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arXiv · 2303.15379

Online $k$-Median with Consistent Clusters

Benjamin Moseley·Heather Newman·Kirk Pruhs
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Abstract

We consider the online $k$-median clustering problem in which $n$ points arrive online and must be irrevocably assigned to a cluster on arrival. As there are lower bound instances that show that an online algorithm cannot achieve a competitive ratio that is a function of $n$ and $k$, we consider a beyond worst-case analysis model in which the algorithm is provided a priori with a predicted budget $B$ that upper bounds the optimal objective value. We give an algorithm that achieves a competitive ratio that is exponential in the the number $k$ of clusters, and show that the competitive ratio of every algorithm must be linear in $k$. To the best of our knowledge this is the first investigation in the literature that considers cluster consistency using competitive analysis.

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Benjamin Moseley, Heather Newman, Kirk Pruhs. 2023-03-27. Online $k$-Median with Consistent Clusters. https://arxiv.org/abs/2303.15379

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