Online bin packing with cardinality constraints resolved

János Balogh, József Békési, G. Dósa, Leah Epstein, Asaf Levin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

Cardinality constrained bin packing or bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k ≥ 2, items having sizes in (0, 1] associated with them are presented one by one to be packed into unit capacity bins, such that the capacities of bins are not exceeded, and no bin receives more than k items. We resolve the online problem in the sense that we prove a lower bound of 2 on the overall asymptotic competitive ratio. This closes the long standing open problem of finding the value of the best possible overall asymptotic competitive ratio, since an algorithm of an absolute competitive ratio 2 for any fixed value of k is known. Additionally, we significantly improve the known lower bounds on the asymptotic competitive ratio for every specific value of k. The novelty of our constructions is based on full adaptivity that creates large gaps between item sizes. Thus, our lower bound inputs do not follow the common practice for online bin packing problems of having a known in advance input consisting of batches for which the algorithm needs to be competitive on every prefix of the input. Last, we show a lower bound strictly larger than 2 on the asymptotic competitive ratio of the online 2-dimensional vector packing problem, and thus provide for the first time a lower bound larger than 2 on the asymptotic competitive ratio for the vector packing problem in any fixed dimension.

Original languageEnglish
Title of host publication25th European Symposium on Algorithms, ESA 2017
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume87
ISBN (Electronic)9783959770491
DOIs
Publication statusPublished - Sep 1 2017
Event25th European Symposium on Algorithms, ESA 2017 - Vienna, Austria
Duration: Sep 4 2017Sep 6 2017

Other

Other25th European Symposium on Algorithms, ESA 2017
CountryAustria
CityVienna
Period9/4/179/6/17

Keywords

  • Bin packing
  • Cardinality constraints
  • Lower bounds
  • Online algorithms

ASJC Scopus subject areas

  • Software

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    Balogh, J., Békési, J., Dósa, G., Epstein, L., & Levin, A. (2017). Online bin packing with cardinality constraints resolved. In 25th European Symposium on Algorithms, ESA 2017 (Vol. 87). [10] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2017.10