Aggregative closure: an extension of transitive closure

Abstract

The aggregative closure operator is defined and its usefulness is demonstrated in a wide variety of applications. The concepts and definitions of closed semirings and the aggregating relational operators provide a mathematical framework for the presentation of algorithms for these applications. A novel algorithm is also presented which is intended for the computation of the aggregate closure. All of these algorithms but the last are generalizations of existing algorithms intended for transitive closure.<>