Fully Dynamic Recognition of Proper Circular-Arc Graphs

Autores
Soulignac, Francisco Juan
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the graph, while vertex operations cost O(logn+d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(logn) time per operation are obtained. Also, an O(Δ) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where Δ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time. As an application, we show how to find a minimal forbidden induced subgraph of a static graph in O(n+m) time.
Fil: Soulignac, Francisco Juan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Materia
CO-CONNECTIVITY
DYNAMIC RECOGNITION
MINIMAL FORBIDDEN INDUCED SUBGRAPHS
PROPER CIRCULAR-ARC GRAPHS
ROUND GRAPHS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98528
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/98528
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Fully Dynamic Recognition of Proper Circular-Arc GraphsSoulignac, Francisco JuanCO-CONNECTIVITYDYNAMIC RECOGNITIONMINIMAL FORBIDDEN INDUCED SUBGRAPHSPROPER CIRCULAR-ARC GRAPHSROUND GRAPHShttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the graph, while vertex operations cost O(logn+d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(logn) time per operation are obtained. Also, an O(Δ) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where Δ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time. As an application, we show how to find a minimal forbidden induced subgraph of a static graph in O(n+m) time.Fil: Soulignac, Francisco Juan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaSpringer2015-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98528Soulignac, Francisco Juan; Fully Dynamic Recognition of Proper Circular-Arc Graphs; Springer; Algorithmica; 71; 4; 4-2015; 904-9680178-4617CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00453-013-9835-7info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00453-013-9835-7info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1111.3548info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:51Zoai:ri.conicet.gov.ar:11336/98528instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:52:51.684CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Fully Dynamic Recognition of Proper Circular-Arc Graphs
title Fully Dynamic Recognition of Proper Circular-Arc Graphs
spellingShingle Fully Dynamic Recognition of Proper Circular-Arc Graphs
Soulignac, Francisco Juan
CO-CONNECTIVITY
DYNAMIC RECOGNITION
MINIMAL FORBIDDEN INDUCED SUBGRAPHS
PROPER CIRCULAR-ARC GRAPHS
ROUND GRAPHS
title_short Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_full Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_fullStr Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_full_unstemmed Fully Dynamic Recognition of Proper Circular-Arc Graphs
title_sort Fully Dynamic Recognition of Proper Circular-Arc Graphs
dc.creator.none.fl_str_mv Soulignac, Francisco Juan
author Soulignac, Francisco Juan
author_facet Soulignac, Francisco Juan
author_role author
dc.subject.none.fl_str_mv CO-CONNECTIVITY
DYNAMIC RECOGNITION
MINIMAL FORBIDDEN INDUCED SUBGRAPHS
PROPER CIRCULAR-ARC GRAPHS
ROUND GRAPHS
topic CO-CONNECTIVITY
DYNAMIC RECOGNITION
MINIMAL FORBIDDEN INDUCED SUBGRAPHS
PROPER CIRCULAR-ARC GRAPHS
ROUND GRAPHS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the graph, while vertex operations cost O(logn+d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(logn) time per operation are obtained. Also, an O(Δ) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where Δ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time. As an application, we show how to find a minimal forbidden induced subgraph of a static graph in O(n+m) time.
Fil: Soulignac, Francisco Juan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
description We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(logn) time, where n is the number of vertices of the graph, while vertex operations cost O(logn+d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in O(logn) time per operation are obtained. Also, an O(Δ) time algorithm for determining if a PCA representation corresponds to a co-bipartite graph is provided, where Δ is the maximum among the degrees of the vertices. When the graph is co-bipartite, a co-bipartition of each of its co-components is obtained within the same amount of time. As an application, we show how to find a minimal forbidden induced subgraph of a static graph in O(n+m) time.
publishDate 2015
dc.date.none.fl_str_mv 2015-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/98528
Soulignac, Francisco Juan; Fully Dynamic Recognition of Proper Circular-Arc Graphs; Springer; Algorithmica; 71; 4; 4-2015; 904-968
0178-4617
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98528
identifier_str_mv Soulignac, Francisco Juan; Fully Dynamic Recognition of Proper Circular-Arc Graphs; Springer; Algorithmica; 71; 4; 4-2015; 904-968
0178-4617
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00453-013-9835-7
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00453-013-9835-7
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1111.3548
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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