A lower bound on the distortion of embedding planar metrics into euclidean space

Ilan Newman; Yuri Rabinovich

doi:10.1007/s00454-002-2813-5

A lower bound on the distortion of embedding planar metrics into euclidean space

Ilan Newman, Yuri Rabinovich

Department of Computer Science

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

Abstract

We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than Ω(√log n). This matches Rao's [14] general upper bound for metric embedding of planar graphs into Euclidean space, thus resolving the question how well do planar metrics embed in Euclidean spaces?

Original language	English
Pages (from-to)	77-81
Number of pages	5
Journal	Discrete and Computational Geometry
Volume	29
Issue number	1
DOIs	https://doi.org/10.1007/s00454-002-2813-5
State	Published - Jan 2003

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-002-2813-5

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abstract = "We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than Ω(√log n). This matches Rao's [14] general upper bound for metric embedding of planar graphs into Euclidean space, thus resolving the question how well do planar metrics embed in Euclidean spaces?",

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AB - We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than Ω(√log n). This matches Rao's [14] general upper bound for metric embedding of planar graphs into Euclidean space, thus resolving the question how well do planar metrics embed in Euclidean spaces?

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A lower bound on the distortion of embedding planar metrics into euclidean space

Abstract

ASJC Scopus subject areas

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