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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/203619
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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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1844614334910562304 |
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13.070432 |