Algorithms for on-line bin-packing problems with cardinality constraints

  • Authors:

  • Luitpold Babel;Bo Chen;Hans Kellerer;Vladimir Kotov

  • Affiliations:

  • EADS Germany, Landshuterstraße 26, D-5705, Unterschleißheim, Germany;Warwick Business School, University of Warwick, Coventry CV4 7AL, UK;Institut für Statistik und Operations Research, Universität Graz, Universitaetstrasse 15, Graz A-8010, Austria;Faculty of Applied Mathematics and Computer Science, University of Minsk, Minsk 220080, Byelorussia

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2004

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Abstract

The bin-packing problem asks for a packing of a list of items of sizes from (0,1] into the smallest possible number of bins having unit capacity. The k-item bin-packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two efficient on-line algorithms for this problem. We show that, for increasing values of k, the bound on the asymptotic worst-case performance ratio of the first algorithm tends towards 2 and that the second algorithm has a ratio of 2. Both algorithms considerably improve upon the best known result of an algorithm, which has an asymptotic bound of 2.7 on its ratio. Moreover, we improve known bounds for all values of k by presenting on-line algorithms for k = 2 and 3 with bounds on their ratios close to optimal.