  In this paper, we study the problem of computing the diameter of a set of $n$
points in $d$-dimensional Euclidean space for a fixed dimension $d$, and
propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+
1/\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \varepsilon\leqslant
1$. We also show that the proposed algorithm can be modified to a
$(1+O(\varepsilon))$-approximation algorithm with $O(n+
1/\varepsilon^{\frac{2d}{3}-\frac{1}{3}})$ running time. These results provide
some improvements in comparison with existing algorithms in terms of simplicity
and data structure.
