Optimal Online Bounded Space Multidimensional Packing

Leah Epstein, Rob Van Stee

Research output: Contribution to conferencePaperpeer-review


We solve an open problem in the literature by providing an online algorithm for multidimensional bin packing that uses only bounded space. To achieve this, we introduce a new technique for classifying the items to be packed. We show that our algorithm is optimal among bounded space algorithms for any dimension d > 1. Its asymptotic performance ratio is (∏∞d) d, where ∏ ≈1.691 is the asymptotic performance ratio of the one-dimensional algorithm HARMONIC. A modified version of this algorithm for the case where all items are hypercubes is also shown to be optimal. Its asymptotic performance ratio is sublinear in d. Additionally, for the special case of packing squares in two-dimensional bins, we present a new unbounded space online algorithm with asymptotic performance ratio of at most 2.271. We also present an approximation algorithm for the offline problem with approximation ratio of 16/11.

Original languageEnglish
Number of pages10
StatePublished - 2004
Externally publishedYes
EventProceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States
Duration: 11 Jan 200413 Jan 2004


ConferenceProceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityNew Orleans, LA.

ASJC Scopus subject areas

  • Software
  • General Mathematics


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