On parallel versus sequential approximation

In this paper we deal with the class NCX of NP Optimization problems that are approximable within constant ratio in NC. This class is the parallel counterpart of the class APX. Our main motivation here is to reduce the study of sequential and parallel approximability to the same framework. To this a...

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Detalles Bibliográficos
Autores: Serna Iglesias, María José|||0000-0001-9729-8648, Xhafa Xhafa, Fatos|||0000-0001-6569-5497
Tipo de recurso: informe técnico
Fecha de publicación:1995
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/96432
Acceso en línea:https://hdl.handle.net/2117/96432
Access Level:acceso abierto
Palabra clave:Parallel approximation
Sequential approximation
Optimization problems
Àrees temàtiques de la UPC::Informàtica
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spelling On parallel versus sequential approximationSerna Iglesias, María José|||0000-0001-9729-8648Xhafa Xhafa, Fatos|||0000-0001-6569-5497Parallel approximationSequential approximationOptimization problemsÀrees temàtiques de la UPC::InformàticaIn this paper we deal with the class NCX of NP Optimization problems that are approximable within constant ratio in NC. This class is the parallel counterpart of the class APX. Our main motivation here is to reduce the study of sequential and parallel approximability to the same framework. To this aim, we first introduce a new kind of NC-reduction that preserves the relative error of the approximate solutions and show that the class NCX has {em complete} problems under this reducibility. An important subset of NCX is the class MAXSNP, we show that MAXSNP-complete problems have a threshold on the parallel approximation ratio that is, there are positive constants $epsilon_1$, $epsilon_2$ such that although the problem can be approximated in P within $epsilon_1$ it cannot be approximated in NC within epsilon_2$, unless P=NC. This result is attained by showing that the problem of approximating the value obtained through a non-oblivious local search algorithm is P-complete, for some values of the approximation ratio. Finally, we show that approximating through non-oblivious local search is in average NC.19951995-03-0120162016-11-09reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/96432reponame: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:2117/964322026-05-27T15:37:01Z
dc.title.none.fl_str_mv On parallel versus sequential approximation
title On parallel versus sequential approximation
spellingShingle On parallel versus sequential approximation
Serna Iglesias, María José|||0000-0001-9729-8648
Parallel approximation
Sequential approximation
Optimization problems
Àrees temàtiques de la UPC::Informàtica
title_short On parallel versus sequential approximation
title_full On parallel versus sequential approximation
title_fullStr On parallel versus sequential approximation
title_full_unstemmed On parallel versus sequential approximation
title_sort On parallel versus sequential approximation
dc.creator.none.fl_str_mv Serna Iglesias, María José|||0000-0001-9729-8648
Xhafa Xhafa, Fatos|||0000-0001-6569-5497
author Serna Iglesias, María José|||0000-0001-9729-8648
author_facet Serna Iglesias, María José|||0000-0001-9729-8648
Xhafa Xhafa, Fatos|||0000-0001-6569-5497
author_role author
author2 Xhafa Xhafa, Fatos|||0000-0001-6569-5497
author2_role author
dc.subject.none.fl_str_mv Parallel approximation
Sequential approximation
Optimization problems
Àrees temàtiques de la UPC::Informàtica
topic Parallel approximation
Sequential approximation
Optimization problems
Àrees temàtiques de la UPC::Informàtica
description In this paper we deal with the class NCX of NP Optimization problems that are approximable within constant ratio in NC. This class is the parallel counterpart of the class APX. Our main motivation here is to reduce the study of sequential and parallel approximability to the same framework. To this aim, we first introduce a new kind of NC-reduction that preserves the relative error of the approximate solutions and show that the class NCX has {em complete} problems under this reducibility. An important subset of NCX is the class MAXSNP, we show that MAXSNP-complete problems have a threshold on the parallel approximation ratio that is, there are positive constants $epsilon_1$, $epsilon_2$ such that although the problem can be approximated in P within $epsilon_1$ it cannot be approximated in NC within epsilon_2$, unless P=NC. This result is attained by showing that the problem of approximating the value obtained through a non-oblivious local search algorithm is P-complete, for some values of the approximation ratio. Finally, we show that approximating through non-oblivious local search is in average NC.
publishDate 1995
dc.date.none.fl_str_mv 1995
1995-03-01
2016
2016-11-09
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/2117/96432
url https://hdl.handle.net/2117/96432
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/pdf
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
repository.mail.fl_str_mv
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score 15,301603

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