Tight bounds for clairvoyant dynamic bin packing

Yossi Azar, Danny Vainstein

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

Abstract

In this paper we focus on the Clairvoyant Dynamic Bin Packing (DBP) problem, which extends the classical online bin packing problem in that items arrive and depart over time and the departure time of an item is known upon its arrival. The problem naturally arises when handling cloud-based networks. We focus specifically on the MinUsageTime cost function which aims to minimize the overall usage time of all bins that are opened during the packing process. Earlierwork has shown a O( log μ/log log μ) upper bound where μ is defined as the ratio between the maximal and minimal durations of all items. We improve the upper bound by giving an O( p log μ)- competitive algorithm. We then provide a matching lower bound of Ω( √log μ) on the competitive ratio of any online algorithm, thus closing the gap with regards to this problem. We then focus on what we call the class of aligned inputs and give a O(log log μ)- competitive algorithm for this case, beating the lower bound of the general case by an exponential factor. Surprisingly enough, the analysis of our algorithm that we present, is closely related to various properties of binary strings.

Original languageEnglish
Title of host publicationSPAA 2017 - Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages77-86
Number of pages10
ISBN (Electronic)9781450345934
DOIs
StatePublished - 24 Jul 2017
Event29th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2017 - Washington, United States
Duration: 24 Jul 201726 Jul 2017

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures
VolumePart F129316

Conference

Conference29th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2017
Country/TerritoryUnited States
CityWashington
Period24/07/1726/07/17

Keywords

  • Analysis of algorithms
  • Clairvoyant Setting
  • Competitive ratio
  • Dynamic bin packing
  • Online algorithms

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