Multidimensional Optimal Bin Packing with Items of Random Size

Consider a probability measure µ on [0, 1]d, and independent random variables X⃗1, ', X⃗n distributed according to µ. Let Vn = VnX⃗1, ', X⃗n resp. Rn = RnX⃗1, ', X⃗n be the minimal number of unit size d-dimensional bins needed to pack items of size X⃗1, ', X⃗n in the vector packing resp. rectangular packing problem. For a large class of distributions µ, we characterize vµ = limn→∞Vn/n and rµ = limn→∞Rn/n.