Optimal computation of total projections with unions of simple chase join expressions

The representative instance has been proposed as a query answering device in systems using the Universal Relation Interface. One approach is to use the total projections of the representative instance to generate the answer for a query. Associated with this approach is the problem of how to generate the total projections of the representative instance efficiently. We propose a generalization of extension joins, called chase join expressions, as a means to compute the total projections when functional dependencies are given as constraints. In particular, we identify an important subclass of chase join expressions called simple chase join expressions and show that the total projections with respect to a set of functional dependencies can be computed by unions of simple chase join expressions when an independent scheme is assumed. We also find a simple and efficient algorithm that minimizes the number of join operations in a union of simple chase join expressions.