Decompositions and Functional Dependencies in Relations

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Abstract

A general study is made of two basic integrity constraints on relations: functional and multivalued dependencies. The latter are studied via an equivalent concept: decompositions. A model is constructed for any possible combination of functional dependencies and decompositions. The model embodies some decompositions as unions of relations having different schemata of functional dependencies. This suggests a new, stronger integrity constraint, the degenerate decomposition. More generally, the theory demonstrates the importance of using the union operation in database design and of allowing different schemata on the operands of a union. Techniques based on the union lead to a method for solving the problem of membership of a decomposition in the closure of a given set of functional dependencies and decompositions. The concept of antiroot is introduced as a tool for describing families of decompositions, and its fundamental importance for database design is indicated. © 1980, ACM. All rights reserved.

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Armstrong, W. W., & Deobel, C. (1980). Decompositions and Functional Dependencies in Relations. ACM Transactions on Database Systems (TODS), 5(4), 404–430. https://doi.org/10.1145/320610.320620

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