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.
arXiv:2502. 08397v3 Announce Type: replace-cross Abstract: Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together.
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.
arXiv:2509. 21785v2 Announce Type: replace-cross Abstract: Discretizing raw features into bucketized attribute representations is a popular step before sharing a dataset.
arXiv:2607. 19704v1 Announce Type: new Abstract: Scaling LLM-based applications to millions of users is bottlenecked by the inference cost and latency of modern foundation models.
arXiv:2401. 10927v3 Announce Type: replace-cross Abstract: In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$.
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.
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.
arXiv:2609. 30477v1 Announce Type: cross Abstract: Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential.
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...
arXiv:2607. 04949v1 Announce Type: new Abstract: We study the problem of k-means clustering on large datasets.
arXiv:2407. 11217v4 Announce Type: replace-cross Abstract: Clustering problems such as $k$-means and $k$-median are staples of unsupervised learning, and many algorithmic techniques have been developed to tackle their numerous aspects.
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...