The design of distributed databases is an optimization problem requiring solutions to several interrelated problems including: data fragmentation, allocation, and local optimization. Each problem can be solved with several di erent approaches thereby making the distributed database design a very di cult task. Although there is a large body of work on the design of data fragmentation, most of them are either ad hoc solutions or formal solutions for special cases (e. g., binary vertical

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... ng). In this paper, we address the general vertical partitioning problem formally. W e rst provide a comparison of work in the area of data clustering and distributed databases to highlight the thrust of this work. We derive an objective function that generalizes and subsumes earlier work on vertical partitioning in databases. The objective function developed in this paper provides a basis for developing heuristic algorithms for vertical partitioning. The objective function also facilitates comparison of previously developed algorithms for vertical partitioning. We also illustrate how the objective function developed for distributed transaction processing can be extended to include additional information, such as transaction types, di erent local and remote accessing costs and replication. Finally, w e indicate the current status of the implementation of a testbed.