Constructive heuristic for the vertex bisection problem

The Vertex Bisection Problem (VBP) consists in partitioning a generic graph into two equally– sized subgraphs and such that the number of vertices in with at least one adjacent vertex in is minimized. This problem is NP–hard with practical applications in the telecommunication industry. In this arti...

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Detalles Bibliográficos
Autores: Norberto Castillo-García, Paula Hernández-Hernández
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:México
Institución:Tecnológico Nacional de México
Repositorio:Redalyc-TNM
OAI Identifier:oai:redalyc.org:47471673005
Acceso en línea:https://www.redalyc.org/articulo.oa?id=47471673005
https://www.redalyc.org/journal/474/47471673005/
https://www.redalyc.org/journal/474/47471673005/html/
https://www.redalyc.org/journal/474/47471673005/47471673005.epub
https://www.redalyc.org/journal/474/47471673005/movil
Access Level:acceso abierto
Palabra clave:Ingeniería
Constructive algorithm
Heuristic optimization
Vertex Bisection Problem
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spelling Constructive heuristic for the vertex bisection problemNorberto Castillo-GarcíaPaula Hernández-HernándezIngenieríaConstructive algorithmHeuristic optimizationVertex Bisection ProblemThe Vertex Bisection Problem (VBP) consists in partitioning a generic graph into two equally– sized subgraphs and such that the number of vertices in with at least one adjacent vertex in is minimized. This problem is NP–hard with practical applications in the telecommunication industry. In this article we propose a new constructive algorithm for VBP based on the Greedy Randomized Adaptive Search Procedure (GRASP) methodology. We call our algorithm CVBP. We compare CVBP with a previously published GRASP–based constructive algorithm (LIT) in order to assess the performance of our algorithm in practice. The results of the experiment showed that CVBP outperformed LIT by 75.83 % in solution quality. The validation of the experimental evidence was performed by the well–known Wilcoxon Signed Rank Sum Test. The test found statistical significance for a confidence level of 99.99 %. Therefore, we consider that our constructive heuristic is a good alternative to stochastically solve the Vertex Bisection Problem.Universidad Nacional Autónoma de México2020info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdf1665-6423https://www.redalyc.org/articulo.oa?id=47471673005https://www.redalyc.org/journal/474/47471673005/https://www.redalyc.org/journal/474/47471673005/html/https://www.redalyc.org/journal/474/47471673005/47471673005.epubhttps://www.redalyc.org/journal/474/47471673005/movil10.14482/INDES.30.1.303.661Journal of Applied Research and Technology (México) Num.4 Vol.18reponame:Redalyc-TNMinstname:Tecnológico Nacional de Méxicoinstacron:TNMenhttp://www.redalyc.org/revista.oa?id=474Journal of Applied Research and Technologyinfo:eu-repo/semantics/openAccessoai:redalyc.org:474716730052024-08-23T20:49:15Z
dc.title.none.fl_str_mv Constructive heuristic for the vertex bisection problem
title Constructive heuristic for the vertex bisection problem
spellingShingle Constructive heuristic for the vertex bisection problem
Norberto Castillo-García
Ingeniería
Constructive algorithm
Heuristic optimization
Vertex Bisection Problem
title_short Constructive heuristic for the vertex bisection problem
title_full Constructive heuristic for the vertex bisection problem
title_fullStr Constructive heuristic for the vertex bisection problem
title_full_unstemmed Constructive heuristic for the vertex bisection problem
title_sort Constructive heuristic for the vertex bisection problem
dc.creator.none.fl_str_mv Norberto Castillo-García
Paula Hernández-Hernández
author Norberto Castillo-García
author_facet Norberto Castillo-García
Paula Hernández-Hernández
author_role author
author2 Paula Hernández-Hernández
author2_role author
dc.subject.none.fl_str_mv Ingeniería
Constructive algorithm
Heuristic optimization
Vertex Bisection Problem
topic Ingeniería
Constructive algorithm
Heuristic optimization
Vertex Bisection Problem
description The Vertex Bisection Problem (VBP) consists in partitioning a generic graph into two equally– sized subgraphs and such that the number of vertices in with at least one adjacent vertex in is minimized. This problem is NP–hard with practical applications in the telecommunication industry. In this article we propose a new constructive algorithm for VBP based on the Greedy Randomized Adaptive Search Procedure (GRASP) methodology. We call our algorithm CVBP. We compare CVBP with a previously published GRASP–based constructive algorithm (LIT) in order to assess the performance of our algorithm in practice. The results of the experiment showed that CVBP outperformed LIT by 75.83 % in solution quality. The validation of the experimental evidence was performed by the well–known Wilcoxon Signed Rank Sum Test. The test found statistical significance for a confidence level of 99.99 %. Therefore, we consider that our constructive heuristic is a good alternative to stochastically solve the Vertex Bisection Problem.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv 1665-6423
https://www.redalyc.org/articulo.oa?id=47471673005
https://www.redalyc.org/journal/474/47471673005/
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https://www.redalyc.org/journal/474/47471673005/47471673005.epub
https://www.redalyc.org/journal/474/47471673005/movil
10.14482/INDES.30.1.303.661
identifier_str_mv 1665-6423
10.14482/INDES.30.1.303.661
url https://www.redalyc.org/articulo.oa?id=47471673005
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https://www.redalyc.org/journal/474/47471673005/47471673005.epub
https://www.redalyc.org/journal/474/47471673005/movil
dc.language.none.fl_str_mv en
language_invalid_str_mv en
dc.relation.none.fl_str_mv http://www.redalyc.org/revista.oa?id=474
dc.rights.none.fl_str_mv Journal of Applied Research and Technology
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Journal of Applied Research and Technology
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Nacional Autónoma de México
publisher.none.fl_str_mv Universidad Nacional Autónoma de México
dc.source.none.fl_str_mv Journal of Applied Research and Technology (México) Num.4 Vol.18
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