 
Summary: Dynamic algorithms for geometric spanners of
small diameter: Randomized solutions
Sunil Arya 1
Department of Computer Science, Hong Kong University of Science and
Technology, Clear Water Bay, Kowloon, Hongkong.
David M. Mount 2
Department of Computer Science and Institute for Advanced Computer Studies,
University of Maryland, College Park, Maryland.
Michiel Smid 3
Department of Computer Science, University of Magdeburg, D39106 Magdeburg,
Germany.
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.
A randomized algorithm is given for constructing a tspanner that, with high
