Online embedding of metrics

Ilan Newman; Yuri Rabinovich

doi:10.1007/s11856-025-2741-2

Online embedding of metrics

Ilan Newman, Yuri Rabinovich

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We study deterministic online embeddings of metric spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces, a tight exponential upper bound on embedding into the line, and a (1 + ϵ)-distortion embedding in ℓ^∞ of a suitably high dimension.

Original language	English
Journal	Israel Journal of Mathematics
DOIs	https://doi.org/10.1007/s11856-025-2741-2
State	Accepted/In press - 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-025-2741-2

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AB - We study deterministic online embeddings of metric spaces into normed spaces and into trees against an adaptive adversary. Main results include a polynomial lower bound on the (multiplicative) distortion of embedding into Euclidean spaces, a tight exponential upper bound on embedding into the line, and a (1 + ϵ)-distortion embedding in ℓ∞ of a suitably high dimension.

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Online embedding of metrics

Abstract

Bibliographical note

ASJC Scopus subject areas

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