Average case complexity analysis of RETE pattern-match algorithm and average size of join in Databases

Abstract

The Rete algorithm [Forg 82] is a very efficient method for comparing a large collection of patterns with a large collection of objects. It is widely used in rule-based expert systems. We studied ([AF 88] or [Alb 88]) the average case complexity of the Rete algorithm on collections of patterns and objects with a random tree structure. Objects and patterns are often made up of a head-symbol and a list of variable or constant arguments (OPSV [Forg 81], Xrete [LCR 88]…). In this paper, we analyse the theoretical performance of RETE algorithm on this widely used type of pattern and object with the theory of generating functions. We extend this work to the study of the performance of composed queries in relational Databases and we generalize Rosenthal's theorem on the average size of an equijoin [Rosen 81]. We give some numerical examples based on our results.