On the Boundedness of Constant-Time-Maintainable Database Schemes

Abstract

Constant-time-maintainable database schemes are highly desirable with respect to constraint enforcement, since it is possible to determine whether any of their consistent states plus an inserted tuple is consistent in time independent of the state size. Several proper subclasses of constant-time-maintainable database schemes are known to be bounded with respect to dependencies and hence very desirable with respect to query answering. However, whether the whole class of constant-time-maintainable database schemes is bounded is not known for sure. In this paper, it is proven that the entire class of constant-time-maintainable database schemes is bounded with respect to dependencies and thus very desirable with respect to query answering in the following cases: (1) only cover-embedded functional dependencies appear as constraints; (2) only equality-generating dependencies appear as constraints and the database scheme has a lossless join. In particular, it is shown that total projections of representative instances can be computed via unions of projections of simple chase join expressions. Since it is known how to optimize these expressions, it is possible to compute total projections optimally. These results show that the class of constant-time-maintainable database schemes is the largest class of database schemes, which are highly desirable with respect to both constraint enforcement and query answering. This class of schemes can be effectively recognized by known algorithms. The previously known largest class of database schemes with these desirable properties is the class of independent database schemes, which is a proper subclass of constant-time-maintainable schemes.