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arXiv · 2512.19654

Clustering with Label Consistency

Diptarka Chakraborty·Hendrik Fichtenberger·Bernhard Haeupler·Silvio Lattanzi·Ashkan Norouzi-Fard·Ola Svensson
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Abstract

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the real-world need for stable point labels, i.e., stable assignments of points to named sets (clusters). In this paper, we address this gap by initiating the study of label-consistent metric clustering. We first introduce a new notion of consistency, measuring the label distance between two consecutive solutions. Then, armed with this new definition, we design new consistent approximation algorithms for the classical $k$-center and $k$-median problems.

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Diptarka Chakraborty, Hendrik Fichtenberger, Bernhard Haeupler, Silvio Lattanzi, Ashkan Norouzi-Fard, Ola Svensson. 2025-12-22. Clustering with Label Consistency. https://arxiv.org/abs/2512.19654

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