Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs

The (k,r)-center problem} asks whether an input graph G has atr most k vertices (called centers) such that every vertex of $ is within distance at most r from some center. In this paper we prove that the (k,r)-center problem, parameterized by k and r, is fixed-parameter tractable (FPT) on planar gra...

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Authors: Demaine, Erik D., Fomin, Fedor V., Hajiaghayi, Mohammad Taghi, Thilikos Touloupas, Dimitrios
Format: report
Publication Date:2003
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/96917
Online Access:https://hdl.handle.net/2117/96917
Access Level:Open access
Keyword:Planar graphs
Map graphs
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphsDemaine, Erik D.Fomin, Fedor V.Hajiaghayi, Mohammad TaghiThilikos Touloupas, DimitriosPlanar graphsMap graphsÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaThe (k,r)-center problem} asks whether an input graph G has atr most k vertices (called centers) such that every vertex of $ is within distance at most r from some center. In this paper we prove that the (k,r)-center problem, parameterized by k and r, is fixed-parameter tractable (FPT) on planar graphs, i.e., it admits an algorithm of complexity f(k,r) n^{O(1)} where the function f is independent of n. In particular, we show that f(k,r)=2^{O(rlog r) sqrt{k}}, where the exponent of the exponential term grows sublinearly in the number of centers. Moreover, we prove that the same type of FPT algorithms can be designed for the more general class of map graphs introduced by Chen, Grigni, and Papadimitriou. Our results combine dynamic-programming algorithms for graphs of small branchwidth and a graph-theoretic result bounding this parameter in terms of k and r. Finally, a byproduct of our algorithm is the existence of a PTAS for the r-domination problem in both planar graphs and map graphs. Our approach builds on the seminal results of Robertson and Seymour on Graph Minors, and as a result is much more powerful than the previous machinery of Alber et al. for exponential speedup on planar graphs. To demonstrate the versatility of our results, we show how our algorithms can be extended to general parameters that are20032003-09-0120162016-11-21reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/postscripthttps://hdl.handle.net/2117/96917reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/969172026-05-27T15:37:01Z
dc.title.none.fl_str_mv Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
title Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
spellingShingle Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
Demaine, Erik D.
Planar graphs
Map graphs
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
title_full Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
title_fullStr Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
title_full_unstemmed Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
title_sort Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs
dc.creator.none.fl_str_mv Demaine, Erik D.
Fomin, Fedor V.
Hajiaghayi, Mohammad Taghi
Thilikos Touloupas, Dimitrios
author Demaine, Erik D.
author_facet Demaine, Erik D.
Fomin, Fedor V.
Hajiaghayi, Mohammad Taghi
Thilikos Touloupas, Dimitrios
author_role author
author2 Fomin, Fedor V.
Hajiaghayi, Mohammad Taghi
Thilikos Touloupas, Dimitrios
author2_role author
author
author
dc.subject.none.fl_str_mv Planar graphs
Map graphs
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Planar graphs
Map graphs
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description The (k,r)-center problem} asks whether an input graph G has atr most k vertices (called centers) such that every vertex of $ is within distance at most r from some center. In this paper we prove that the (k,r)-center problem, parameterized by k and r, is fixed-parameter tractable (FPT) on planar graphs, i.e., it admits an algorithm of complexity f(k,r) n^{O(1)} where the function f is independent of n. In particular, we show that f(k,r)=2^{O(rlog r) sqrt{k}}, where the exponent of the exponential term grows sublinearly in the number of centers. Moreover, we prove that the same type of FPT algorithms can be designed for the more general class of map graphs introduced by Chen, Grigni, and Papadimitriou. Our results combine dynamic-programming algorithms for graphs of small branchwidth and a graph-theoretic result bounding this parameter in terms of k and r. Finally, a byproduct of our algorithm is the existence of a PTAS for the r-domination problem in both planar graphs and map graphs. Our approach builds on the seminal results of Robertson and Seymour on Graph Minors, and as a result is much more powerful than the previous machinery of Alber et al. for exponential speedup on planar graphs. To demonstrate the versatility of our results, we show how our algorithms can be extended to general parameters that are
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-09-01
2016
2016-11-21
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/96917
url https://hdl.handle.net/2117/96917
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/postscript
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
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