Optimal transportation distances are a fundamental family of parameterized distances for
histograms in the probability simplex. Despite their appealing theoretical properties …

We give algorithms for geometric graph problems in the modern parallel models such as
MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of …

This paper presents a novel theoretical measure, μEMD, based on the earth mover's
distance (EMD), for quantifying the density shift caused by electronic excitations in …

We study the problem of learning from data representations that are invariant to
transformations, and at the same time selective, in the sense that two points have the same …

Over the last decade, an immense amount of data has become available. From collections of
photos, to genetic data, and to network traffic statistics, modern technologies and cheap …

We introduce a new class of objectives for optimal transport computations of datasets in high-
dimensional Euclidean spaces. The new objectives are parametrized by $\rho\geq 1$, and …

A technique introduced by Indyk and Woodruff (STOC 2005) has inspired several recent
advances in data-stream algorithms. We show that a number of these results follow eas-ily …

We study streaming algorithms for the fundamental geometric problem of computing the cost
of the Euclidean Minimum Spanning Tree (MST) on an n-point set X⊂ ℝ d. In the streaming …

We show there is a distribution over linear mappings R: l1n-> l1O (d log d), such that with
arbitrarily large constant probability, for any fixed d-dimensional subspace L, for all x∈ L we …

We study streaming algorithms for two fundamental geometric problems: computing the cost
of a Minimum Spanning Tree (MST) of an n-point set X⊂{1, 2,…, Δ} d, and computing the …