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Randomized and deterministic algorithms for geometric spanners of small diameter

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3 Author(s)
Arya, S. ; Max-Planck-Inst. fur Inf., Saarbrucken, Germany ; Mount, D.M. ; Smid, M.

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 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

Published in:

Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on

Date of Conference:

20-22 Nov 1994