 
Summary: Randomized and deterministic algorithms for geometric spanners of
small diameter
Sunil Arya
David M. Mount
Michiel Smid
Abstract
Let S be a set of n points in IRd
and let t > 1 be a real
number. A tspanner for S is a directed graph having
the points of S as its vertices, such that for any pair
p and q of points there is a path from p to q of length
at most t times the Euclidean distance between p and
q. Such a path is called a tspanner path. The spanner
diameter of such a spanner is defined as the smallest
integer D such that for any pair p and q of points there
is a tspanner path from p to q containing at most D
edges.
Randomized and deterministic algorithms are given
for constructing tspanners consisting of O(n) edges and
having O(log n) diameter. Also, it is shown how to
