Consistent $k$-Median: Simpler, Better and Robust

• URL: http://arxiv.org/abs/2008.06101v1
• Date: Thu, 13 Aug 2020 20:24:28 GMT
• Title: Consistent $k$-Median: Simpler, Better and Robust
• Authors: Xiangyu Guo, Janardhan Kulkarni, Shi Li, Jiayi Xian
• Abstract summary: We show that a simple local-search based online algorithm can give a bicriteria constant approximation for the problem with $O(k2 log2 (nD))$ swaps of medians (recourse) in total. When restricted to the problem without outliers, our algorithm is simpler, deterministic and gives better approximation ratio and recourse.
• Score: 20.692372082600972
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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].

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