@conference {15588,
title = {Randomized and deterministic algorithms for geometric spanners of small diameter},
booktitle = {Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on},
year = {1994},
month = {1994/11//},
pages = {703 - 712},
abstract = {Let S be a set of n points in IR^{d} and let t gt;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 p. 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. Randomized and deterministic algorithms are given for constructing t-spanners consisting of O(n) edges and having O(log n) diameter. Also, it is shown how to maintain the randomized t-spanner under random insertions and deletions. Previously, no results were known for spanners with low spanner diameter and for maintaining spanners under insertions and deletions},
keywords = {computational geometry, deletions, deterministic algorithms, directed graph, directed graphs, geometric spanners, insertions, randomised algorithms, randomized algorithms},
doi = {10.1109/SFCS.1994.365722},
author = {Arya,S. and Mount, Dave and Smid,M.}
}