Hengjie Zhang, Columbia University

Abstract

We study graph spanners for point-set in the high-dimensional Euclidean space. On the one hand, we prove that spanners with stretch <sqrt{2} and subquadratic size are not possible, even if we add Steiner points. On the other hand, if we add extra nodes to the graph (non-metric Steiner points), then we can obtain (1+eps)-approximate spanners of subquadratic size. We show how to construct a spanner of size n^{2-Omega(eps^3)}, as well as a directed version of the spanner of size n^{2-Omega(eps^2)}.

We use our directed spanner to obtain an algorithm for computing (1+eps)-approximation to Earth-Mover Distance (optimal transport) between two sets of size n in time n^{2-Omega(eps^2)}.

This is the joint work with Alexandr Andoni.

See: https://theory.cs.rutgers.edu/theory_seminar