Consistent k-Median: Simpler, Better and Robust

08/13/2020

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by   Xiangyu Guo, et al.

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In this paper we introduce and study the online consistent k-clustering with outliers problem, generalizing the non-outlier version of the problem studied in [Lattanzi-Vassilvitskii, ICML17]. We show that a simple local-search based online algorithm can give a bicriteria constant approximation for the problem with O(k^2 log^2 (nD)) swaps of medians (recourse) in total, where D is the diameter of the metric. When restricted to the problem without outliers, our algorithm is simpler, deterministic and gives better approximation ratio and recourse, compared to that of [Lattanzi-Vassilvitskii, ICML17].