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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/12316

Title: Efficient evaluation of specific queries in constraint databases
Authors: GRIMSON, Rafael
Heintz, Joos
KUIJPERS, Bart
Issue Date: 2011
Publisher: ELSEVIER SCIENCE BV
Citation: INFORMATION PROCESSING LETTERS, 111(19). p. 941-944
Abstract: Let F(1),...,F(s) is an element of R[X(1),...,X(n)] be polynomials of degree at most d, and suppose that F(1),...,F(s) are represented by a division free arithmetic circuit of non-scalar complexity size L. Let A be the arrangement of R(n) defined by F(1),...,F(s). For any point x is an element of R(n), we consider the task of determining the signs of the values F(1)(x),...,F(s)(x) (sign condition query) and the task of determining the connected component of A to which x belongs (point location query). By an extremely simple reduction to the well-known case where the polynomials F1,...,Fs are affine linear (i.e., polynomials of degree one), we show first that there exists a database of (possibly enormous) size s(O(L+n)) which allows the evaluation of the sign condition query using only (Ln)(O(1)) log(s) arithmetic operations. The key point of this paper is the proof that this upper bound is almost optimal. By the way, we show that the point location query can be evaluated using d(O(n)) log(s) arithmetic operations. Based on a different argument, analogous complexity upper-bounds are exhibited with respect to the bit-model in case that F(1),...,F(s) belong to Z[X(1),...,X(n)] and satisfy a certain natural genericity condition. Mutatis mutandis our upper-bound results may be applied to the sparse and dense representations of F(1),...,F(s). (C) 2011 Elsevier B.V. All rights reserved.
Notes: [Heintz, J] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Comp, RA-1428 Buenos Aires, DF, Argentina. [Grimson, R] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, RA-1428 Buenos Aires, DF, Argentina. [Grimson, R; Heintz, J] Consejo Nacl Invest Cient & Tecn, RA-1428 Buenos Aires, DF, Argentina. [Heintz, J] Univ Cantabria, Fac Ciencias, Dept Matemat Estadist & Comp, Santander 39071, Spain. [Grimson, R; Kuijpers, B] Hasselt Univ, Database & Theoret Comp Sci Res Grp, B-3590 Diepenbeek, Belgium. rgrimson@dm.uba.ar; joos@dc.uba.ar; bart.kuijpers@uhasselt.be
URI: http://hdl.handle.net/1942/12316
DOI: 10.1016/j.ipl.2011.06.015
ISI #: 000295307300002
ISSN: 0020-0190
Category: A1
Type: Journal Contribution
Validation: ecoom, 2012
Appears in Collections: Research publications

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