Encyclopedia of Database Systems

Living Edition
| Editors: Ling Liu, M. Tamer Özsu

Join Dependency

  • Solmaz KolahiEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7993-3_1249-2




A join dependency (JD) over a relation schema R[U] is an expression of the form ®[X1,...,Xn], where X1 ∪  …  ∪ Xn = U. An instance I of R[U] satisfies ®[X1,...,Xn] if \( I={\pi}_{X_1}(I)\ddot{\mathrm{I}}\dots \ddot{\mathrm{I}}{\pi}_{X_n}(I) \). In other words, an instance satisfies the join dependency if it is equal to the join of its projections on the sets of attributes X1,...,Xn. A multivalued dependency X→→Y is a special case of a join dependency on two sets, and can be expressed as ⋈ [XY, X(UXY)] where XY represents XY.

Key Points

Join dependencies are particularly important in connection with the decomposition technique for schema design and normalization. The main goal of the decomposition technique is to avoid redundancies due to data dependencies by decomposing a relation into smaller parts. A good decomposition should have the lossless join property, meaning that no information should be lost after the decomposition. In other words, the original database instance should be retrievable by joining the smaller relations, and this can be expressed by a JD. The following figure shows an instance of the relation schema R[A, B, C, D] that satisfies the join dependency ⋈ [BC, AB, AD].

Join dependencies are usually considered together with functional and multivalued dependencies (FDs and MVDs) in normalization. The implication problem of a JD from a set of JDs, MVDs, and FDs is known to be NP-hard. In addition, the implication problem of JDs cannot be axiomatized. That is, there is no sound and complete set of rules that can be used to check whether a dependency is implied by a set of JDs. However, there is a powerful tool, called chase, that could be used to reason about these dependencies in exponential time and space [1].


Recommended Reading

  1. 1.
    Abiteboul S, Hull R, Vianu V. Foundations of databases. Reading: Addison-Wesley; 1995.Google Scholar

Copyright information

© Springer Science+Business Media LLC 2016

Authors and Affiliations

  1. 1.University of British ColumbiaVancouverCanada

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK