Uniformly-distributed random generation of join orders

Abstract

In this paper we study the space of operator trees that can be used to answer a join query, with the goal of generating elements form this space at random. We solve the problem for queries with acyclic query graphs. We first count, in O(n3) time, the exact number of trees that can be used to evaluate a given query on n relations. The intermediate results of the counting procedure then serve to generate random, uniformly distributed operator trees in O(n2) time per tree. We also establish a mapping between the N operator trees for a query and the integers 1 through N —i. e. a ranking— and describe ranking and unranking procedures with complexity O(n2) and O(n2 log n), respectively.