Dual bin packing with items of random sizes |
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Authors: | WanSoo T Rhee Michel Talagrand |
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Institution: | (1) Faculty of Management Science, The Ohio State University, 43210 Columbus, OH, USA;(2) Equipe d'Analyse, U.A. au C.N.R.S., University of Paris VI, 75230 Paris 05, France;(3) Department of Mathematics, The Ohio State University, 43210 Columbus, OH, USA |
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Abstract: | Given a collection of items and a number of unit size bins, the dual bin packing problem requires finding the largest number of items that can be packed in these bins. In our stochastic model, the item sizesX
1, ,X
n
are independent identically distributed according to a given probability measure . Denote byN
n
=N
n
(X
1, ,X
n
) the largest number of these items that can be packed in an bins, where 0<a<1 is a constant. We show thatb = lim
n![rarr](/content/r158619232754517/xxlarge8594.gif)
E(N
n
)/n exists, and that the random variable (N
n
–nb)/
converges in distribution. The limit is identified as the distribution of the supremum of a certain Gaussian process cannonically attached to .
This research is in part supported by NSF grant CCR-8801517 and CCR-9000611.This research is in part supported by NSF grant DMS-8801180. |
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Keywords: | Dual bin packing Gaussian process probability |
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