Related papers: The Heterogeneous Capacitated $k$-Center Problem

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 $(C \cup F, dist)$ with facility costs $open : F \to…

Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to…

This article presents a matheuristic algorithm for the single-source capacitated facility location problem (SSCFLP) and its variants: SSCFLP with K facilities (SSCKFLP), SSCFLP with contiguous service areas (CFLSAP), and SSCFLP with K…

We consider constellations of disks which are unions of disjoint hyperbolic disks in the unit disk with fixed radii and unfixed centers. We study the problem of maximizing the conformal capacity of a constellation with a fixed number of…

In the Non-Uniform $k$-Center problem, a generalization of the famous $k$-center clustering problem, we want to cover the given set of points in a metric space by finding a placement of balls with specified radii. In $t$-NU$k$C Problem, we…

We consider the $k$-center problem on the space of fixed-size point sets in the plane under the $L_{\infty}$-bottleneck distance. While this problem is motivated by persistence diagrams in topological data analysis, we illustrate it as a…

We study fair clustering problems in a setting where distance information is obtained from two sources: a strong oracle providing exact distances, but at a high cost, and a weak oracle providing potentially inaccurate distance estimates at…

When selecting locations for a set of facilities, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In…

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…

We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns…

Given a stream of points in a metric space, is it possible to maintain a constant approximate clustering by changing the cluster centers only a small number of times during the entire execution of the algorithm? This question received…

Center-based clustering techniques are fundamental in some areas of machine learning such as data summarization. Generic $k$-center algorithms can produce biased cluster representatives so there has been a recent interest in fair $k$-center…

The Non-Uniform $k$-center (NUkC) problem has recently been formulated by Chakrabarty, Goyal and Krishnaswamy [ICALP, 2016] as a generalization of the classical $k$-center clustering problem. In NUkC, given a set of $n$ points $P$ in a…

We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…

Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…

In Bayesian peer-to-peer decentralized data fusion, the underlying distributions held locally by autonomous agents are frequently assumed to be over the same set of variables (homogeneous). This requires each agent to process and…

\textit{Clustering problems} often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure. Among the clustering problems,…

To deliver high performance in power limited systems, architects have turned to using heterogeneous systems, either CPU+GPU or mixed CPU-hardware systems. However, in systems with different processor types and task affinities, scheduling…

We present a randomized distributed approximation algorithm for the metric uncapacitated facility location problem. The algorithm is executed on a bipartite graph in the Congest model yielding a (1.861 + epsilon) approximation factor, where…

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group…