The (k, z)-clustering problem consists of finding a set of k points called centers, such that the
sum of distances raised to the power of z of every data point to its closest center is …

Motivated by data analysis and machine learning applications, we consider the popular high-
dimensional Euclidean k-median and k-means problems. We propose a new primal-dual …

Abstract The $ k $-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is often the
practitioners' choice algorithm for optimizing the popular $ k $-means clustering objective …

In the classic Correlation Clustering problem introduced by Bansal, Blum, and Chawla ‍
(FOCS 2002), the input is a complete graph where edges are labeled either+ or−, and the …

Clustering with capacity constraints is a fundamental problem that attracted significant
attention throughout the years. In this paper, we give the first FPT constant-factor …

We study the differentially private (DP) $ k $-means and $ k $-median clustering problems of
$ n $ points in $ d $-dimensional Euclidean space in the massively parallel computation …

We study optimization problems in a metric space $(\mathcal {X}, d) $ where we can
compute distances in two ways: via a “strong” oracle that returns exact distances $ d (x, y) …

Given a set of points in d-dimensional space, an explainable clustering is one where the
clusters are specified by a tree of axis-aligned threshold cuts. Dasgupta et al.(ICML 2020) …

We show that the RandomCoordinateCut algorithm gives the optimal competitive ratio for
explainable $ k $-medians in $\ell_1 $. The problem of explainable $ k $-medians was …

We consider the approximability of center-based clustering problems where the points to be
clustered lie in a metric space, and no candidate centers are specified. We call such …