Rank selection in multidimensional data

Suppose we have a set of K-dimensional records stored in a general purpose spatial index like a K-d tree. The index efficiently supports insertions, ordinary exact searches, orthogonal range searches, nearest neighbor searches, etc. Here we consider whether we can also efficiently support search by...

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Detalles Bibliográficos
Autores: Duch Brown, Amalia|||0000-0003-4371-1286, Jiménez Gómez, Rosa María, Martínez Parra, Conrado|||0000-0003-1302-9067
Tipo de recurso: informe técnico
Fecha de publicación:2009
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/87150
Acceso en línea:https://hdl.handle.net/2117/87150
Access Level:acceso abierto
Palabra clave:Search problems
Tree data structures
Rank selection
Multidimensional data
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Rank selection in multidimensional dataDuch Brown, Amalia|||0000-0003-4371-1286Jiménez Gómez, Rosa MaríaMartínez Parra, Conrado|||0000-0003-1302-9067Search problemsTree data structuresRank selectionMultidimensional dataÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaSuppose we have a set of K-dimensional records stored in a general purpose spatial index like a K-d tree. The index efficiently supports insertions, ordinary exact searches, orthogonal range searches, nearest neighbor searches, etc. Here we consider whether we can also efficiently support search by rank, that is, to locate the i-th smallest element along the j-th coordinate. We answer this question in the affirmative by developing a simple algorithm with expected cost O(na(1/K) log n), where n is the size of the K-d tree and a(1/K) < 1 for any K ¿ 2. The only requirement to support the search by rank is that each node in the K-d tree stores the size of the subtree rooted at that node (or some equivalent information). This is not too space demanding. Furthermore, it can be used to randomize the update algorithms to provide guarantees on the expected performance of the various operations on K-d trees. Although selection in multidimensional data can be solved more efficiently than with our algorithm, those solutions will rely on ad-hoc data structures or superlinear space. Our solution adds to an existing data structure (K-d trees) the capability of search by rank with very little overhead. The simplicity of the algorithm makes it easy to implement, practical and very flexible; however, its correctness and efficiency are far from self-evident. Furthermore, it can be easily adapted to other spatial indexes as well.20092009-11-0420162016-05-18reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/87150reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/871502026-05-27T15:37:01Z
dc.title.none.fl_str_mv Rank selection in multidimensional data
title Rank selection in multidimensional data
spellingShingle Rank selection in multidimensional data
Duch Brown, Amalia|||0000-0003-4371-1286
Search problems
Tree data structures
Rank selection
Multidimensional data
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Rank selection in multidimensional data
title_full Rank selection in multidimensional data
title_fullStr Rank selection in multidimensional data
title_full_unstemmed Rank selection in multidimensional data
title_sort Rank selection in multidimensional data
dc.creator.none.fl_str_mv Duch Brown, Amalia|||0000-0003-4371-1286
Jiménez Gómez, Rosa María
Martínez Parra, Conrado|||0000-0003-1302-9067
author Duch Brown, Amalia|||0000-0003-4371-1286
author_facet Duch Brown, Amalia|||0000-0003-4371-1286
Jiménez Gómez, Rosa María
Martínez Parra, Conrado|||0000-0003-1302-9067
author_role author
author2 Jiménez Gómez, Rosa María
Martínez Parra, Conrado|||0000-0003-1302-9067
author2_role author
author
dc.subject.none.fl_str_mv Search problems
Tree data structures
Rank selection
Multidimensional data
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Search problems
Tree data structures
Rank selection
Multidimensional data
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description Suppose we have a set of K-dimensional records stored in a general purpose spatial index like a K-d tree. The index efficiently supports insertions, ordinary exact searches, orthogonal range searches, nearest neighbor searches, etc. Here we consider whether we can also efficiently support search by rank, that is, to locate the i-th smallest element along the j-th coordinate. We answer this question in the affirmative by developing a simple algorithm with expected cost O(na(1/K) log n), where n is the size of the K-d tree and a(1/K) < 1 for any K ¿ 2. The only requirement to support the search by rank is that each node in the K-d tree stores the size of the subtree rooted at that node (or some equivalent information). This is not too space demanding. Furthermore, it can be used to randomize the update algorithms to provide guarantees on the expected performance of the various operations on K-d trees. Although selection in multidimensional data can be solved more efficiently than with our algorithm, those solutions will rely on ad-hoc data structures or superlinear space. Our solution adds to an existing data structure (K-d trees) the capability of search by rank with very little overhead. The simplicity of the algorithm makes it easy to implement, practical and very flexible; however, its correctness and efficiency are far from self-evident. Furthermore, it can be easily adapted to other spatial indexes as well.
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-11-04
2016
2016-05-18
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/87150
url https://hdl.handle.net/2117/87150
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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