  Given a real number $t>1$, a geometric $t$-spanner is a geometric graph for a
point set in $\mathbb{R}^d$ with straight lines between vertices such that the
ratio of the shortest-path distance between every pair of vertices in the graph
(with Euclidean edge lengths) to their actual Euclidean distance is at most
$t$. An imprecise point set is modeled by a set $R$ of regions in
$\mathbb{R}^d$. If one chooses a point in each region of $R$, then the
resulting point set is called a precise instance of~$R$. An imprecise
$t$-spanner for an imprecise point set $R$ is a graph $G=(R,E)$ such that for
each precise instance $S$ of $R$, graph $G_S=(S,E_S)$, where $E_S$ is the set
of edges corresponding to $E$, is a $t$-spanner.
  In this paper, we show that, given a real number $t>1$, there is an imprecise
point set $R$ of $n$ straight-line segments in the plane such that any
imprecise $t$-spanner for $R$ has $\Omega(n^2)$ edges. Then, we propose an
algorithm that computes a Well-Separated Pair Decomposition (WSPD) of size
${\cal O}(n)$ for a set of $n$ pairwise disjoint $d$-dimensional balls with
arbitrary sizes. Given a real number $t>1$ and given a set of $n$ pairwise
disjoint $d$-balls with arbitrary sizes, we use this WSPD to compute in ${\cal
O}(n\log n+n/(t-1)^d)$ time an imprecise $t$-spanner with ${\cal O}(n/(t-1)^d)$
edges for balls.
