A Stochastic Analysis of the NFD Bin-Packing Algorithm

Abstract We consider the Next-Fit-Decreasing (NFD) algorithm for the one-dimensional bin packing problem. The input consists of n pieces of i.i.d. sizes. Bounds on the first two moments of the number of bins used in the packing are established for arbitrary size distributions. These bounds are asymptotically tight. For the uniform distribution we also exhibit numerical results and examine their dependence on the support of the size distribution.