Fully Dynamic Recognition of Proper Circular-Arc Graphs

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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 gra...

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Autor principal: Soulignac, F.J.
Formato: JOUR
Materias:
Co-connectivity
Dynamic recognition
Minimal forbidden induced subgraphs
Proper circular-arc graphs
Round graphs
Algorithms
Graphic methods
Connectivity algorithms
Decremental algorithms
Forbidden induced subgraphs
Fully dynamic algorithms
Induced subgraphs
Graph theory
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01784617_v71_n4_p904_Soulignac
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01784617_v71_n4_p904_Soulignac
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spelling todo:paper_01784617_v71_n4_p904_Soulignac2023-10-03T15:08:18Z Fully Dynamic Recognition of Proper Circular-Arc Graphs Soulignac, F.J. Co-connectivity Dynamic recognition Minimal forbidden induced subgraphs Proper circular-arc graphs Round graphs Algorithms Graphic methods Connectivity algorithms Decremental algorithms Dynamic recognition Forbidden induced subgraphs Fully dynamic algorithms Induced subgraphs Proper circular-arc graphs Round graphs Graph theory 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. © 2013, Springer Science+Business Media New York. Fil:Soulignac, F.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01784617_v71_n4_p904_Soulignac
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Co-connectivity
Dynamic recognition
Minimal forbidden induced subgraphs
Proper circular-arc graphs
Round graphs
Algorithms
Graphic methods
Connectivity algorithms
Decremental algorithms
Dynamic recognition
Forbidden induced subgraphs
Fully dynamic algorithms
Induced subgraphs
Proper circular-arc graphs
Round graphs
Graph theory
spellingShingle Co-connectivity
Dynamic recognition
Minimal forbidden induced subgraphs
Proper circular-arc graphs
Round graphs
Algorithms
Graphic methods
Connectivity algorithms
Decremental algorithms
Dynamic recognition
Forbidden induced subgraphs
Fully dynamic algorithms
Induced subgraphs
Proper circular-arc graphs
Round graphs
Graph theory
Soulignac, F.J.
Fully Dynamic Recognition of Proper Circular-Arc Graphs
topic_facet Co-connectivity
Dynamic recognition
Minimal forbidden induced subgraphs
Proper circular-arc graphs
Round graphs
Algorithms
Graphic methods
Connectivity algorithms
Decremental algorithms
Dynamic recognition
Forbidden induced subgraphs
Fully dynamic algorithms
Induced subgraphs
Proper circular-arc graphs
Round graphs
Graph theory
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. © 2013, Springer Science+Business Media New York.
format JOUR
author Soulignac, F.J.
author_facet Soulignac, F.J.
author_sort Soulignac, F.J.
title Fully Dynamic Recognition of Proper Circular-Arc 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
url http://hdl.handle.net/20.500.12110/paper_01784617_v71_n4_p904_Soulignac
work_keys_str_mv AT soulignacfj fullydynamicrecognitionofpropercirculararcgraphs
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