On Line Bin Packing with Items of Random Size

Consider an i.i.d. sequence of random variables X1, ', Xn distributed according to a given distribution µ on [0, 1]. Let cµ be the asymptotic optimal packing ratio, i.e., cµ = 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 ncµ + On1/2log n3/4 bins.