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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.~\cite{ChGrVM06}. We give a simple $\frac 32$-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 $k \geq 3$. Additionally, we design an efficient approximation algorithm, for which the approximation ratio can be made arbitrarily close to $\frac 75$.