Truly asymptotic lower bounds for online vector bin packing

János Balogh, Ilan Reuven Cohen, Leah Epstein, Asaf Levin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this work, we consider online d-dimensional vector bin packing. It is known that no algorithm can have a competitive ratio of o(d/log2 d) in the absolute sense, although upper bounds for this problem have always been presented in the asymptotic sense. Since variants of bin packing are traditionally studied with respect to the asymptotic measure, and since the two measures are different, we focus on the asymptotic measure and prove new lower bounds of the asymptotic competitive ratio. The existing lower bounds prior to this work were known to be smaller than 3, even for very large d. Here, we significantly improved on the best known lower bounds of the asymptotic competitive ratio (and as a byproduct, on the absolute competitive ratio) for online vector packing of vectors with d ≥ 3 dimensions, for every dimension d. To obtain these results, we use several different constructions, one of which is an adaptive construction with a lower bound of Ω(d). Our main result is that the lower bound of Ω(d/log2 d) on the competitive ratio holds also in the asymptotic sense. This result holds also against randomized algorithms, and requires a careful adaptation of constructions for online coloring, rather than simple black-box reductions.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021
EditorsMary Wootters, Laura Sanita
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772075
DOIs
StatePublished - 1 Sep 2021
Event24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021 - Virtual, Seattle, United States
Duration: 16 Aug 202118 Aug 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume207
ISSN (Print)1868-8969

Conference

Conference24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021
Country/TerritoryUnited States
CityVirtual, Seattle
Period16/08/2118/08/21

Bibliographical note

Publisher Copyright:
© János Balogh, Ilan Reuven Cohen, Leah Epstein, and Asaf Levin; licensed under Creative Commons License CC-BY 4.0

Keywords

  • Approximation algorithms
  • Bin packing
  • Online algorithms
  • Vector packing

ASJC Scopus subject areas

  • Software

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