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 …

Parameterization and approximation are two popular ways of coping with NP-hard
problems. More recently, the two have also been combined to derive many interesting …

We study the task of differentially private clustering. For several basic clustering problems,
including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient …

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 …

$ k $-means clustering is a well-studied problem due to its wide applicability. Unfortunately,
there exist strong theoretical limits on the performance of any algorithm for the $ k $-means …

k-median and k-means are the two most popular objectives for clustering algorithms.
Despite intensive effort, a good understanding of the approximability of these objectives …

The k-means objective is arguably the most widely-used cost function for modeling
clustering tasks in a metric space. In practice and historically, k-means is thought of in a …

The Uncapacitated Facility Location (UFL) problem is one of the most fundamental
clustering problems: Given a set of clients C and a set of facilities F in a metric space (C∪ F …

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 …