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For a distributed database system to function efficiently, the fragments of the database need to be located, judiciously at various sites across the relevant communications network. The problem of allocating these fragments to the most appropriate sites is a difficult one to solve, however, with most approaches available relying on heuristic techniques. Optimal approaches are usually based on mathematical programming, and formulations available for this problem are based on the linearization of nonlinear binary integer programs and have been observed to be ineffective except on very small problems. This paper presents new integer programming formulations for the nonredundant version of the fragment allocation problem. This formulation is extended to address problems which have both storage and processing capacity constraints; the approach is observed to be particularly effective in the presence of capacity restrictions. Extensive computational tests conducted over a variety of parameter values indicate that the reformulations are very effective even on relatively large problems, thereby reducing the need for heuristic approaches.