Showing papers by "Yuri Rabinovich published in 2002"
TL;DR: A simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than $Omega(\sqrt{\log n})$ is exhibited, thus resolving the question how well do planar metrics embed in Euclidan spaces.
Abstract: We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than $\Omega(\sqrt{\log n})$ . 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?
54 citations
05 Jun 2002
TL;DR: A simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than $\Omega(\sqrt\log n\,)$ is exhibited, resolving the question of how well do planar metrics embed in Euclidan spaces.
Abstract: (MATH) We exhibit a simple infinite family of series-parallel graphs that cannot be metrically embedded into Euclidean space with distortion smaller than $\Omega(\sqrt\log n\,)$. This matches Rao's general upper bound for metric embedding of planar graphs into Euclidean space, [14], thus resolving the question of how well do planar metrics embed in Euclidean spaces.
19 citations