An analytic solution to the alibi query in the space-time prisms model for moving object data

Autores
Kuijpers, Bart; Grimson, Rafael; Othmans, Walied
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When speed limitations in these sample points are also known, space-time prisms (also called beads) (Pfoser and Jensen 1999, Egenhofer 2003, Miller 2005) can be used to model the uncertainty about an object's location in between sample points. In this setting, a query of particular interest that has been studied in the literature of geographic information systems (GIS) is the alibi query. This boolean query asks whether two moving objects could have physically met. This adds up to deciding whether the chains of space-time prisms (also called necklaces of beads) of these objects intersect. This problem can be reduced to deciding whether two space-time prisms intersect. The alibi query can be seen as a constraint database query. In the constraint database model, spatial and spatiotemporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the standard first-order query language for constraint databases and the alibi query can be expressed in it. The evaluation of the alibi query in the constraint database model relies on the elimination of a block of three existential quantifiers. Implementations of general purpose elimination algorithms, such as those provided by QEPCAD, Redlog, and Mathematica, are, for practical purposes, too slow in answering the alibi query for two specific space-time prisms. These software packages completely fail to answer the alibi query in the parametric case (i.e., when it is formulated in terms of parameters representing the sample points and speed constraints). The main contribution of this article is an analytical solution to the parametric alibi query, which can be used to answer the alibi query on two specific space-time prisms in constant time (a matter of milliseconds in our implementation). It solves the alibi query for chains of space-time prisms in time proportional to the sum of the lengths of the chains. To back this claim up, we implemented our method in Mathematica alongside the traditional quantifier elimination method. The solutions we propose are based on the geometric argumentation and they illustrate the fact that some practical problems require creative solutions, where at least in theory, existing systems could provide a solution.
Fil: Kuijpers, Bart. Hasselt University; Bélgica
Fil: Grimson, Rafael. Hasselt University; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Othmans, Walied. Hasselt University; Bélgica
Materia
Alibi Query
Constraint Databases
Moving Objects
Space-Time Prism
Spatiotemporal
Uncertainty
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/68097

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spelling An analytic solution to the alibi query in the space-time prisms model for moving object dataKuijpers, BartGrimson, RafaelOthmans, WaliedAlibi QueryConstraint DatabasesMoving ObjectsSpace-Time PrismSpatiotemporalUncertaintyhttps://purl.org/becyt/ford/1.5https://purl.org/becyt/ford/1Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When speed limitations in these sample points are also known, space-time prisms (also called beads) (Pfoser and Jensen 1999, Egenhofer 2003, Miller 2005) can be used to model the uncertainty about an object's location in between sample points. In this setting, a query of particular interest that has been studied in the literature of geographic information systems (GIS) is the alibi query. This boolean query asks whether two moving objects could have physically met. This adds up to deciding whether the chains of space-time prisms (also called necklaces of beads) of these objects intersect. This problem can be reduced to deciding whether two space-time prisms intersect. The alibi query can be seen as a constraint database query. In the constraint database model, spatial and spatiotemporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the standard first-order query language for constraint databases and the alibi query can be expressed in it. The evaluation of the alibi query in the constraint database model relies on the elimination of a block of three existential quantifiers. Implementations of general purpose elimination algorithms, such as those provided by QEPCAD, Redlog, and Mathematica, are, for practical purposes, too slow in answering the alibi query for two specific space-time prisms. These software packages completely fail to answer the alibi query in the parametric case (i.e., when it is formulated in terms of parameters representing the sample points and speed constraints). The main contribution of this article is an analytical solution to the parametric alibi query, which can be used to answer the alibi query on two specific space-time prisms in constant time (a matter of milliseconds in our implementation). It solves the alibi query for chains of space-time prisms in time proportional to the sum of the lengths of the chains. To back this claim up, we implemented our method in Mathematica alongside the traditional quantifier elimination method. The solutions we propose are based on the geometric argumentation and they illustrate the fact that some practical problems require creative solutions, where at least in theory, existing systems could provide a solution.Fil: Kuijpers, Bart. Hasselt University; BélgicaFil: Grimson, Rafael. Hasselt University; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Othmans, Walied. Hasselt University; BélgicaTaylor & Francis2011-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/68097Kuijpers, Bart; Grimson, Rafael; Othmans, Walied; An analytic solution to the alibi query in the space-time prisms model for moving object data; Taylor & Francis; International Journal Of Geographical Information Science; 25; 2; 2-2011; 293-3221365-8816CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1080/13658810902967397info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/13658810902967397info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:08:39Zoai:ri.conicet.gov.ar:11336/68097instacron: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:34982025-09-29 10:08:39.433CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An analytic solution to the alibi query in the space-time prisms model for moving object data
title An analytic solution to the alibi query in the space-time prisms model for moving object data
spellingShingle An analytic solution to the alibi query in the space-time prisms model for moving object data
Kuijpers, Bart
Alibi Query
Constraint Databases
Moving Objects
Space-Time Prism
Spatiotemporal
Uncertainty
