Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard

This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedd...

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Detalles Bibliográficos
Autores: Garrido Vizuete, María de los Angeles, Márquez Pérez, Alberto
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1997
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/33425
Acceso en línea:http://hdl.handle.net/11441/33425
https://doi.org/10.1007/3-540-63938-1_56
Access Level:acceso abierto
Palabra clave:Theory of Computation
Discrete Mathematics
Computer-Aided Engineering (CAD, CAE) and Design
Discrete Mathematics in Computer Science
Combinatorics
Algorithm Analysis and Problem Complexity
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spelling Embedding a graph in the grid of a surface with the minimum number of bends is NP-hardGarrido Vizuete, María de los AngelesMárquez Pérez, AlbertoTheory of ComputationDiscrete MathematicsComputer-Aided Engineering (CAD, CAE) and DesignDiscrete Mathematics in Computer ScienceCombinatoricsAlgorithm Analysis and Problem ComplexityThis paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedding essentially equivalent to a given embedding, and that given a graph, testing if there exists a surface such that the graph admits a rectilinear embedding in that surface are NP-complete problems and hence the corresponding optimization problems are NP-hard.Matemática Aplicada I1997info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/33425https://doi.org/10.1007/3-540-63938-1_56reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésGraph Drawing, 1353, 124-133.info:eu-repo/semantics/openAccessoai:idus.us.es:11441/334252026-06-17T12:51:07Z
dc.title.none.fl_str_mv Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
title Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
spellingShingle Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
Garrido Vizuete, María de los Angeles
Theory of Computation
Discrete Mathematics
Computer-Aided Engineering (CAD, CAE) and Design
Discrete Mathematics in Computer Science
Combinatorics
Algorithm Analysis and Problem Complexity
title_short Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
title_full Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
title_fullStr Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
title_full_unstemmed Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
title_sort Embedding a graph in the grid of a surface with the minimum number of bends is NP-hard
dc.creator.none.fl_str_mv Garrido Vizuete, María de los Angeles
Márquez Pérez, Alberto
author Garrido Vizuete, María de los Angeles
author_facet Garrido Vizuete, María de los Angeles
Márquez Pérez, Alberto
author_role author
author2 Márquez Pérez, Alberto
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Theory of Computation
Discrete Mathematics
Computer-Aided Engineering (CAD, CAE) and Design
Discrete Mathematics in Computer Science
Combinatorics
Algorithm Analysis and Problem Complexity
topic Theory of Computation
Discrete Mathematics
Computer-Aided Engineering (CAD, CAE) and Design
Discrete Mathematics in Computer Science
Combinatorics
Algorithm Analysis and Problem Complexity
description This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedding essentially equivalent to a given embedding, and that given a graph, testing if there exists a surface such that the graph admits a rectilinear embedding in that surface are NP-complete problems and hence the corresponding optimization problems are NP-hard.
publishDate 1997
dc.date.none.fl_str_mv 1997
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/11441/33425
https://doi.org/10.1007/3-540-63938-1_56
url http://hdl.handle.net/11441/33425
https://doi.org/10.1007/3-540-63938-1_56
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Graph Drawing, 1353, 124-133.
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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