Optimal (Euclidean) Metric Compression
Name
20m1371324.pdf
Description
Published version
Size
675.87 KB
Format
Adobe PDF
Checksum (MD5)
d91b0a71663d4653c7e263170cf824c7
Author(s)
Indyk, Piotr
Wagner, Tal
Date Issued
June 2022
Journal
SIAM Journal on Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Indyk, Piotr and Wagner, Tal. 2022. "Optimal (Euclidean) Metric Compression." SIAM Journal on Computing, 51 (3).
Version
Final published version
Abstract
We study the problem of representing all distances between 𝑛 points in ℝ𝑑, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for ℓ1 (also known as Manhattan)-metrics, and for general metrics. Our bounds for Euclidean metrics mark the first improvement over compression schemes based on discretizing the classical dimensionality reduction theorem of Johnson and Lindenstrauss [Contemp. Math. 26 (1984), pp. 189--206]. Since it is known that no better dimension reduction is possible, our results establish that Euclidean metric compression is possible beyond dimension reduction.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/20M1371324
