A characterization of constant-time maintainability for BCNF database schemes

Abstract

The maintenance problem (for database states) of a database scheme R with respect to a set of functional dependencies F is the following decision problem. Let r be a consistent state of R with respect to F and assume we insert a tuple t into r p ε r. Is r ∪ { t } a consistent state of R with respect to F ? R is said to be constant-time-maintainable with respect to F if there is an algorithm that solves the maintenance problem of R with respect to F in time independent of the state size. A characterization of constant-time-maintainability for the class of BCNF database schemes is given. An efficient algorithm that tests this characterization is shown, as well as an algorithm for solving the maintenance problem in time independent of the state size. It is also proven that constant-time-maintainable BCNF database schemes are bounded. In particular, it is shown that total projections of the representative instance can be computed via unions of projections of extension joins. Throughout we assume that database schemes are cover embedding and BCNF, and that functional dependencies are given in the form of key dependencies.