On the 3-distortion of a path.

Pierre Dehornoy (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We prove that, when a path of length n is embedded in R^2, the 3-distortion is an Omega(n^{1/2}), and that, when embedded in R^d, the 3-distortion is an O(n^{1/d-1}).

Mots clés: distortion; triangle; non-expanding embedding

Domaines: Géométrie algorithmique [cs.CG]

Pierre Dehornoy. On the 3-distortion of a path.. European Journal of Combinatorics, 2008, http://www.elsevier.com/wps/find/journaldescription.cws_home/622824/description#description. ⟨10.1016/j.ejc.2006.11.002⟩. ⟨hal-00017449v2⟩