Optimizing relational algebra operations using generic equivalence discriminators and lazy products

We show how to efficiently evaluate generic map-filter-product queries, generalizations of select-project-join (SPJ) queries in relational algebra, based on a combination of two novel techniques: generic discrimination-based joins and lazy (formal) products. Discrimination-based joins are based on the notion of (equivalence) discriminator. A discriminator partitions a list of values according to a user-specified equivalence relation on keys the values are associated with. Equivalence relations can be specified in an expressive embedded language for denoting equivalence relations. We show that discriminators can be constructed generically (by structural recursion on equivalence expressions), purely functionally, and efficiently (worst-case linear time). The array-based basic multiset discrimination algorithm of Cai and Paige (1995) provides a base discriminator that is both asymptotically and practically efficient. In contrast to hashing, discrimination is fully abstract (only de...

• Type: Conference
• Year: 2010
• Where: PEPM
• Authors: Fritz Henglein
• Keywords: Equivalence Expressions, Equivalence Relations, PEPM 2010, Software Engineering, User-specified Equivalence Relation