Lower bounds for set intersection queries

"Furthermore we consider the case q = O(n) with an additional space restriction. We only allow to use m memory locations, where m [<or =] n[superscript 3/2]. We show a tight bound of [theta](n²m[superscript 1/3]) for a sequence of O(n) operations, again ignoring polynomial in log n factors.""@en
"Abstract: "We consider the following set intersection reporting problem. We have a collection of initially empty sets and would like to process an intermixed sequence of n updates (insertions into and deletions from individual sets) and q queries (reporting the intersection of two sets). We cast this problem in the arithmetic model of computation of Fredman [Fre81] and Yao [Yao85] and show that any algorithm that fits in this model must take time [omega](q + n[square root of]q) to process a sequence of n updates and q queries, ignoring factors that are polynomial in log n. We show that this bound is tight in this model of computation, again to within a polynomial in log n factor, improving upon a result of Yellin [Yel92]."@en