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Consider an i.i.d. sequence of random variables X1, …, Xn distributed according to a given distribution μ on [0, 1]. Let c(μ) be the asymptotic optimal packing ratio, i.e., c(μ) = limn→∞ETn/n, where Tn is the minimum number of unit size bins needed to pack X1, …, Xn. We prove the existence of an on line algorithm, dependent on μ, that packs X1, …, Xn in nc(μ) + O(n1/2(log n)3/4) bins.
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Rhee et al. (1993) studied this question.
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