Optimal Bin Packing with Items of Random Sizes

Abstract

Consider a probability μ on [0, 1] and i.i.d. random variables X1, X2, …, Xn distributed like μ. Let Qn denote the optimal (minimum) number of unit size bins needed to pack items of size X1, X2, …, Xn. We characterize the class of μ which have the property that limn→∞ Qn/n = E(X1) a.s., or equivalently that the expected level of occupancy of bins converges to one.