title_short An analytic solution to the alibi query in the space-time prisms model for moving object data
title_full An analytic solution to the alibi query in the space-time prisms model for moving object data
title_fullStr An analytic solution to the alibi query in the space-time prisms model for moving object data
title_full_unstemmed An analytic solution to the alibi query in the space-time prisms model for moving object data
title_sort An analytic solution to the alibi query in the space-time prisms model for moving object data
dc.creator.none.fl_str_mv Kuijpers, Bart
Grimson, Rafael
Othmans, Walied
author Kuijpers, Bart
author_facet Kuijpers, Bart
Grimson, Rafael
Othmans, Walied
author_role author
author2 Grimson, Rafael
Othmans, Walied
author2_role author
author
dc.subject.none.fl_str_mv Alibi Query
Constraint Databases
Moving Objects
Space-Time Prism
Spatiotemporal
Uncertainty
topic Alibi Query
Constraint Databases
Moving Objects
Space-Time Prism
Spatiotemporal
Uncertainty
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.5
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When speed limitations in these sample points are also known, space-time prisms (also called beads) (Pfoser and Jensen 1999, Egenhofer 2003, Miller 2005) can be used to model the uncertainty about an object's location in between sample points. In this setting, a query of particular interest that has been studied in the literature of geographic information systems (GIS) is the alibi query. This boolean query asks whether two moving objects could have physically met. This adds up to deciding whether the chains of space-time prisms (also called necklaces of beads) of these objects intersect. This problem can be reduced to deciding whether two space-time prisms intersect. The alibi query can be seen as a constraint database query. In the constraint database model, spatial and spatiotemporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the standard first-order query language for constraint databases and the alibi query can be expressed in it. The evaluation of the alibi query in the constraint database model relies on the elimination of a block of three existential quantifiers. Implementations of general purpose elimination algorithms, such as those provided by QEPCAD, Redlog, and Mathematica, are, for practical purposes, too slow in answering the alibi query for two specific space-time prisms. These software packages completely fail to answer the alibi query in the parametric case (i.e., when it is formulated in terms of parameters representing the sample points and speed constraints). The main contribution of this article is an analytical solution to the parametric alibi query, which can be used to answer the alibi query on two specific space-time prisms in constant time (a matter of milliseconds in our implementation). It solves the alibi query for chains of space-time prisms in time proportional to the sum of the lengths of the chains. To back this claim up, we implemented our method in Mathematica alongside the traditional quantifier elimination method. The solutions we propose are based on the geometric argumentation and they illustrate the fact that some practical problems require creative solutions, where at least in theory, existing systems could provide a solution.
Fil: Kuijpers, Bart. Hasselt University; Bélgica
Fil: Grimson, Rafael. Hasselt University; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Othmans, Walied. Hasselt University; Bélgica
description Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When speed limitations in these sample points are also known, space-time prisms (also called beads) (Pfoser and Jensen 1999, Egenhofer 2003, Miller 2005) can be used to model the uncertainty about an object's location in between sample points. In this setting, a query of particular interest that has been studied in the literature of geographic information systems (GIS) is the alibi query. This boolean query asks whether two moving objects could have physically met. This adds up to deciding whether the chains of space-time prisms (also called necklaces of beads) of these objects intersect. This problem can be reduced to deciding whether two space-time prisms intersect. The alibi query can be seen as a constraint database query. In the constraint database model, spatial and spatiotemporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the standard first-order query language for constraint databases and the alibi query can be expressed in it. The evaluation of the alibi query in the constraint database model relies on the elimination of a block of three existential quantifiers. Implementations of general purpose elimination algorithms, such as those provided by QEPCAD, Redlog, and Mathematica, are, for practical purposes, too slow in answering the alibi query for two specific space-time prisms. These software packages completely fail to answer the alibi query in the parametric case (i.e., when it is formulated in terms of parameters representing the sample points and speed constraints). The main contribution of this article is an analytical solution to the parametric alibi query, which can be used to answer the alibi query on two specific space-time prisms in constant time (a matter of milliseconds in our implementation). It solves the alibi query for chains of space-time prisms in time proportional to the sum of the lengths of the chains. To back this claim up, we implemented our method in Mathematica alongside the traditional quantifier elimination method. The solutions we propose are based on the geometric argumentation and they illustrate the fact that some practical problems require creative solutions, where at least in theory, existing systems could provide a solution.
publishDate 2011
dc.date.none.fl_str_mv 2011-02
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/11336/68097
Kuijpers, Bart; Grimson, Rafael; Othmans, Walied; An analytic solution to the alibi query in the space-time prisms model for moving object data; Taylor & Francis; International Journal Of Geographical Information Science; 25; 2; 2-2011; 293-322
1365-8816
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68097
identifier_str_mv Kuijpers, Bart; Grimson, Rafael; Othmans, Walied; An analytic solution to the alibi query in the space-time prisms model for moving object data; Taylor & Francis; International Journal Of Geographical Information Science; 25; 2; 2-2011; 293-322
1365-8816
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1080/13658810902967397
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/abs/10.1080/13658810902967397
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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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