Efficient evaluation of specific queries in constraint databases

Autores
Grimson, Rafael; Heintz, Joos Ulrich; Kuijpers, Bart
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let F1,...,FsεR[X1,...,Xn] be polynomials of degree at most d, and suppose that F1,...,F s are represented by a division free arithmetic circuit of non-scalar complexity size L. Let A be the arrangement of Rn defined by F 1,...,Fs. For any point xεRn, we consider the task of determining the signs of the values F1(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 F 1,...,Fs are affine linear (i.e., polynomials of degree one), we show first that there exists a database of (possibly enormous) size sO(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 dO(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,...,Fs belong to Z[X1,...,Xn] 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,...,Fs.
Fil: Grimson, Rafael. Hasselt University; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina
Fil: Heintz, Joos Ulrich. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Kuijpers, Bart. Hasselt University; Bélgica
Materia
COMPUTATIONAL COMPLEXITY
CONSTRAINT DATABASES
QUERY EVALUATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/115004

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network_name_str CONICET Digital (CONICET)
spelling Efficient evaluation of specific queries in constraint databasesGrimson, RafaelHeintz, Joos UlrichKuijpers, BartCOMPUTATIONAL COMPLEXITYCONSTRAINT DATABASESQUERY EVALUATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let F1,...,FsεR[X1,...,Xn] be polynomials of degree at most d, and suppose that F1,...,F s are represented by a division free arithmetic circuit of non-scalar complexity size L. Let A be the arrangement of Rn defined by F 1,...,Fs. For any point xεRn, we consider the task of determining the signs of the values F1(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 F 1,...,Fs are affine linear (i.e., polynomials of degree one), we show first that there exists a database of (possibly enormous) size sO(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 dO(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,...,Fs belong to Z[X1,...,Xn] 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,...,Fs.Fil: Grimson, Rafael. Hasselt University; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Heintz, Joos Ulrich. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Kuijpers, Bart. Hasselt University; BélgicaElsevier Science2011-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/115004Grimson, Rafael; Heintz, Joos Ulrich; Kuijpers, Bart; Efficient evaluation of specific queries in constraint databases; Elsevier Science; Information Processing Letters; 111; 19; 10-2011; 941-9440020-0190CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0020019011001864info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ipl.2011.06.015info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:05:19Zoai:ri.conicet.gov.ar:11336/115004instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:05:19.439CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Efficient evaluation of specific queries in constraint databases
title Efficient evaluation of specific queries in constraint databases
spellingShingle Efficient evaluation of specific queries in constraint databases
Grimson, Rafael
COMPUTATIONAL COMPLEXITY
CONSTRAINT DATABASES
QUERY EVALUATION
title_short Efficient evaluation of specific queries in constraint databases
title_full Efficient evaluation of specific queries in constraint databases
title_fullStr Efficient evaluation of specific queries in constraint databases
title_full_unstemmed Efficient evaluation of specific queries in constraint databases
title_sort Efficient evaluation of specific queries in constraint databases
dc.creator.none.fl_str_mv Grimson, Rafael
Heintz, Joos Ulrich
Kuijpers, Bart
author Grimson, Rafael
author_facet Grimson, Rafael
Heintz, Joos Ulrich
Kuijpers, Bart
author_role author
author2 Heintz, Joos Ulrich
Kuijpers, Bart
author2_role author
author
dc.subject.none.fl_str_mv COMPUTATIONAL COMPLEXITY
CONSTRAINT DATABASES
QUERY EVALUATION
topic COMPUTATIONAL COMPLEXITY
CONSTRAINT DATABASES
QUERY EVALUATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let F1,...,FsεR[X1,...,Xn] be polynomials of degree at most d, and suppose that F1,...,F s are represented by a division free arithmetic circuit of non-scalar complexity size L. Let A be the arrangement of Rn defined by F 1,...,Fs. For any point xεRn, we consider the task of determining the signs of the values F1(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 F 1,...,Fs are affine linear (i.e., polynomials of degree one), we show first that there exists a database of (possibly enormous) size sO(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 dO(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,...,Fs belong to Z[X1,...,Xn] 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,...,Fs.
Fil: Grimson, Rafael. Hasselt University; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina
Fil: Heintz, Joos Ulrich. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Kuijpers, Bart. Hasselt University; Bélgica
description Let F1,...,FsεR[X1,...,Xn] be polynomials of degree at most d, and suppose that F1,...,F s are represented by a division free arithmetic circuit of non-scalar complexity size L. Let A be the arrangement of Rn defined by F 1,...,Fs. For any point xεRn, we consider the task of determining the signs of the values F1(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 F 1,...,Fs are affine linear (i.e., polynomials of degree one), we show first that there exists a database of (possibly enormous) size sO(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 dO(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,...,Fs belong to Z[X1,...,Xn] 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,...,Fs.
publishDate 2011
dc.date.none.fl_str_mv 2011-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/115004
Grimson, Rafael; Heintz, Joos Ulrich; Kuijpers, Bart; Efficient evaluation of specific queries in constraint databases; Elsevier Science; Information Processing Letters; 111; 19; 10-2011; 941-944
0020-0190
CONICET Digital
CONICET
url http://hdl.handle.net/11336/115004
identifier_str_mv Grimson, Rafael; Heintz, Joos Ulrich; Kuijpers, Bart; Efficient evaluation of specific queries in constraint databases; Elsevier Science; Information Processing Letters; 111; 19; 10-2011; 941-944
0020-0190
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0020019011001864
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ipl.2011.06.015
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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