Algorithms and Applications for Universal Quanti cation in Relational

Queries containing universal quanti cation are used in many applications, including business intelligence applications and in particular data mining. We present a comprehensive survey of the structure and performance of algorithms for universal quanti cation. We introduce a framework that results in a complete classi cation of input data for universal quanti cation. Then we go on to identify the most eÆcient algorithm for each such class. One of the input data classes has not been covered so far. For this class, we propose several new algorithms. Thus, for the rst time, we are able to identify the optimal algorithm to use for any given input dataset. These two classi cations of optimal algorithms and input data are important for query optimization. They allow a query optimizer to make the best selection when optimizing at intermediate steps for the quanti cation problem. In addition to the classi cation, we show the relationship between relational division and the set containment join and we illustrate the usefulness of employing universal quanti cations by presenting a novel approach for frequent itemset discovery.