MPI-I-92-127

We consider the following {\em 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 {\em arithmetic\/} model of computation of Fredman and Yao and show that any algorithm that fits in this model must take $\Omega(q + n \sqrt{q})$ to process a sequence of $n$ updates and $q$ queries, ignoring factors that are polynomial in $\log n$. By adapting an algorithm due to Yellin we can show that this bound is tight in this model of computation, again to within a polynomial in $\log n$ factor.