Characterization of rankings generated by pseudo-Boolean functions

In this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pse...

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Autores: Unanue Gual, Imanol, Merino Maestre, María, Lozano Alonso, José Antonio
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/68311
Acceso en línea:http://hdl.handle.net/10810/68311
Access Level:acceso abierto
Palabra clave:binary-based combinatorial optimization problems
pseudo-boolean functions
rankings
dyck words
theoretical analysis
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spelling Characterization of rankings generated by pseudo-Boolean functionsUnanue Gual, ImanolMerino Maestre, MaríaLozano Alonso, José Antoniobinary-based combinatorial optimization problemspseudo-boolean functionsrankingsdyck wordstheoretical analysisIn this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pseudo-Boolean functions of degree , several observations are made. First, we verify that pseudo-Boolean functions of degree , where is the search space dimension, cannot generate all the possible rankings of the solutions. Secondly, the sufficient condition for a ranking to be generated by a pseudo-Boolean function of dimension is presented, and also the necessary condition is conjectured. Finally, we observe that the same argument is not sufficient to prove which ranking can be generated by pseudo-Boolean functions of degree .This research has been partially supported by the Spanish Ministry of Science and Innovation [PID2022-137442NB-I00, PID2019-104933GB-I00 funded by MCIN/AEI/10.13039/501100011033] and BCAM Severo Ochoa accreditation, Spain [CEX2021-001142-S]; the Basque Government, Spain [BERC 2022–2025. IT1504-22, IT1494-22]; and the University of the Basque Country UPV/EHU [GIU20/054]. Open Access funding provided by University of Basque Country.Elsevier202420242024info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/68311reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésinfo:eu-repo/grantAgreement/MICIN/PID2022-137442NB-I00/info:eu-repo/grantAgreement/MICIN/PID2019-104933GB-I00/https://www.sciencedirect.com/science/article/pii/S2210650224000786info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/3.0/es/© 2024 The Author(s). Published by Elsevier B.V. This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.oai:addi.ehu.eus:10810/683112026-06-18T09:23:17Z
dc.title.none.fl_str_mv Characterization of rankings generated by pseudo-Boolean functions
title Characterization of rankings generated by pseudo-Boolean functions
spellingShingle Characterization of rankings generated by pseudo-Boolean functions
Unanue Gual, Imanol
binary-based combinatorial optimization problems
pseudo-boolean functions
rankings
dyck words
theoretical analysis
title_short Characterization of rankings generated by pseudo-Boolean functions
title_full Characterization of rankings generated by pseudo-Boolean functions
title_fullStr Characterization of rankings generated by pseudo-Boolean functions
title_full_unstemmed Characterization of rankings generated by pseudo-Boolean functions
title_sort Characterization of rankings generated by pseudo-Boolean functions
dc.creator.none.fl_str_mv Unanue Gual, Imanol
Merino Maestre, María
Lozano Alonso, José Antonio
author Unanue Gual, Imanol
author_facet Unanue Gual, Imanol
Merino Maestre, María
Lozano Alonso, José Antonio
author_role author
author2 Merino Maestre, María
Lozano Alonso, José Antonio
author2_role author
author
dc.subject.none.fl_str_mv binary-based combinatorial optimization problems
pseudo-boolean functions
rankings
dyck words
theoretical analysis
topic binary-based combinatorial optimization problems
pseudo-boolean functions
rankings
dyck words
theoretical analysis
description In this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pseudo-Boolean functions of degree , several observations are made. First, we verify that pseudo-Boolean functions of degree , where is the search space dimension, cannot generate all the possible rankings of the solutions. Secondly, the sufficient condition for a ranking to be generated by a pseudo-Boolean function of dimension is presented, and also the necessary condition is conjectured. Finally, we observe that the same argument is not sufficient to prove which ranking can be generated by pseudo-Boolean functions of degree .
publishDate 2024
dc.date.none.fl_str_mv 2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/68311
url http://hdl.handle.net/10810/68311
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICIN/PID2022-137442NB-I00/
info:eu-repo/grantAgreement/MICIN/PID2019-104933GB-I00/
https://www.sciencedirect.com/science/article/pii/S2210650224000786
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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