Maintaining constrained transitive closure by conjunctive queries

Abstract

Recently there has been considerable effort on the maintenance of database views in general, and of deductive database views in particular. Such work considered the incremental maintenance of deductive views defined by expensive database queries, including the transitive closure query. An interesting approach is to use only first-order queries in this maintenance, after small changes (e.g. one tuple insertions and deletions) to base relations. In this paper we consider such incremental maintenance of views defined by constrained transitive closure queries, for the insertion case. The constraints may refer to node costs such as height, voltage and temperature at spatial locations of interest, and to edge costs such as distances between spatial locations. When the constraints are based on node costs, we divide the maintenance problem into several cases, depending on the nature of the constraints. For some cases, the constrained transitive closure becomes bounded in the sense that the recursion can be removed and thus the maintenance problem becomes trivial. For the other cases we provide complete solutions for maintaining the constrained transitive closure. The size of the auxiliary relations can be kept bounded by the size of the transitive closure of the graphs. We also illustrate how to maintain the constrained transitive closure in the presence of other kinds of constraints. However, whether such views can be maintained in first-order after the deletion of edges is a major open problem, even for the constraint-free transitive closure of directed graphs.