2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2000)

Redondo Beach, California

Nov. 12, 2000 to Nov. 14, 2000

ISSN: 0272-5428

ISBN: 0-7695-0850-2

pp: 582

M. Mitzenmacher , Paris-Sud Univ., France

C. Kenyon , Paris-Sud Univ., France

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=/spl alpha/k and 0.66/spl les//spl alpha/>2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0,a], for 0.66/spl les/a>2/3. This implies that the expected asymptotic performance ratio of best-fit bin packing is strictly greater than 1 for these distributions.

INDEX TERMS

bin packing; probability; performance index; linear waste; best-fit bin packing; discrete distribution; continuous skewed distributions; asymptotic performance ratio

CITATION

M. Mitzenmacher,
C. Kenyon,
"Linear waste of best fit bin packing on skewed distributions",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 582, 2000, doi:10.1109/SFCS.2000.892326