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Abstract:
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.
