Consistent k-Median: Simpler, Better and Robust

Xiangyu Guo, Janardhan Kulkarni, Shi Li, Jiayi Xian

Abstract:

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].