Fast Matrix Multiplication for Query Processing

Abstract

This paper studies how to use fast matrix multiplication to speed up query processing. As observed, computing a two-table join and then projecting away the join attribute is essentially the Boolean matrix multiplication problem, which can be significantly improved with fast matrix multiplication. Moving beyond this basic two-table query, we introduce output-sensitive algorithms for general join-project queries using fast matrix multiplication. These algorithms have achieved a polynomially large improvement over the classic Yannakakis framework. To the best of our knowledge, this is the first theoretical improvement for general acyclic join-project queries since 1981.