Equi-depth multidimensional histograms
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Statistical estimators for aggregate relational algebra queries
ACM Transactions on Database Systems (TODS)
Complete rules for n-ary relationship cardinality constraints
Data & Knowledge Engineering
Computational problems related to the design of normal form relational schemas
ACM Transactions on Database Systems (TODS)
Testing implications of data dependencies
ACM Transactions on Database Systems (TODS)
Graph Algorithms for Functional Dependency Manipulation
Journal of the ACM (JACM)
A general framework for the view selection problem for data warehouse design and evolution
Proceedings of the 3rd ACM international workshop on Data warehousing and OLAP
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Inclusion dependencies and their interaction with functional dependencies
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
On the implication problem for cardinality constraints and functional dependencies
Annals of Mathematics and Artificial Intelligence
IEEE Transactions on Knowledge and Data Engineering
Using Constraints for Efficient Query Processing in Nondeterministic Databases
IEEE Transactions on Knowledge and Data Engineering
Resampling in an Indefinite Database to Approximate Functional Dependencies
PKDD '98 Proceedings of the Second European Symposium on Principles of Data Mining and Knowledge Discovery
On The Satisfiability of Dependency Constraints in Entity-Relationship Schemata
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Bounding the cardinality of aggregate views through domain-derived constraints
Data & Knowledge Engineering - Special issue: Advances in OLAP
Data exchange: semantics and query answering
Theoretical Computer Science - Database theory
Exact algorithms and applications for Tree-like Weighted Set Cover
Journal of Discrete Algorithms
Incorporating cardinality constraints and synonym rules into conditional functional dependencies
Information Processing Letters
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
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Numerical dependencies (NDs) are database constraints that limit the number of distinct Y-values that can appear together with any X-value, where both X and Y are sets of attributes in a relation schema. While it is known that NDs are not finitely axiomatizable, there is no study on how to efficiently derive NDs using a set of sound (yet necessarily incomplete) rules. In this paper, after proving that solving the entailment problem for NDs using the chase procedure has exponential space complexity, we show that, given a set of inference rules similar to those used for functional dependencies, the membership problem for NDs is NP-hard. We then provide a graph-based characterization of NDs, which is exploited to design an efficient branch & bound algorithm for ND derivation. Our algorithm adopts several optimization strategies that provide considerable speed-up over a naive approach, as confirmed by the results of extensive tests we made for efficiency and effectiveness using six different datasets.