In the first three sections of this paper, the authors quickly and clearly define their terminology, provide a terse historical framework, survey previous pioneering work, and give a brief exegesis of work done on multifarious topics related to the Universal Relation. The remainder of the paper states and proves the authors’ algorithms for efficiently computing total projections for independent schemes.
The authors propose using simple chase join expressions (scjes) as an efficient and natural way to simulate total projections. They show that for any X ⊆ U, the X-total projection of CHASEF(Tr) can be computed efficiently by a union of scjes when an independent scheme is assumed. They briefly review related research and compare it to their work.
The efficient algorithm proposed here uses a number of precomputations performed only at the beginning, when the scheme is defined and its independence is verified. These precomputations include the closures of all the sets of attributes involved in functional dependencies, and some subexpressions associated with the attributes. Thus, each time a total projection is needed, the union of scjes is generated efficiently. Finally, the authors use their previous work on scje optimizations to show that optimal expressions can be produced efficiently. This paper is well organized and excellently written.
