%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 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
%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