About: Online bin packing: Old algorithms and new results

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In the bin packing problem we are given an instance consisting of a sequence of items with sizes between $0$ and $1$. The objective is to pack these items into the smallest possible number of bins of unit size. {\sc FirstFit} and {\sc BestFit} algorithms are simple online algorithms introduced in early seventies, when it was also shown that their asymptotic approximation ratio is equal to $1.7$. We present a simple proof of this bound and survey recent developments that lead to the proof that also the absolute approximation ratio of these algorithms is exactly $1.7$. More precisely, if the optimum needs $\OPT$ bins, the algorithms use at most $\lfloor1.7\cdot\mbox{\sc OPT}\rfloor$ bins and for each value of $\OPT$, there are instances that actually need so many bins. We also discuss bounded-space bin packing, where the online algorithm is allowed to keep only a fixed number of bins open for future items. In this model, a variant of {\sc BestFit} also has asymptotic approximation ratio $1.7$, although it is possible that the bound is significantly smaller if also the offline solution is required to satisfy the bounded-space restriction. In the bin packing problem we are given an instance consisting of a sequence of items with sizes between $0$ and $1$. The objective is to pack these items into the smallest possible number of bins of unit size. {\sc FirstFit} and {\sc BestFit} algorithms are simple online algorithms introduced in early seventies, when it was also shown that their asymptotic approximation ratio is equal to $1.7$. We present a simple proof of this bound and survey recent developments that lead to the proof that also the absolute approximation ratio of these algorithms is exactly $1.7$. More precisely, if the optimum needs $\OPT$ bins, the algorithms use at most $\lfloor1.7\cdot\mbox{\sc OPT}\rfloor$ bins and for each value of $\OPT$, there are instances that actually need so many bins. We also discuss bounded-space bin packing, where the online algorithm is allowed to keep only a fixed number of bins open for future items. In this model, a variant of {\sc BestFit} also has asymptotic approximation ratio $1.7$, although it is possible that the bound is significantly smaller if also the offline solution is required to satisfy the bounded-space restriction. (en)
Title	Online bin packing: Old algorithms and new results Online bin packing: Old algorithms and new results (en)
skos:prefLabel	Online bin packing: Old algorithms and new results Online bin packing: Old algorithms and new results (en)
skos:notation	RIV/00216208:11320/14:10286486!RIV15-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GBP202/12/G061)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Sgall, Jiří
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	34586
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10286486
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	bin packing; approximation algorithms (en)
http://linked.open.../riv/klicoveSlovo	approximation algorithms bin packing
http://linked.open...ontrolniKodProRIV	[89000C77E133]
http://linked.open...v/mistoKonaniAkce	Budapest, Hungary
http://linked.open...i/riv/mistoVydani	Berlin
http://linked.open...i/riv/nazevZdroje	10th Conference on Computability in Europe (CiE)
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Center of excellence - Institute for theoretical computer science (CE-ITI)
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Sgall, Jiří
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2014-06-23 (xsd:date)
issn	0302-9743
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-319-08019-2_38
http://purl.org/ne...btex#hasPublisher	Springer-Verlag
https://schema.org/isbn	978-3-319-08018-5
http://localhost/t...ganizacniJednotka	11320

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