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We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the $k$-center…

Machine Learning · Computer Science 2018-02-19 Flavio Chierichetti , Ravi Kumar , Silvio Lattanzi , Sergei Vassilvitskii

We study the $k$-center problem in the context of individual fairness. Let $P$ be a set of $n$ points in a metric space and $r_x$ be the distance between $x \in P$ and its $\lceil n/k \rceil$-th nearest neighbor. The problem asks to…

Data Structures and Algorithms · Computer Science 2025-03-26 Matthijs Ebbens , Nicole Funk , Jan Höckendorff , Christian Sohler , Vera Weil

We consider the classic Facility Location, $k$-Median, and $k$-Means problems in metric spaces of doubling dimension $d$. We give nearly linear-time approximation schemes for each problem. The complexity of our algorithms is…

Data Structures and Algorithms · Computer Science 2020-05-21 Vincent Cohen-Addad , Andreas Emil Feldmann , David Saulpic

Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…

Data Structures and Algorithms · Computer Science 2025-05-23 Ameet Gadekar , Suhas Thejaswi

In metric $k$-clustering, we are given as input a set of $n$ points in a general metric space, and we have to pick $k$ centers and cluster the input points around these chosen centers, so as to minimize an appropriate objective function. In…

Data Structures and Algorithms · Computer Science 2024-11-06 Sayan Bhattacharya , Martín Costa , Ermiya Farokhnejad

We study (Euclidean) $k$-median and $k$-means with constraints in the streaming model. There have been recent efforts to design unified algorithms to solve constrained $k$-means problems without using knowledge of the specific constraint at…

Data Structures and Algorithms · Computer Science 2021-06-15 Melanie Schmidt , Julian Wargalla

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 best known approximation bound for high dimensional Euclidean…

Data Structures and Algorithms · Computer Science 2022-08-31 Vincent Cohen-Addad , Jason Li

Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular $k$-median and $k$-means variants which, given a set $P$ of points from a metric…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-01 Alessio Mazzetto , Andrea Pietracaprina , Geppino Pucci

We study the problem of fairness in k-centers clustering on data with disjoint demographic groups. Specifically, this work proposes a variant of fairness which restricts each group's number of centers with both a lower bound…

Data Structures and Algorithms · Computer Science 2022-07-26 Huy Lê Nguyen , Thy Nguyen , Matthew Jones

The $k$-center problem is a classical clustering problem in which one is asked to find a partitioning of a point set $P$ into $k$ clusters such that the maximum radius of any cluster is minimized. It is well-studied. But what if we add up…

Data Structures and Algorithms · Computer Science 2024-10-01 Lukas Drexler , Annika Hennes , Abhiruk Lahiri , Melanie Schmidt , Julian Wargalla

A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.…

Data Structures and Algorithms · Computer Science 2019-04-25 Sepideh Aghamolaei , Mohammad Ghodsi

The $k$-center problem requires the selection of $k$ points (centers) from a given metric pointset $W$ so to minimize the maximum distance of any point of $W$ from the closest center. This paper focuses on a fair variant of the problem,…

Data Structures and Algorithms · Computer Science 2025-03-10 Matteo Ceccarello , Andrea Pietracaprina , Geppino Pucci , Francesco Visonà

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering…

Data Structures and Algorithms · Computer Science 2018-11-27 Ioana O. Bercea , Martin Groß , Samir Khuller , Aounon Kumar , Clemens Rösner , Daniel R. Schmidt , Melanie Schmidt

We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…

Data Structures and Algorithms · Computer Science 2015-08-04 Konstantin Makarychev , Yury Makarychev , Maxim Sviridenko , Justin Ward

Data summarization tasks are often modeled as $k$-clustering problems, where the goal is to choose $k$ data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to…

Machine Learning · Computer Science 2024-10-18 Ameet Gadekar , Aristides Gionis , Suhas Thejaswi

The current best approximation algorithms for $k$-median rely on first obtaining a structured fractional solution known as a bi-point solution, and then rounding it to an integer solution. We improve this second step by unifying and…

Data Structures and Algorithms · Computer Science 2022-10-25 Kishen N. Gowda , Thomas Pensyl , Aravind Srinivasan , Khoa Trinh

In a recent work, [19] studied the following "fair" variants of classical clustering problems such as $k$-means and $k$-median: given a set of $n$ data points in $\mathbb{R}^d$ and a binary type associated to each data point, the goal is to…

Data Structures and Algorithms · Computer Science 2019-12-18 Lingxiao Huang , Shaofeng H. -C. Jiang , Nisheeth K. Vishnoi

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

Data Structures and Algorithms · Computer Science 2015-04-13 Anup Bhattacharya , Ragesh Jaiswal , Amit Kumar

We consider the $k$-clustering problem with $\ell_p$-norm cost, which includes $k$-median, $k$-means and $k$-center, under an individual notion of fairness proposed by Jung et al. [2020]: given a set of points $P$ of size $n$, a set of $k$…

Data Structures and Algorithms · Computer Science 2022-03-02 Ali Vakilian , Mustafa Yalçıner

We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…

Data Structures and Algorithms · Computer Science 2022-07-26 Shichuan Deng , Jian Li , Yuval Rabani