Manor Mendel

Fast construction of nets in low dimensional metrics, and their applications

We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate nearest neighbor search, well-separated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near-linear and the space being used is linear.

Euclidean quotients of finite metric spaces

This paper is devoted to the study of quotients of finite metric spaces. The basic type of question we ask is: Given a finite metric space M and α⩾1, what is the largest quotient of (a subset of) M which well embeds into Hilbert space. We obtain asymptotically tight bounds for these questions, and prove that they exhibit phase transitions. We also study the analogous problem for embeddings into lp, and the particular case of the hypercube.

Some Low Distortion Metric Ramsey Problems

Abstract In this note we consider the metric Ramsey problem for the normed spaces

On metric ramsey-type phenomena

\ell_p

Nonlinear spectral calculus and super-expanders

. Namely, given some

Ramsey partitions and proximity data structures

1\le p \le \infty

Better algorithms for unfair metrical task systems and applications

and

Some applications of Ball’s extension theorem

\alpha \ge 1

Randomized k -server algorithms for growth-rate bounded graphs

, and an integer

Low dimensional embeddings of ultrametrics

n