OPTIMAL (EUCLIDEAN) METRIC COMPRESSION

Piotr Indyk, Tal Wagner

Research output: Contribution to journalArticlepeer-review

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 ℓ 1 (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.

Original languageEnglish
Pages (from-to)467-491
Number of pages25
JournalSIAM Journal on Computing
Volume51
Issue number3
DOIs
StatePublished - 2022
Externally publishedYes

Funding

FundersFunder number
National Science FoundationIIS-144747, DMS-2022448
Simons Foundation

    Keywords

    • dimension reduction
    • distance oracle
    • distance sketch
    • metric sketch
    • quantization

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