Tight bounds for online vector bin packing

Yossi Azar, Ilan Cohen, Seny Kamara, Bruce Shepherd

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

43 Scopus citations


In the d-dimensional bin packing problem (VBP), one is given vectors x 1, x2,..., xn 2 Rd and the goal is to find a partition into a minimum number of feasible sets: {1, 2 :..., n} = ∪s i Bi. A set Bi is feasible if jεBi xj ≤ 1, where 1 denotes the all 1's vector. For online VBP, it has been outstanding for almost 20 years to clarify the gap between the best lower bound Ω(1) on the competitive ratio versus the best upper bound of O(d). We settle this by describing a (d1-ε) lower bound. We also give strong lower bounds (of Ω(d 1/B-ε) ) if the bin size B Z+ is allowed to grow. Finally, we discuss almost-matching upper bound results for general values of B; we show an upper bound whose exponent is additively shifted by 1" from the lower bound exponent.

Original languageEnglish
Title of host publicationSTOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing
Number of pages10
StatePublished - 2013
Externally publishedYes
Event45th Annual ACM Symposium on Theory of Computing, STOC 2013 - Palo Alto, CA, United States
Duration: 1 Jun 20134 Jun 2013

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference45th Annual ACM Symposium on Theory of Computing, STOC 2013
Country/TerritoryUnited States
CityPalo Alto, CA


  • Bin packing
  • Competitive ratio
  • Graph-colouring
  • Lower bounds
  • Online algorithms
  • Vector packing


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