 Classical results show that, when the dimension d\in N and \epsilon >0 are constant, every set S of n points in d-space admits an (1+ \epsilon )-spanners with O(n) edges and weight proportional to that of the Euclidean MST of S. Tight bounds on the dependence on \epsilon >0 for constant d\in N have been established only recently.
<clarity>  Classical results show that, when the dimension d\in N and \epsilon >0 are constant, every set S of n points in d-space admits an (1+ \epsilon )-spanners with O(n) edges and weight proportional to that of the Euclidean MST of S. Tight bounds on the dependence on \epsilon >0 for constant d\in N have been established only recently.
 Classical results show that, when the dimension d\in N and \epsilon >0 are constant, every set S of n points in d-space admits an (1+ \epsilon )-spanners with O(n) edges and weight proportional to that of the Euclidean MST of S. Tight bounds on the dependence on \varepsilon >0 for constant d\in N have been established only recently.