Schema Design for Uncertain Databases

ABSTRACT We address schema design in uncertain databases. Since uncertain data is relational in nature, decomposition be- comes a key issue in design. Decomposition relies on depen- dency theory, and primarily on functional dependencies. We study the theory of functional dependencies (FDs) for uncertain relations. We dene,several kinds of horizontal FDs and vertical FDs, each of which is consistent with con- ventional FDs when,an uncertain relation doesn’t contain any uncertainty. In addition to standard forms of decom- positions allowed by ordinary relations, our FDs allow more complex decompositions specic,to uncertain data. We show how our theory of FDs can be used for lossless decomposition of uncertain relations. We then present algorithms and com- plexity results for three fundamental problems with respect to FDs over ordinary and uncertain relations: (1) Testing whether a relation instance satises,an FD; (2) Finding all FDs satised,by a relation instance; and (3) Inferring all FDs that hold in the result of a query over uncertain rela- tions with FDs. We also give a sound and complete axiom- atization of horizontal and vertical FDs. We look at keys as a special case of FDs. Finally, we briey consider uncertain data that contains condence,values.