  Given a sequence $A$ of $n$ numbers and an integer (target) parameter $1\leq
i\leq n$, the (exact) selection problem asks to find the $i$-th smallest
element in $A$. An element is said to be $(i,j)$-mediocre if it is neither
among the top $i$ nor among the bottom $j$ elements of $S$. The approximate
selection problem asks to find a $(i,j)$-mediocre element for some given $i,j$;
as such, this variant allows the algorithm to return any element in a
prescribed range. In the first part, we revisit the selection problem in the
two-party model introduced by Andrew Yao (1979) and then extend our study of
exact selection to the multiparty model. In the second part, we deduce some
communication complexity benefits that arise in approximate selection. In
particular, we present a deterministic protocol for finding an approximate
median among $k$ players.
