Restricted Hamming-Huffman Trees

Autores
Lin, Min Chih; de Souza Oliveira, Fabiano; Pinto, Paulo E. D.; Sampaio, Moysés S.; Szwarcfiter, Jayme L.
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study a special case of HammingHuffman trees, in which both data compression and data error detection are tackled on the same structure. Given a hypercube Qn of dimension n, we are interested in some aspects of its vertex neighborhoods. For a subset L of vertices of Qn, the neighborhood of L is defined as the union of the neighborhoods of the vertices of L. The minimum neighborhood problem is that of determining the minimum neighborhood cardinality over all those sets L. This is a well-known problem that has already been solved. Our interest lies in determining optimal HammingHuffman trees, a problem that remains open and which is related to minimum neighborhoods in Qn. In this work, we consider a restricted version of HammingHuffman trees, called [k]-HHT s, which admit symbol leaves in at most k different levels. We present an algorithm to build optimal [2]-HHT s. For uniform frequencies, we prove that an optimal HHT is always a [5]-HHT and that there exists an optimal HHT which is a [4]-HHT. Also, considering experimental results, we conjecture that there exists an optimal tree which is a [3]-HHT.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: de Souza Oliveira, Fabiano. Universidade do Estado de Rio do Janeiro; Brasil
Fil: Pinto, Paulo E. D.. Universidade do Estado de Rio do Janeiro; Brasil
Fil: Sampaio, Moysés S.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Universidade do Estado de Rio do Janeiro; Brasil
Materia
HAMMINGHUFFMAN CODES
HYPERCUBE GRAPHS
MINIMUM NEIGHBORHOOD
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/203619

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spelling Restricted Hamming-Huffman TreesLin, Min Chihde Souza Oliveira, FabianoPinto, Paulo E. D.Sampaio, Moysés S.Szwarcfiter, Jayme L.HAMMINGHUFFMAN CODESHYPERCUBE GRAPHSMINIMUM NEIGHBORHOODhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study a special case of HammingHuffman trees, in which both data compression and data error detection are tackled on the same structure. Given a hypercube Qn of dimension n, we are interested in some aspects of its vertex neighborhoods. For a subset L of vertices of Qn, the neighborhood of L is defined as the union of the neighborhoods of the vertices of L. The minimum neighborhood problem is that of determining the minimum neighborhood cardinality over all those sets L. This is a well-known problem that has already been solved. Our interest lies in determining optimal HammingHuffman trees, a problem that remains open and which is related to minimum neighborhoods in Qn. In this work, we consider a restricted version of HammingHuffman trees, called [k]-HHT s, which admit symbol leaves in at most k different levels. We present an algorithm to build optimal [2]-HHT s. For uniform frequencies, we prove that an optimal HHT is always a [5]-HHT and that there exists an optimal HHT which is a [4]-HHT. Also, considering experimental results, we conjecture that there exists an optimal tree which is a [3]-HHT.Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: de Souza Oliveira, Fabiano. Universidade do Estado de Rio do Janeiro; BrasilFil: Pinto, Paulo E. D.. Universidade do Estado de Rio do Janeiro; BrasilFil: Sampaio, Moysés S.. Universidade Federal do Rio de Janeiro; BrasilFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Universidade do Estado de Rio do Janeiro; BrasilEDP Sciences2022-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/203619Lin, Min Chih; de Souza Oliveira, Fabiano; Pinto, Paulo E. D.; Sampaio, Moysés S.; Szwarcfiter, Jayme L.; Restricted Hamming-Huffman Trees; EDP Sciences; RAIRO - Operations Research; 56; 3; 6-2022; 1823-18392804-7303CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/ro/2022066info:eu-repo/semantics/altIdentifier/url/https://www.rairo-ro.org/articles/ro/abs/2022/03/ro210431/ro210431.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:32:11Zoai:ri.conicet.gov.ar:11336/203619instacron: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 10:32:11.789CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Restricted Hamming-Huffman Trees
title Restricted Hamming-Huffman Trees
spellingShingle Restricted Hamming-Huffman Trees
Lin, Min Chih
HAMMINGHUFFMAN CODES
HYPERCUBE GRAPHS
MINIMUM NEIGHBORHOOD
title_short Restricted Hamming-Huffman Trees
title_full Restricted Hamming-Huffman Trees
title_fullStr Restricted Hamming-Huffman Trees
title_full_unstemmed Restricted Hamming-Huffman Trees
title_sort Restricted Hamming-Huffman Trees
dc.creator.none.fl_str_mv Lin, Min Chih
de Souza Oliveira, Fabiano
Pinto, Paulo E. D.
