An Efficient Algorithm for Minimizing Time Granularity Periodical Representations

This paper addresses the technical problem of efficiently reducing the periodic representation of a time granularity to its minimal form. The minimization algorithm presented in the paper has an immediate practical application: it allows users to intuitively define granularities (and more generally, recurring events) with algebraic expressions that are then internally translated to mathematical characterizations in terms of minimal periodic sets. Minimality plays a crucial role, since the value of the recurring period has been shown to dominate the complexity when processing periodic sets.