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COMGEO
1999
ACM

Dynamic algorithms for geometric spanners of small diameter: Randomized solutions

9 years 6 months ago
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...
Sunil Arya, David M. Mount, Michiel H. M. Smid
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1999
Where COMGEO
Authors Sunil Arya, David M. Mount, Michiel H. M. Smid
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