Some distributions that allow perfect packing

Authors:
Wansoo T. Rhee;Michel Talagrand
Affiliations:
Ohio State Univ., Columbus;Univ. of Paris VI, Paris, France
Venue:
Journal of the ACM (JACM)
Year:
1988

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Abstract

A probability distribution &mgr; on [0, 1] allows perfect packing if n items of size X1, … , Xn, independent and identically distributed according to &mgr; can be packed in unit size bins in such a way that the expected wasted space is o(n). A large class of distributions that allow perfect packing is exhibited. As a corollary, the intervals [a, b] for which the uniform distribution on [a, b] allows perfect packing are determined.