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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/115004
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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/ |
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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) |
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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 |
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13.13397 |