Euclidean Spanners in High Dimensions
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Indyk_euclidean spanners.pdf
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Author(s)
Har-Peled, Sariel
Indyk, Piotr
Sidiropoulos, Anastasios
Date Issued
2013
Journal
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Har-Peled, Sariel, Piotr Indyk, and Anastasios Sidiropoulos. "Euclidean Spanners in High Dimensions." Khanna, Sanjeev, ed. Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013.
Version
Final published version
Abstract
A classical result in metric geometry asserts that any n-point metric admits a linear-size spanner of dilation O(log n) [PS89]. More generally, for any c > 1, any metric space admits a spanner of size O(n[superscript 1+1/c]), and dilation at most c. This bound is tight assuming the well-known girth conjecture of Erdős [Erd63].
We show that for a metric induced by a set of n points in high-dimensional Euclidean space, it is possible to obtain improved dilation/size trade-offs. More specifically, we show that any n-point Euclidean metric admits a near-linear size spanner of dilation O(√log n). Using the LSH scheme of Andoni and Indyk [AI06] we further show that for any c > 1, there exist spanners of size roughly O(n[superscript1+1/c[superscript 2]]) and dilation O(c). Finally, we also exhibit super-linear lower bounds on the size of spanners with constant dilation.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/1.9781611973105.57
