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http://hdl.handle.net/1942/9214
Title: | Some lower bounds for the complexity of the linear programming feasibility problem over the reals | Authors: | GRIMSON, Rafael KUIJPERS, Bart |
Issue Date: | 2009 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF COMPLEXITY, 25(1). p. 25-37 | Abstract: | We analyze the arithmetic complexity of the linear programming feasibility problem over the reals. For the case of polyhedra defined by 2n half-spaces in R-n we prove that the set l((2n,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 > I Such that, if dense or sparse representation is used to code polynomials, the length of any quantifier-free formula expressing the set l((2n,n)) is bounded from below by Omega(c(n)). Other related complexity results are stated; in particular, a lower bound for algebraic computation trees based oil the notion of limiting hypersurface is presented. (C) 2008 Elsevier Inc. All rights reserved. | Notes: | [Grimson, Rafael; Kuijpers, Bart] Hasselt Univ, Theoret Comp Sci Grp, Diepenbeek, Belgium. [Grimson, Rafael; Kuijpers, Bart] Transnatl Univ Limburg, Limburg, Belgium. [Grimson, Rafael] Univ Buenos Aires, Dept Matemat, RA-1053 Buenos Aires, DF, Argentina. | Keywords: | Lower bounds; Linear programming; Algebraic complexity; Limiting hypersurface; Elimination theory | Document URI: | http://hdl.handle.net/1942/9214 | ISSN: | 0885-064X | e-ISSN: | 1090-2708 | DOI: | 10.1016/j.jco.2008.07.002 | ISI #: | 000262046900003 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2010 |
Appears in Collections: | Research publications |
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