 
Summary: Efficient Construction of a Bounded Degree Spanner
with Low Weight
Sunil Arya
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 graph having the points of S as its vertices such that for any pair p, q
of points there is a path between them of length at most t times the Euclidean
distance between p and q.
An efficient implementation of a greedy algorithm is given that constructs a
tspanner having bounded degree such that the total length of all its edges is
bounded by O(log n) times the length of a minimum spanning tree for S. The
algorithm has running time O(n logd
n).
Applying recent results of Das, Narasimhan and Salowe to this tspanner
gives an O(n logd
n) time algorithm for constructing a tspanner having bounded
degree and whose total edge length is proportional to the length of a minimum
spanning tree for S. Previously, no o(n2) time algorithms were known for con
