  Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$
Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and
some (or none or all) points of $S$. A Steiner tree with length of longest edge
minimized is called a bottleneck Steiner tree. In this paper, we study the
Euclidean bottleneck Steiner tree problem: given two sets, $P$ and $S$, and a
positive integer $k \le m$, find a bottleneck Steiner tree of $P$ with at most
$k$ Steiner points. The problem has application in the design of wireless
communication networks.
  We first show that the problem is NP-hard and cannot be approximated within
factor $\sqrt{2}$, unless $P=NP$. Then, we present a polynomial-time
approximation algorithm with performance ratio 2.
