An on-line algorithm for multidimensional bin packing

  • Authors:

  • János Csirik;André Van Vliet

  • Affiliations:

  • Department of Applied Computer Science, József Attila University, P.O. Box 652, H-6701 Szeged, Hungary;Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

  • Venue:
  • Operations Research Letters
  • Year:
  • 1993

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Abstract

In this paper we present an on-line algorithm for the d-dimensional bin packing problem. We use the idea of rounding up the size of an item to a size that can be packed efficiently. Although our algorithm is not a generalization of the 1-dimensional HARMONIC"M algorithm [6], we can use its worst case analysis to prove that our algorithm yields an asymptotic worst case ratio of (1.691 ...)^d. Further, we show that for uniformly distributed items the algorithm has an expected asymptotic efficiency of (2(16@p^2 - 1))^d.