@article {15569,
	title = {Dynamic algorithms for geometric spanners of small diameter: Randomized solutions},
	journal = {Computational Geometry: Theory and Applications},
	volume = {13},
	year = {1994},
	month = {1994///},
	pages = {13 - 91},
	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 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 t-spanner 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 t-spanner path from p to q containing at most D edges. A randomized algorithm is given for constructing a t-spanner that, with high probability, contains O(n) edges and has spanner diameter O(log n). A data structure of size O(n log  d  n) is given that maintains this t-spanner in O(log  d  n log log n)  expected amortized time per insertion and deletion, in the model of random updates, as introduced by Mulmuley.  Keywords: Computational geometry, proximity problems, skip lists, randomization, dynamic data structures. Preprint submitted to Els...},
	author = {Arya,Sunil and Mount, Dave and Smid,Michiel}
}
