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Clustering in Varying Metrics
Deeparnab Chakrabarty, Jonathan Conroy, Ankita Sarkar
https://arxiv.org/abs/2510.07860 https://arxiv.org/pdf/2510.07860

Clustering in Varying Metrics
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the clustering costs -- e.g., the average or maximum -- where the cost is measured via $k$-center/median/means objectives. More generally, we minimize a norm $Ψ$ over the $T$ cost values. We show that for $T \geq 3$, the problem is inapproximable to any finite facto…