Online k-Median with Consistent Clusters

03/27/2023

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by   Benjamin Moseley, et al.

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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.