An Index for Set Intersection With Post-Filtering

This paper studies how to design an index structure on a collection of sets
$S_{1}, S_{2},{\ldots }, S_{n}$
to answer the following queries: given distinct set ids
$a, b \in [1, n]$
, report
$F(S_{a} \cap S_{b})$
where
$F(.)$
is a filtering function. We present a solution that can support a great variety of filtering functions — range research, skyline, convex hull, nearest neighbor search, quantile (to name just a few) — with attractive performance guarantees. The guarantees are sensitive to the set collection's
pseudoarboricity
, a new notion for quantifying the density of
$\lbrace S_{1}, S_{2},{\ldots }, S_{n}\rbrace$
. Our index structures are simple to understand and implement.