Consistent k-Median: Simpler, Better and Robust - Guo, Xiangyu; Kulkarni, Janardhan (Jana); Li, Shi; Xian, Jiayi (International Conference on Artificial Intelligence and Statistics (AISTATS) 2021, 2021)
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^2log^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].