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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Detalhes bibliográficos
Autores: Unanue, I., Merino, M., Lozano, J.A.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1786
Acesso em linha:http://hdl.handle.net/20.500.11824/1786
https://doi.org/10.1016/j.swevo.2024.101540
Access Level:acceso abierto
Palavra-chave:Binary-based combinatorial optimization problemsPseudo-Boolean functionsRankingsDyck wordsTheoretical analysis
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spelling Characterization of rankings generated by pseudo-Boolean functionsUnanue, I.Merino, M.Lozano, J.A.Binary-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.202420242024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1786https://doi.org/10.1016/j.swevo.2024.101540reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://doi.org/10.1016/j.swevo.2024.101540info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-SReconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/17862026-06-19T12:47:47Z
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, I.
Binary-based combinatorial optimization problemsPseudo-Boolean functionsRankingsDyck wordsTheoretical 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, I.
Merino, M.
Lozano, J.A.
author Unanue, I.
author_facet Unanue, I.
Merino, M.
Lozano, J.A.
author_role author
author2 Merino, M.
Lozano, J.A.
author2_role author
author
dc.subject.none.fl_str_mv Binary-based combinatorial optimization problemsPseudo-Boolean functionsRankingsDyck wordsTheoretical analysis
topic Binary-based combinatorial optimization problemsPseudo-Boolean functionsRankingsDyck wordsTheoretical 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
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1786
https://doi.org/10.1016/j.swevo.2024.101540
url http://hdl.handle.net/20.500.11824/1786
https://doi.org/10.1016/j.swevo.2024.101540
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.swevo.2024.101540
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-S
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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