Bounds for online bin packing with cardinality constraints

Abstract We study a bin packing problem in which a bin can contain at most k items of total size at most 1, where k ≥ 2 is a given parameter. Items are presented one by one in an online fashion. We analyze the best absolute competitive ratio of the problem and prove tight bounds of 2 for any k ≥ 4 ....

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Bibliographic Details
Main Authors: Békési József
Dósa György
Epstein Leah
Format: Article
Published: 2016
Series:INFORMATION AND COMPUTATION 249
Subjects:
doi:10.1016/j.ic.2016.06.001

mtmt:3076541
Online Access:http://publicatio.bibl.u-szeged.hu/28450
Description
Summary:Abstract We study a bin packing problem in which a bin can contain at most k items of total size at most 1, where k ≥ 2 is a given parameter. Items are presented one by one in an online fashion. We analyze the best absolute competitive ratio of the problem and prove tight bounds of 2 for any k ≥ 4 . Additionally, we present bounds for relatively small values of k with respect to the asymptotic competitive ratio and the absolute competitive ratio. In particular, we provide tight bounds on the absolute competitive ratio of First Fit for k = 2 , 3 , 4 , and improve the known lower bounds on asymptotic competitive ratios for multiple values of k. Our method for obtaining a lower bound on the asymptotic competitive ratio using a certain type of an input is general, and we also use it to obtain an alternative proof of the known lower bound on the asymptotic competitive ratio of standard online bin packing.
Physical Description:190-204
ISSN:0890-5401