Schema Design for Uncertain Databases

Abstract

We address schema design in uncertain databases such as are found in Trio. Since uncertain data is relational in nature, decomposition becomes a key issue in design. Decomposition relies on dependency theory, and primarily on functional dependencies. We study the theory of functional dependencies (FDs) for uncertain relations. We define several kinds of {\em horizonal} FDs and {\em vertical} FDs, each of which is consistent with conventional FDs when an uncertain relation doesn't contain any uncertainty. In addition to standard forms of decompositions allowed by ordinary relations, our FDs allow more complex decompositions specific to uncertain data. First we give a sound and complete axiomatization of horizontal and vertical FDs. Next we show how our theory of FDs can be used for lossless decomposition of uncertain relations. We then present algorithms and complexity results for three fundamental problems with respect to FDs over ordinary and uncertain relations: (1) {\em Testing} whether a relation instance satisfies an FD; (2) {\em Finding} all FDs satisfied by a relation instance; and (3) {\em Inferring} all FDs that hold in the result of a query over uncertain relations with FDs. Finally, we look at keys as a special case of FDs, and briefly consider uncertain data that contains {\em confidence} values.