The paper presents new algorithms for fair k‑center clustering in Euclidean spaces, where a dataset is divided into groups and each group has a limit on the number of centers that can be chosen. A parameterized approximation algorithm achieves a 2.732 ratio, which is improved to 2.414 with exponential time in k. By integrating this into a one‑pass streaming framework, the authors obtain streaming approximations of 4.464 (improvable to 3.828) and a polynomial‑time streaming algorithm with a 4.732 ratio, further reduced to 4.42, surpassing previous state‑of‑the‑art results. Experiments confirm that these methods outperform existing approaches in clustering accuracy.
By Zeyu Lin, Chaoqi Jia, Longkun Guo, Chao Chen
arXiv:2609.07974v1 Announce Type: cross
Abstract: Fairness in clustering has attracted sustained research interest, motivated by the need to ensure equitable representation of protected groups in mac...
By Kangke Cheng, Guanlin Mo, Shihong Song, Hu Ding
arXiv:2607. 26202v1 Announce Type: cross Abstract: The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering, but for a fixed number $k$ of centers its worst-case expected approximation ratio is $\Theta(\log k)$.
By Vaclav Rozhon
arXiv:2511. 17823v2 Announce Type: replace Abstract: Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning.
By Naitik Gada (Rochester Institute of Technology)
arXiv:2411. 01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al.
By Maximilian Fleissner, Maedeh Zarvandi, Debarghya Ghoshdastidar
arXiv:2601. 06351v2 Announce Type: replace Abstract: Anticlustering is an NP-hard combinatorial optimization problem that consists of partitioning a set of objects into equal-sized groups called anticlusters such that the objects in the same anticluster are as dissimilar as possible and thereby representative of the entire set of objects.
By Philipp Baumann, Olivier Goldschmidt, Dorit S. Hochbaum, Jason Yang
arXiv:2602. 08542v3 Announce Type: replace-cross Abstract: Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center.
By Emilio Cruciani, Sebastian Forster, Antonis Skarlatos
arXiv:2608. 16270v1 Announce Type: new Abstract: Coreset selection reduces the cost of model training by replacing a large training set with a small representative subset.
By Yingfan Liu, Leiyu Zhang, Jiadong Xie, Mingzhe Wang, Jeffrey Xu Yu, Jiangtao Cui
The paper introduces the Universal Clustering Problem (UCP), a framework that captures the optimisation core common to many clustering methods by maximizing a polynomial‑time computable partition utility over a finite metric space. It proves UCP is NP‑hard through reductions from graph colouring and exact cover by 3‑sets, showing that popular algorithms such as k‑means, GMMs, DBSCAN, spectral clustering, and affinity propagation inherit this intractability. The authors argue that this unified hardness explains typical failure modes—like local optima and greedy merge traps—and suggest moving toward stability‑aware objectives and interaction‑driven formulations with explicit guarantees.
By Angshul Majumdar
arXiv:2304. 13917v4 Announce Type: replace Abstract: In recent years, there has been a surge in effort to formalize notions of fairness in machine learning.
By Haris Aziz, Barton E. Lee, Sean Morota Chu, Jeremy Vollen
arXiv:2609.06394v1 Announce Type: cross
Abstract: Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computat...
By Diptarka Chakraborty, Satyaki Mukherjee, Gaurav Vallabhdas Revankar, Hoang-Son Tran
arXiv:2607. 04949v1 Announce Type: new Abstract: We study the problem of k-means clustering on large datasets.
By Cristian Boldrin, Fabio Vandin