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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.