%0 Conference Paper %B Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on %D 1994 %T Randomized and deterministic algorithms for geometric spanners of small diameter %A Arya,S. %A Mount, Dave %A Smid,M. %K computational geometry %K deletions %K deterministic algorithms %K directed graph %K directed graphs %K geometric spanners %K insertions %K randomised algorithms %K randomized algorithms %X Let S be a set of n points in IRd 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 %B Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on %P 703 - 712 %8 1994/11// %G eng %R 10.1109/SFCS.1994.365722