A generalization of the model of permutations for binary search trees

The classical model of permutations, that allows the study of consecutive insertions in BST, fails when it considers intermixed deletions and insertions (Knott paradox). Our model solves this paradox by considering the inserted and deleted keys as Jonassen & Knuth proposed in [Jo,Knu 78], and al...

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Detalles Bibliográficos
Autor: Messeguer Peypoch, Xavier|||0000-0001-7430-4857
Tipo de recurso: informe técnico
Fecha de publicación:1991
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:2117/330452
Acceso en línea:https://hdl.handle.net/2117/330452
Access Level:acceso abierto
Palabra clave:Trees (Graph theory)
Arbres (Teoria de grafs)
Àrees temàtiques de la UPC::Informàtica
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repository_id_str
spelling A generalization of the model of permutations for binary search treesMesseguer Peypoch, Xavier|||0000-0001-7430-4857Trees (Graph theory)Arbres (Teoria de grafs)Àrees temàtiques de la UPC::InformàticaThe classical model of permutations, that allows the study of consecutive insertions in BST, fails when it considers intermixed deletions and insertions (Knott paradox). Our model solves this paradox by considering the inserted and deleted keys as Jonassen & Knuth proposed in [Jo,Knu 78], and allows the development of the invariant theory of functions applied to algorithms, following the Knuth approach as in [Knu 77]. The model also explains the pattern defined by the first random insertions followed by random deletion, by applying the invariant properties of algorithms without computing combinatorial expressions. The model suggests a new line of research to face the general problem of intermixed randon insertions and deletions.19911991-09-3020202020-10-19reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/330452reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3304522026-05-27T15:37:01Z
dc.title.none.fl_str_mv A generalization of the model of permutations for binary search trees
title A generalization of the model of permutations for binary search trees
spellingShingle A generalization of the model of permutations for binary search trees
Messeguer Peypoch, Xavier|||0000-0001-7430-4857
Trees (Graph theory)
Arbres (Teoria de grafs)
Àrees temàtiques de la UPC::Informàtica
title_short A generalization of the model of permutations for binary search trees
title_full A generalization of the model of permutations for binary search trees
title_fullStr A generalization of the model of permutations for binary search trees
title_full_unstemmed A generalization of the model of permutations for binary search trees
title_sort A generalization of the model of permutations for binary search trees
dc.creator.none.fl_str_mv Messeguer Peypoch, Xavier|||0000-0001-7430-4857
author Messeguer Peypoch, Xavier|||0000-0001-7430-4857
author_facet Messeguer Peypoch, Xavier|||0000-0001-7430-4857
author_role author
dc.subject.none.fl_str_mv Trees (Graph theory)
Arbres (Teoria de grafs)
Àrees temàtiques de la UPC::Informàtica
topic Trees (Graph theory)
Arbres (Teoria de grafs)
Àrees temàtiques de la UPC::Informàtica
description The classical model of permutations, that allows the study of consecutive insertions in BST, fails when it considers intermixed deletions and insertions (Knott paradox). Our model solves this paradox by considering the inserted and deleted keys as Jonassen & Knuth proposed in [Jo,Knu 78], and allows the development of the invariant theory of functions applied to algorithms, following the Knuth approach as in [Knu 77]. The model also explains the pattern defined by the first random insertions followed by random deletion, by applying the invariant properties of algorithms without computing combinatorial expressions. The model suggests a new line of research to face the general problem of intermixed randon insertions and deletions.
publishDate 1991
dc.date.none.fl_str_mv 1991
1991-09-30
2020
2020-10-19
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
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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/2117/330452
url https://hdl.handle.net/2117/330452
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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Attribution-NonCommercial-NoDerivs 3.0 Spain
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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
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