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Mapping composition is a fundamental operation in metadata
driven applications. Given a mapping over schemas S1 and S2 and
a mapping over schemas S2 and S3, the composition problem is
to compute an equivalent mapping over S1 and S3. We describe
a new composition algorithm that targets practical applications. It
incorporates view unfolding. It eliminates as many S2 symbols as
possible, even if not all can be eliminated. It covers constraints
expressed using arbitrary monotone relational operators and, to a
lesser extent, non-monotone operators. And it introduces the new
technique of left composition. We describe our implementation, explain
how to extend it to support user-defined operators, and present
experimental results which validate its effectiveness.