Linear waste of best fit bin packing on skewed distributions

Authors:
Claire Kenyon;Michael Mitzenmacher
Affiliations:
Université Paris-Sud, Paris, France;Harvard University, Cambridge, MA
Venue:
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Year:
2002

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Abstract

We prove that Best Fit bin packing has linear waste on the discrete distribution U{j, k} (where items are drawn uniformly from the set {1/k,2/k ..... j/k}) for sufficiently large k when j = αk and 0.66 ≥ α 2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0, a], for 0.66 ≥ a 2/3. This implies that the expected asymptotic performance ratio of Best Fit is strictly greater than 1 for these distributions.