Multidimensional optimal bin packing with items of random size

Consider a probability measure μ on [0,1]^d, and independent random variables &bmacr;X1,...,&bmacr;Xn distributed according to μ. Let Vn=Vn(&bmacr;X1,...,&bmacr;Xn) (resp. Rn=R(&bmacr;X1,...,&bmacr;Xn)) be the minimal number of unit size d-dimensional bins needed to pack itesm of size &bmacr;X1,...,&bmacr;Xn in the vector packing (resp. rectangular packing) problem. For a large class of distributions μ, we characterize v(μ)=limnÅ⇒Å•Vn/n and r(μ)=limnÅ⇒Å•Rn/n.