Girth and Euclidean distortion

Nathan Linial, Avner Magen, Assaf Naor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we partially prove a conjecture that was raised by Linial, London and Rabinovich in [11]. Let G be a k-regular graph, k ≥ 3, with girth g. We show that every embedding f : G → ℓ2 has distortion Ω(√g). The original conjecture which remains open is that the Euclidean distortion is bounded below by Ω(g). Two proofs are given, one based on semi-definite programming, and the other on Markov Type, a concept that considers random walks on metrics.

Original languageEnglish (US)
Title of host publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
Pages705-711
Number of pages7
StatePublished - 2002
EventProceedings of the 34th Annual ACM Symposium on Theory of Computing - Montreal, Que., Canada
Duration: May 19 2002May 21 2002

Other

OtherProceedings of the 34th Annual ACM Symposium on Theory of Computing
CountryCanada
CityMontreal, Que.
Period5/19/025/21/02

ASJC Scopus subject areas

  • Software

Cite this

Linial, N., Magen, A., & Naor, A. (2002). Girth and Euclidean distortion. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 705-711)

Girth and Euclidean distortion. / Linial, Nathan; Magen, Avner; Naor, Assaf.

Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2002. p. 705-711.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Linial, N, Magen, A & Naor, A 2002, Girth and Euclidean distortion. in Conference Proceedings of the Annual ACM Symposium on Theory of Computing. pp. 705-711, Proceedings of the 34th Annual ACM Symposium on Theory of Computing, Montreal, Que., Canada, 5/19/02.
Linial N, Magen A, Naor A. Girth and Euclidean distortion. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2002. p. 705-711
Linial, Nathan ; Magen, Avner ; Naor, Assaf. / Girth and Euclidean distortion. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2002. pp. 705-711
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