Supporting Temporal Reasoning by Mapping Calendar Expressions to Minimal
  Periodic Sets
  In the recent years several research efforts have focused on the concept of
time granularity and its applications. A first stream of research investigated
the mathematical models behind the notion of granularity and the algorithms to
manage temporal data based on those models. A second stream of research
investigated symbolic formalisms providing a set of algebraic operators to
define granularities in a compact and compositional way. However, only very
limited manipulation algorithms have been proposed to operate directly on the
algebraic representation making it unsuitable to use the symbolic formalisms in
applications that need manipulation of granularities.
  This paper aims at filling the gap between the results from these two streams
of research, by providing an efficient conversion from the algebraic
representation to the equivalent low-level representation based on the
mathematical models. In addition, the conversion returns a minimal
representation in terms of period length. Our results have a major practical
impact: users can more easily define arbitrary granularities in terms of
algebraic operators, and then access granularity reasoning and other services
operating efficiently on the equivalent, minimal low-level representation. As
an example, we illustrate the application to temporal constraint reasoning with
multiple granularities.
  From a technical point of view, we propose an hybrid algorithm that
interleaves the conversion of calendar subexpressions into periodical sets with
the minimization of the period length. The algorithm returns set-based
granularity representations having minimal period length, which is the most
relevant parameter for the performance of the considered reasoning services.
Extensive experimental work supports the techniques used in the algorithm, and
shows the efficiency and effectiveness of the algorithm.
