# Consistent k-Median: Simpler, Better and Robust

@article{Guo2021ConsistentKS, title={Consistent k-Median: Simpler, Better and Robust}, author={Xiangyu Guo and Janardhan Kulkarni and Shi Li and Jiayi Xian}, journal={ArXiv}, year={2021}, volume={abs/2008.06101} }

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…

## 3 Citations

### Online and Consistent Correlation Clustering

- Computer ScienceICML
- 2022

This work studies the correlation clustering problem in the classic online setting with recourse in an online manner and develops an algorithm that achieves logarithmic recourse per vertex in the worst case and complement this result with a tight lower bound.

### Optimal Fully Dynamic k-Centers Clustering

- Computer ScienceArXiv
- 2021

It is proved that any algorithm for k-clustering tasks in arbitrary metric spaces, including k-means, k-medians, and k-centers, must make at least Ω(nk) distance queries to achieve any non-trivial approximation factor.

### Consistent k-Clustering for General Metrics

- Computer ScienceSODA
- 2021

This work shows how to maintain a constant-factor approximation for the $k-median problem by performing an optimal (up to polylogarithimic factors) number $\widetilde{O}(k)$ of center swaps.

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