Discrete & Computational Geometry

, Volume 29, Issue 1, pp 77–81

A Lower Bound on the Distortion of Embedding Planar Metrics into Euclidean Space

Authors

  • Ilan Newman
    • Computer Science Department, University of Haifa, Haifa 31905, Israel ilan@cs.haifa.ac.il, yuri@cs.haifa.ac.il
  • Yuri Rabinovich
    • Computer Science Department, University of Haifa, Haifa 31905, Israel ilan@cs.haifa.ac.il, yuri@cs.haifa.ac.il

DOI: 10.1007/s00454-002-2813-5

Cite this article as:
Newman, I. & Rabinovich, Y. Discrete Comput Geom (2002) 29: 77. doi:10.1007/s00454-002-2813-5

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?

Copyright information

© 2002 Springer-Verlag New York Inc.