Consistent $k$-Median: Simpler, Better and Robust
This work addresses clustering problems with outliers for applications requiring online updates, offering a robust and efficient solution with incremental improvements over existing methods.
The paper tackles the online consistent k-clustering with outliers problem by proposing a simple local-search based algorithm that achieves a bicriteria constant approximation with O(k^2 log^2(nD)) median swaps, improving upon prior work in simplicity, approximation ratio, and recourse for the non-outlier case.
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].