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In the standard planar $k$-center clustering problem, one is given a set $P$ of $n$ points in the plane, and the goal is to select $k$ center points, so as to minimize the maximum distance over points in $P$ to their nearest center. Here we…

Computational Geometry · Computer Science 2021-09-29 Hongyao Huang , Georgiy Klimenko , Benjamin Raichel

We study the problem of explainable clustering in the setting first formalized by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). A $k$-clustering is said to be explainable if it is given by a decision tree where each internal node…

Data Structures and Algorithms · Computer Science 2021-10-26 Buddhima Gamlath , Xinrui Jia , Adam Polak , Ola Svensson

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

Data Structures and Algorithms · Computer Science 2025-11-24 Hendrik Fichtenberger , Michael Kapralov , Ekaterina Kochetkova , Silvio Lattanzi , Davide Mazzali , Weronika Wrzos-Kaminska

We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$ points $P$ in a metric space, let $\delta(x)$ for $x\in P$ be the radius of the smallest ball…

Data Structures and Algorithms · Computer Science 2024-02-14 MohammadHossein Bateni , Vincent Cohen-Addad , Alessandro Epasto , Silvio Lattanzi

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

Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…

Data Structures and Algorithms · Computer Science 2010-12-15 Nir Ailon , Noa Avigdor-Elgrabli , Edo Liberty

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Data Structures and Algorithms · Computer Science 2018-07-20 Fedor V. Fomin , Petr A. Golovach , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that…

Data Structures and Algorithms · Computer Science 2011-05-10 Konstantin Voevodski , Maria-Florina Balcan , Heiko Roglin , Shang-Hua Teng , Yu Xia

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

Machine Learning · Computer Science 2020-09-23 Sanjoy Dasgupta , Nave Frost , Michal Moshkovitz , Cyrus Rashtchian

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

Data Structures and Algorithms · Computer Science 2017-10-17 Tamal K. Dey , Alfred Rossi , Anastasios Sidiropoulos

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

Data Structures and Algorithms · Computer Science 2023-11-02 David P. Woodruff , Peilin Zhong , Samson Zhou

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…

Computer Science and Game Theory · Computer Science 2024-02-07 Jakob Burkhardt , Ioannis Caragiannis , Karl Fehrs , Matteo Russo , Chris Schwiegelshohn , Sudarshan Shyam

We study the problem of partitioning a set of $n$ objects in a metric space into $k$ clusters $V_1,\dots,V_k$. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric…

Data Structures and Algorithms · Computer Science 2025-01-10 Matthias Kaul , Kelin Luo , Matthias Mnich , Heiko Röglin

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

Databases · Computer Science 2026-02-19 Aryan Esmailpour , Stavros Sintos

In the Max-k-diameter problem, we are given a set of points in a metric space, and the goal is to partition the input points into k parts such that the maximum pairwise distance between points in the same part of the partition is minimized.…

Computational Geometry · Computer Science 2024-04-08 Henry Fleischmann , Kyrylo Karlov , Karthik C. S. , Ashwin Padaki , Stepan Zharkov

Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…

Data Structures and Algorithms · Computer Science 2024-04-26 Vicente Balmaseda , Ying Xu , Yixin Cao , Nate Veldt

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

Machine Learning · Computer Science 2023-10-26 Moses Charikar , Monika Henzinger , Lunjia Hu , Maxmilian Vötsch , Erik Waingarten

We present an efficient algorithm for the min-max correlation clustering problem. The input is a complete graph where edges are labeled as either positive $(+)$ or negative $(-)$, and the objective is to find a clustering that minimizes the…

Data Structures and Algorithms · Computer Science 2025-02-19 Nairen Cao , Steven Roche , Hsin-Hao Su

Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…

Data Structures and Algorithms · Computer Science 2023-10-19 Lukas Drexler , Jan Eube , Kelin Luo , Dorian Reineccius , Heiko Röglin , Melanie Schmidt , Julian Wargalla

In this paper, we consider the Minimum-Load $k$-Clustering/Facility Location (MLkC) problem where we are given a set $P$ of $n$ points in a metric space that we have to cluster and an integer $k$ that denotes the number of clusters.…

Computational Geometry · Computer Science 2021-07-21 Sayan Bandyapadhyay , Fedor V. Fomin , Petr A. Golovach , Nidhi Purohit , Kirill Simonov