DOI: |
http://dx.doi.org/10.1016/j.jco.2008.07.002 |
Título revista: | Journal of Complexity
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Título revista abreviado: | J. Complexity
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ISSN: | 0885064X
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0885064X_v25_n1_p25_Grimson |
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Citas:
---------- APA ----------
Grimson, R. & Kuijpers, B.
(2009)
. Some lower bounds for the complexity of the linear programming feasibility problem over the reals. Journal of Complexity, 25(1), 25-37.
http://dx.doi.org/10.1016/j.jco.2008.07.002---------- CHICAGO ----------
Grimson, R., Kuijpers, B.
"Some lower bounds for the complexity of the linear programming feasibility problem over the reals"
. Journal of Complexity 25, no. 1
(2009) : 25-37.
http://dx.doi.org/10.1016/j.jco.2008.07.002---------- MLA ----------
Grimson, R., Kuijpers, B.
"Some lower bounds for the complexity of the linear programming feasibility problem over the reals"
. Journal of Complexity, vol. 25, no. 1, 2009, pp. 25-37.
http://dx.doi.org/10.1016/j.jco.2008.07.002---------- VANCOUVER ----------
Grimson, R., Kuijpers, B. Some lower bounds for the complexity of the linear programming feasibility problem over the reals. J. Complexity. 2009;25(1):25-37.
http://dx.doi.org/10.1016/j.jco.2008.07.002