Competitive multi-dimensional dynamic bin packing via l-shape bin packing

  • Authors:

  • Prudence W. H. Wong;Fencol C. C. Yung

  • Affiliations:

  • Department of Computer Science, University of Liverpool, UK;Department of Computer Science, University of Liverpool, UK

  • Venue:
  • WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
  • Year:
  • 2009

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Abstract

We study d-dimensional dynamic bin packing for general d-dimensional boxes, for d≥2. This problem is a generalization of the bin packing problem in which items may arrive and depart dynamically. Our main result is a 3d-competitive online algorithm. We further study the 2- and 3-dimensional problem closely and improve the competitive ratios. Technically speaking, our d-dimensional result is due to a space efficient offline single bin packing algorithm, which is a variant of d-dimensional NFDH. We introduce an interesting notion of d-dimensional L-shape bin and show that effective offline packing into L-shape bin leads to effective online dynamic packing into unit-sized bins. We also investigate the resource augmentation version of the problem where the online algorithm can use d-dimensional bins of size s1 ×s2 ×⋯×sd for si≥1 while the optimal offline algorithm uses unit-sized bins. We give conditions for the online algorithm to match the performance of the optimal offline algorithm, i.e., 1-competitive.