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Abstract:
Let $S$ be a set of $n$ points in $\IR^d$ and let $t>1$ be
a real number. A $t$-spanner 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 $t$-spanner 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 $O(n \log^d n)$.
Also, an application to the problem of distance enumeration
is given.
