Trees and Euclidean metrics

Nathan Linial; Avner Magen; Michael E. Saks

doi:10.1145/276698.276726

Trees and Euclidean metrics

Nathan Linial^*, Avner Magen, Michael E. Saks

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Conference article › peer-review

13 Scopus citations

Abstract

To study a finite metric space (X,d), an approximation in the form of a metric that is introduced from a norm is needed. The quality of such an approximation is quantified by the distortion of the corresponding embedding. Embedding into Euclidean spaces is discussed including an introduction of the notation c₂(X,d) - the least distortion with which (X,d) may be embedded in any Euclidean space.

Original language	American English
Pages (from-to)	169-175
Number of pages	7
Journal	Conference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs	https://doi.org/10.1145/276698.276726
State	Published - 1998
Event	Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA Duration: 23 May 1998 → 26 May 1998

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title = "Trees and Euclidean metrics",

abstract = "To study a finite metric space (X,d), an approximation in the form of a metric that is introduced from a norm is needed. The quality of such an approximation is quantified by the distortion of the corresponding embedding. Embedding into Euclidean spaces is discussed including an introduction of the notation c2(X,d) - the least distortion with which (X,d) may be embedded in any Euclidean space.",

author = "Nathan Linial and Avner Magen and Saks, {Michael E.}",

year = "1998",

doi = "10.1145/276698.276726",

language = "American English",

pages = "169--175",

journal = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",

issn = "0734-9025",

publisher = "Association for Computing Machinery (ACM)",

note = "Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing ; Conference date: 23-05-1998 Through 26-05-1998",

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TY - JOUR

T1 - Trees and Euclidean metrics

AU - Linial, Nathan

AU - Magen, Avner

AU - Saks, Michael E.

PY - 1998

Y1 - 1998

N2 - To study a finite metric space (X,d), an approximation in the form of a metric that is introduced from a norm is needed. The quality of such an approximation is quantified by the distortion of the corresponding embedding. Embedding into Euclidean spaces is discussed including an introduction of the notation c2(X,d) - the least distortion with which (X,d) may be embedded in any Euclidean space.

AB - To study a finite metric space (X,d), an approximation in the form of a metric that is introduced from a norm is needed. The quality of such an approximation is quantified by the distortion of the corresponding embedding. Embedding into Euclidean spaces is discussed including an introduction of the notation c2(X,d) - the least distortion with which (X,d) may be embedded in any Euclidean space.

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U2 - 10.1145/276698.276726

DO - 10.1145/276698.276726

M3 - Conference article

AN - SCOPUS:0031624266

SN - 0734-9025

SP - 169

EP - 175

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing

Y2 - 23 May 1998 through 26 May 1998

ER -

Trees and Euclidean metrics

Abstract

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