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A precise characterization of the subcube allocation problem and a general methodology to solve it are presented. Subcube allocation and coalescing algorithms that have the goal of minimizing fragmentation are developed. The concept of a maximal set of subcubes (MSS), which is useful in making allocations that result in a tightly packed hypercube, is introduced. The problems of allocating subcubes and of forming an MSS are formulated as decision problems and shown to be NP-hard. It is proved analytically that the buddy strategy is optimal under restricted conditions, and it is shown using simulation that its performance is actually poor under more realistic conditions. A heuristic procedure for efficiently coalescing a released cube with the existing free cubes is suggested. This coalescing approach is coupled with a simple best-fit allocation scheme to form the basis of a class of MSS-based strategies that give a substantial performance (hit ratio) improvement over the buddy strategy. Simulation results comparing several different allocation and coalescing strategies, which show that the MSS-based schemes provide a marked performance improvement over previous techniques, are presented.