Finding the minimum -weighted dominating sets using heuristic algorithms

In this work, we propose, analyze, and solve a generalization of the -dominating set problem in a graph, when we consider a weighted graph. Given a graph with weights in its edges, a set of vertices is a -weighted dominating set if for every vertex outside the set, the sum of the weights from it to...

Full description

Bibliographic Details
Authors: Barrena, Eva, Bermudo Navarrete, Sergio, Hernández-Díaz, Alfredo G., Zamudio, José A., López Sánchez, Ana Dolores
Format: article
Publication Date:2024
Country:España
Institution:Universidad Pablo de Olavide (UPO)
Repository:RIO. Repositorio Institucional Olavide
Language:English
OAI Identifier:oai:rio.upo.es:10433/21817
Online Access:https://hdl.handle.net/10433/21817
Access Level:Open access
Keyword:Edge-weight
Dominating set
Metaheuristic algorithm
Iterated greedy algorithm
id ES_a08fc7137e37f9039b59db10190e9f14
oai_identifier_str oai:rio.upo.es:10433/21817
network_acronym_str ES
network_name_str España
repository_id_str
spelling Finding the minimum -weighted dominating sets using heuristic algorithmsBarrena, EvaBermudo Navarrete, SergioHernández-Díaz, Alfredo G.Zamudio, José A.López Sánchez, Ana DoloresEdge-weightDominating setMetaheuristic algorithmIterated greedy algorithmIn this work, we propose, analyze, and solve a generalization of the -dominating set problem in a graph, when we consider a weighted graph. Given a graph with weights in its edges, a set of vertices is a -weighted dominating set if for every vertex outside the set, the sum of the weights from it to its adjacent vertices in the set is bigger than or equal to . The -weighted domination number is the minimum cardinality among all -weighted dominating sets. Since the problem of finding the -weighted domination number is -hard, we have proposed several problem-adapted construction and reconstruction techniques and embedded them in an Iterated Greedy algorithm. The resulting sixteen variants of the Iterated Greedy algorithm have been compared with an exact algorithm. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. To the best of our knowledge, the -weighted dominating set problem has never been studied before in the literature and, therefore, there is no other state-of-the-art algorithm to solve it. We have also included a comparison with a particular case of our problem, the minimum dominating set problem and, on average, we achieve same quality results within around 50% of computation time.Elsevier20242024-10-1820242024-10-1820242024-10-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10433/21817reponame:RIO. Repositorio Institucional Olavideinstname:Universidad Pablo de Olavide (UPO)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:rio.upo.es:10433/218172026-06-13T12:46:27Z
dc.title.none.fl_str_mv Finding the minimum -weighted dominating sets using heuristic algorithms
title Finding the minimum -weighted dominating sets using heuristic algorithms
spellingShingle Finding the minimum -weighted dominating sets using heuristic algorithms
Barrena, Eva
Edge-weight
Dominating set
Metaheuristic algorithm
Iterated greedy algorithm
title_short Finding the minimum -weighted dominating sets using heuristic algorithms
title_full Finding the minimum -weighted dominating sets using heuristic algorithms
title_fullStr Finding the minimum -weighted dominating sets using heuristic algorithms
title_full_unstemmed Finding the minimum -weighted dominating sets using heuristic algorithms
title_sort Finding the minimum -weighted dominating sets using heuristic algorithms
dc.creator.none.fl_str_mv Barrena, Eva
Bermudo Navarrete, Sergio
Hernández-Díaz, Alfredo G.
Zamudio, José A.
López Sánchez, Ana Dolores
author Barrena, Eva
author_facet Barrena, Eva
Bermudo Navarrete, Sergio
Hernández-Díaz, Alfredo G.
Zamudio, José A.
López Sánchez, Ana Dolores
author_role author
author2 Bermudo Navarrete, Sergio
Hernández-Díaz, Alfredo G.
Zamudio, José A.
López Sánchez, Ana Dolores
author2_role author
author
author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Edge-weight
Dominating set
Metaheuristic algorithm
Iterated greedy algorithm
topic Edge-weight
Dominating set
Metaheuristic algorithm
Iterated greedy algorithm
description In this work, we propose, analyze, and solve a generalization of the -dominating set problem in a graph, when we consider a weighted graph. Given a graph with weights in its edges, a set of vertices is a -weighted dominating set if for every vertex outside the set, the sum of the weights from it to its adjacent vertices in the set is bigger than or equal to . The -weighted domination number is the minimum cardinality among all -weighted dominating sets. Since the problem of finding the -weighted domination number is -hard, we have proposed several problem-adapted construction and reconstruction techniques and embedded them in an Iterated Greedy algorithm. The resulting sixteen variants of the Iterated Greedy algorithm have been compared with an exact algorithm. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. To the best of our knowledge, the -weighted dominating set problem has never been studied before in the literature and, therefore, there is no other state-of-the-art algorithm to solve it. We have also included a comparison with a particular case of our problem, the minimum dominating set problem and, on average, we achieve same quality results within around 50% of computation time.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-10-18
2024
2024-10-18
2024
2024-10-18
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10433/21817
url https://hdl.handle.net/10433/21817
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 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
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:RIO. Repositorio Institucional Olavide
instname:Universidad Pablo de Olavide (UPO)
instname_str Universidad Pablo de Olavide (UPO)
reponame_str RIO. Repositorio Institucional Olavide
collection RIO. Repositorio Institucional Olavide
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869415020947832832
score 15,812455

Similar Items