Online bin packing: Old algorithms and new results

Kód výsledku v IS VaVaI

RIV/00216208:11320/14:10286486 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1007/978-3-319-08019-2_38

DOI - Digital Object Identifier

10.1007/978-3-319-08019-2_38

Jazyk výsledku

angličtina

Název v původním jazyce

Online bin packing: Old algorithms and new results

Popis výsledku v původním jazyce

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} algorithmsare 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 $lfloor1.7cdotmbox{sc OPT}rfloor$ 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

Název v anglickém jazyce

Online bin packing: Old algorithms and new results

Popis výsledku anglicky

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} algorithmsare 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 $lfloor1.7cdotmbox{sc OPT}rfloor$ 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

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

10th Conference on Computability in Europe (CiE)

ISBN

978-3-319-08018-5

ISSN

0302-9743

e-ISSN

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Počet stran výsledku

11

Strana od-do

362-372

Název nakladatele

Springer

Místo vydání

Berlin

Místo konání akce

Budapest, Hungary

Datum konání akce

23. 6. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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