NNS lower bounds via metric expansion for l∞ and EMD

Abstract

We give new lower bounds for randomized NNS data structures in the cell probe model based on robust metric expansion for two metric spaces: l ∞ and Earth Mover Distance (EMD) in high dimensions. In particular, our results imply stronger non-embedability for these metric spaces into l1. The main components of our approach are a strengthening of the isoperimetric inequality for the distribution on l∞ introduced by Andoni et al [FOCS'08] and a robust isoperimetric inequality for EMD on quotients of the boolean hypercube. © 2012 Springer-Verlag.