Improved Results for a Memory Allocation Problem

Abstract

We consider a memory allocation problem. This problem can be modeled as a version of bin packing where items may be split, but each bin may contain at most two (parts of) items. This problem was recently introduced by Chung et al. (Theory Comput. Syst. 39(6):829–849, 2006). We give a simple $\frac{3}{2}$ -approximation algorithm for this problem which is in fact an online algorithm. This algorithm also has good performance for the more general case where each bin may contain at most k parts of items. We show that this general case is strongly NP-hard for any k≥3. Additionally, we design an efficient approximation algorithm, for which the approximation ratio can be made arbitrarily close to $\frac{7}{5}$ .