Fundamental techniques for order optimization
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
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SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
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IDEAS '99 Proceedings of the 1999 International Symposium on Database Engineering & Applications
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ICDE '05 Proceedings of the 21st International Conference on Data Engineering
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Proceedings of the 14th International Conference on Extending Database Technology
Fundamentals of order dependencies
Proceedings of the VLDB Endowment
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Dependencies play an important role in databases. We study order dependencies (ODs)--and unidirectional order dependencies (UODs), a proper sub-class of ODs--which describe the relationships among lexicographical orderings of sets of tuples. We consider lexicographical ordering, as by the order-by operator in SQL, because this is the notion of order used in SQL and within query optimization. Our main goal is to investigate the inference problem for ODs, both in theory and in practice. We show the usefulness of ODs in query optimization. We establish the following theoretical results: (i) a hierarchy of order dependency classes; (ii) a proof of co-NP-completeness of the inference problem for the subclass of UODs (and ODs); (iii) a proof of co-NP-completeness of the inference problem of functional dependencies (FDs) from ODs in general, but demonstrate linear time complexity for the inference of FDs from UODs; (iv) a sound and complete elimination procedure for inference over ODs; and (v) a sound and complete polynomial inference algorithm for sets of UODs over restricted domains.