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
Pages (from-to)	967-993
Number of pages	27
Journal	Israel Journal of Mathematics
Volume	267
Issue number	2
DOIs	https://doi.org/10.1007/s11856-025-2741-2
State	Published - Jun 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s11856-025-2741-2

Cite this

@article{d038938d073d46e3b9dba6cb4264e3a1,

title = "Online embedding of metrics",

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.",

author = "Ilan Newman and Yuri Rabinovich",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = jun,

doi = "10.1007/s11856-025-2741-2",

language = "English",

volume = "267",

pages = "967--993",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Online embedding of metrics

AU - Newman, Ilan

AU - Rabinovich, Yuri

PY - 2025/6

Y1 - 2025/6

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85218708818

U2 - 10.1007/s11856-025-2741-2

DO - 10.1007/s11856-025-2741-2

M3 - Article

AN - SCOPUS:85218708818

SN - 0021-2172

VL - 267

SP - 967

EP - 993

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

Online embedding of metrics

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this