On the online bin packing problem

Abstract

A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach [3,5, 8,10,11,12]. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889. It is also shown that the analysis of Harmonic+1 presented in [11] is incorrect; this is a fundamental logical flaw, not an error in calculation or an omitted case. The asymptotic performance ratio of Harmonic+1 is at least 1.59217. Thus Harmonic++ provides the best upper bound for the online bin packing problem to date. © 2011 Springer-Verlag Berlin Heidelberg.