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The mapping semantics that combines the schema-level and the data-level mappings is called bi-level mappings. Bi-level mappings enhance data sharing overcoming the limitations of the non-combined approaches. This paper presents an algorithm for composing two bi-level mappings by using tableaux. Composition of mappings between peers has several computational advantages in a peer data management system, such as yielding more efficient query translation, pruning redundant paths, and better query execution plans. We also present a distributed algorithm for computing direct mapping between two end peers of a series of peers connected by a chain of mappings.

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