An iterated greedy algorithm for finding the minimum dominating set in graphs

A dominating set in a graph is a set of vertices such that every vertex outside the set is adjacent to a vertex in the set. The domination number is the minimum cardinality of a dominating set in the graph. The problem of finding the minimum dominating set is a combinatorial optimization problem tha...

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Bibliographic Details
Authors: Casado, Alejandra, Bermudo Navarrete, Sergio, López Sánchez, Ana Dolores, Hernández-Díaz, Alfredo G.
Format: article
Publication Date:2023
Country:España
Institution:Universidad Pablo de Olavide (UPO)
Repository:RIO. Repositorio Institucional Olavide
Language:English
OAI Identifier:oai:rio.upo.es:10433/22300
Online Access:https://hdl.handle.net/10433/22300
Access Level:Open access
Keyword:Domination number
Exact algorithm
Iterated greedy
Greedy heuristics
Minimum dominating set
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spelling An iterated greedy algorithm for finding the minimum dominating set in graphsCasado, AlejandraBermudo Navarrete, SergioLópez Sánchez, Ana DoloresHernández-Díaz, Alfredo G.Domination numberExact algorithmExact algorithmIterated greedyGreedy heuristicsMinimum dominating setA dominating set in a graph is a set of vertices such that every vertex outside the set is adjacent to a vertex in the set. The domination number is the minimum cardinality of a dominating set in the graph. The problem of finding the minimum dominating set is a combinatorial optimization problem that has been proved to be NP-hard. Given the difficulty of this problem, an Iterated Greedy algorithm is proposed for its solution and it is compared to the solution given by an exact algorithm and by the state-of-art algorithms. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. Specifically, from the set of instances which can be optimally solved, the proposed method presents an average deviation of 0.04%. Regarding the more complex set of instances, where the exact method is not able to reach the optimal value, the proposed method achieves an average deviation of 1.23% with respect to the best-known solution.Elsevier20252025-01-1420232023-12-2320232023-12-23journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10433/22300reponame:RIO. Repositorio Institucional Olavideinstname:Universidad Pablo de Olavide (UPO)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:rio.upo.es:10433/223002026-06-13T12:46:27Z
dc.title.none.fl_str_mv An iterated greedy algorithm for finding the minimum dominating set in graphs
title An iterated greedy algorithm for finding the minimum dominating set in graphs
spellingShingle An iterated greedy algorithm for finding the minimum dominating set in graphs
Casado, Alejandra
Domination number
Exact algorithm
Exact algorithm
Iterated greedy
Greedy heuristics
Minimum dominating set
title_short An iterated greedy algorithm for finding the minimum dominating set in graphs
title_full An iterated greedy algorithm for finding the minimum dominating set in graphs
title_fullStr An iterated greedy algorithm for finding the minimum dominating set in graphs
title_full_unstemmed An iterated greedy algorithm for finding the minimum dominating set in graphs
title_sort An iterated greedy algorithm for finding the minimum dominating set in graphs
dc.creator.none.fl_str_mv Casado, Alejandra
Bermudo Navarrete, Sergio
López Sánchez, Ana Dolores
Hernández-Díaz, Alfredo G.
author Casado, Alejandra
author_facet Casado, Alejandra
Bermudo Navarrete, Sergio
López Sánchez, Ana Dolores
Hernández-Díaz, Alfredo G.
author_role author
author2 Bermudo Navarrete, Sergio
López Sánchez, Ana Dolores
Hernández-Díaz, Alfredo G.
author2_role author
author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Domination number
Exact algorithm
Exact algorithm
Iterated greedy
Greedy heuristics
Minimum dominating set
topic Domination number
Exact algorithm
Exact algorithm
Iterated greedy
Greedy heuristics
Minimum dominating set
description A dominating set in a graph is a set of vertices such that every vertex outside the set is adjacent to a vertex in the set. The domination number is the minimum cardinality of a dominating set in the graph. The problem of finding the minimum dominating set is a combinatorial optimization problem that has been proved to be NP-hard. Given the difficulty of this problem, an Iterated Greedy algorithm is proposed for its solution and it is compared to the solution given by an exact algorithm and by the state-of-art algorithms. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. Specifically, from the set of instances which can be optimally solved, the proposed method presents an average deviation of 0.04%. Regarding the more complex set of instances, where the exact method is not able to reach the optimal value, the proposed method achieves an average deviation of 1.23% with respect to the best-known solution.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-12-23
2023
2023-12-23
2025
2025-01-14
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/10433/22300
url https://hdl.handle.net/10433/22300
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-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/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-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/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_ 1869423221277720576
score 15,812455

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