Optimal online algorithms for multidimensional packing problems

Leah Epstein, Rob Van Stee

Research output: Contribution to journalArticlepeer-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 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. Furthermore, we extend the techniques used in these algorithms to give optimal algorithms for online bounded space variable-sized packing and resource augmented packing.

Original languageEnglish
Pages (from-to)431-448
Number of pages18
JournalSIAM Journal on Computing
Issue number2
StatePublished - 2006


  • Multidimensional bin packing
  • Online algorithms
  • Optimal algorithms

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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