Frequent itemset discovery with SQL using universal quantification

Algorithms for finding frequent itemsets fall into two broad categories: algorithms that are based on non-trivial SQL statements to query and update a database, and algorithms that employ sophisticated in-memory data structures, where the data is stored in flat files. Most performance experiments have shown that SQL-based approaches are inferior to main-memory algorithms. However, the current trend of database vendors to integrate analysis functionalities into their query execution and optimization components, i.e., "closer to the data," suggests to revisit these results and to search for new, potentially better solutions. We investigate approaches based on SQL-92 and present a new approach called Quiver that employs universal and existential quantifications. In the table schema for itemsets of our approach, a group of tuples represents a single itemset. Such a "vertical" layout is similar to the popular layout used for the transaction table, which is the input of frequent itemset discovery. We show that current DBMS do not provide efficient query processing strategies for dealing with quantified queries, mostly due to the lack of an adequate SQL syntax for set containment tests. Performance tests using a query processor prototype and a novel query operator, called set containment division, promise an improved performance for quantified queries like those used for Quiver.