An optimal online algorithm for bounded space variable-sized bin packing

Abstract

An online algorithm for variable-sized bin packing, based on the HARMONIC algorithm of Lee and Lee [11], is investigated. This algorithm is based on one proposed by Csirik [4]. It is shown that the algorithm is optimal among those which use bounded space. An interesting feature of the analysis is that, although it is shown that our algorithm achieves a performance ratio arbitrarily close to the optimum value, it is not known precisely what that value is. The case where bins of capacity 1 and α ∈ (0, 1) are used is studied in greater detail. It is shown that among algorithms which are allowed to chose α, the optimal performance ratio lies in [1.37530, 1.37532].