Fair clustering is a constrained clustering problem where we need to partition a set of
colored points. The fraction of points of each color in every cluster should be more or less …

We introduce a novel definition for a small set R of k points being" representative" of a larger
set in a metric space. Given a set V (eg, documents or voters) to represent, and a set C of …

We study the complexity of the classic capacitated k-median and k-means problems
parameterized by the number of centers, k. These problems are notoriously difficult since the …

We study the capacitated k-facility location problem, in which we are given a set of clients
with demands, a set of facilities with capacities and a positive integer k. It costs fi to open …

In this article, we study the uniform capacitated k-median (CKM) problem. In the problem, we
are given a set F of potential facility locations, a set C of clients, a metric d over F∪ C, an …

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 …

In the capacitated k-median (CKM) problem, we are given a set F of facilities, each facility i∊
F with a capacity ui, a set C of clients, a metric d over F∪ C and an integer k. The goal is to …

Capacitated k-median is one of the few outstanding optimization problems for which the
existence of a polynomial time constant factor approximation algorithm remains an open …

We study the Capacitated k-Median problem for which existing constant-factor
approximation algorithms are all pseudo-approximations that violate either the capacities or …

We study the Capacitated k-Median problem, for which all the known constant factor
approximation algorithms violate either the number of facilities or the capacities. While the …