Randomized and deterministic algorithms for geometric spanners of small diameter

Let S be a set of n points in IR/sup d/ 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...

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Bibliographic Details
Published in:Foundations of Computer Science, 35th Symposium on (FOCS '94) pp. 703 - 712
Main Authors: Arya, S., Mount, D.M., Smid, M.
Format: Conference Proceeding
Language:English
Published: IEEE Comput. Soc. Press 1994
Subjects:
Computer science
Contracts
Data structures
Euclidean distance
Tree graphs
ISBN:0818665807, 9780818665806
Online Access:Get full text
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Summary:Let S be a set of n points in IR/sup d/ 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.< >
ISBN:0818665807
9780818665806
DOI:10.1109/SFCS.1994.365722