Dynamic algorithms for geometric spanners of small diameter: Randomized solutions

Let S be a set of n points in IRd 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 logd n) is given that maintains this t-spanner in O(logd n log log n) expected amortized time per insertion and deletion, in the model of random updates, as introduced by Mulmuley. Key words: Computational geometry, proximity problems, skip lists, randomization, dynamic data structures. Preprint submitted to Elsevier P...

• Type: Journal
• Year: 1999
• Where: COMGEO
• Authors: Sunil Arya, David M. Mount, Michiel H. M. Smid
• Keywords: Applied Computing, COMGEO 1999, Directed Graph, Real Number, T-spanner Path