Sampaio, Moysés S.
Szwarcfiter, Jayme L.
author Lin, Min Chih
author_facet Lin, Min Chih
de Souza Oliveira, Fabiano
Pinto, Paulo E. D.
Sampaio, Moysés S.
Szwarcfiter, Jayme L.
author_role author
author2 de Souza Oliveira, Fabiano
Pinto, Paulo E. D.
Sampaio, Moysés S.
Szwarcfiter, Jayme L.
author2_role author
author
author
author
dc.subject.none.fl_str_mv HAMMINGHUFFMAN CODES
HYPERCUBE GRAPHS
MINIMUM NEIGHBORHOOD
topic HAMMINGHUFFMAN CODES
HYPERCUBE GRAPHS
MINIMUM NEIGHBORHOOD
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study a special case of HammingHuffman trees, in which both data compression and data error detection are tackled on the same structure. Given a hypercube Qn of dimension n, we are interested in some aspects of its vertex neighborhoods. For a subset L of vertices of Qn, the neighborhood of L is defined as the union of the neighborhoods of the vertices of L. The minimum neighborhood problem is that of determining the minimum neighborhood cardinality over all those sets L. This is a well-known problem that has already been solved. Our interest lies in determining optimal HammingHuffman trees, a problem that remains open and which is related to minimum neighborhoods in Qn. In this work, we consider a restricted version of HammingHuffman trees, called [k]-HHT s, which admit symbol leaves in at most k different levels. We present an algorithm to build optimal [2]-HHT s. For uniform frequencies, we prove that an optimal HHT is always a [5]-HHT and that there exists an optimal HHT which is a [4]-HHT. Also, considering experimental results, we conjecture that there exists an optimal tree which is a [3]-HHT.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: de Souza Oliveira, Fabiano. Universidade do Estado de Rio do Janeiro; Brasil
Fil: Pinto, Paulo E. D.. Universidade do Estado de Rio do Janeiro; Brasil
Fil: Sampaio, Moysés S.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil. Universidade do Estado de Rio do Janeiro; Brasil
description We study a special case of HammingHuffman trees, in which both data compression and data error detection are tackled on the same structure. Given a hypercube Qn of dimension n, we are interested in some aspects of its vertex neighborhoods. For a subset L of vertices of Qn, the neighborhood of L is defined as the union of the neighborhoods of the vertices of L. The minimum neighborhood problem is that of determining the minimum neighborhood cardinality over all those sets L. This is a well-known problem that has already been solved. Our interest lies in determining optimal HammingHuffman trees, a problem that remains open and which is related to minimum neighborhoods in Qn. In this work, we consider a restricted version of HammingHuffman trees, called [k]-HHT s, which admit symbol leaves in at most k different levels. We present an algorithm to build optimal [2]-HHT s. For uniform frequencies, we prove that an optimal HHT is always a [5]-HHT and that there exists an optimal HHT which is a [4]-HHT. Also, considering experimental results, we conjecture that there exists an optimal tree which is a [3]-HHT.
publishDate 2022
dc.date.none.fl_str_mv 2022-06
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/11336/203619
Lin, Min Chih; de Souza Oliveira, Fabiano; Pinto, Paulo E. D.; Sampaio, Moysés S.; Szwarcfiter, Jayme L.; Restricted Hamming-Huffman Trees; EDP Sciences; RAIRO - Operations Research; 56; 3; 6-2022; 1823-1839
2804-7303
CONICET Digital
CONICET
url http://hdl.handle.net/11336/203619
identifier_str_mv Lin, Min Chih; de Souza Oliveira, Fabiano; Pinto, Paulo E. D.; Sampaio, Moysés S.; Szwarcfiter, Jayme L.; Restricted Hamming-Huffman Trees; EDP Sciences; RAIRO - Operations Research; 56; 3; 6-2022; 1823-1839
2804-7303
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/ro/2022066
info:eu-repo/semantics/altIdentifier/url/https://www.rairo-ro.org/articles/ro/abs/2022/03/ro210431/ro210431.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
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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