@inproceedings{14769,
  abstract     = {For a set of points in Rd, the Euclidean k-means problems consists of finding k centers such that the sum of distances squared from each data point to its closest center is minimized. Coresets are one the main tools developed recently to solve this problem in a big data context. They allow to compress the initial dataset while preserving its structure: running any algorithm on the coreset provides a guarantee almost equivalent to running it on the full data. In this work, we study coresets in a fully-dynamic setting: points are added and deleted with the goal to efficiently maintain a coreset with which a k-means solution can be computed. Based on an algorithm from Henzinger and Kale [ESA'20], we present an efficient and practical implementation of a fully dynamic coreset algorithm, that improves the running time by up to a factor of 20 compared to our non-optimized implementation of the algorithm by Henzinger and Kale, without sacrificing more than 7% on the quality of the k-means solution.},
  author       = {Henzinger, Monika H and Saulpic, David and Sidl, Leonhard},
  booktitle    = {2024 Proceedings of the Symposium on Algorithm Engineering and Experiments},
  location     = {Alexandria, VA, United States},
  pages        = {220--233},
  publisher    = {Society for Industrial & Applied Mathematics},
  title        = {{Experimental evaluation of fully dynamic k-means via coresets}},
  doi          = {10.1137/1.9781611977929.17},
  year         = {2024},
}

@inproceedings{14768,
  abstract     = {In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic k-median and k-means problems, there are no known deterministic dimensionality reduction procedure or coreset construction that avoid an exponential dependency on the input dimension d, the precision parameter $\varepsilon^{-1}$ or k. Furthermore, there is no coreset construction that succeeds with probability $1-1/n$ and whose size does not depend on the number of input points, n. This has led researchers in the area to ask what is the power of randomness for clustering sketches [Feldman WIREs Data Mining Knowl. Discov’20].Similarly, the best approximation ratio achievable deterministically without a complexity exponential in the dimension are $1+\sqrt{2}$ for k-median [Cohen-Addad, Esfandiari, Mirrokni, Narayanan, STOC’22] and 6.12903 for k-means [Grandoni, Ostrovsky, Rabani, Schulman, Venkat, Inf. Process. Lett.’22]. Those are the best results, even when allowing a complexity FPT in the number of clusters k: this stands in sharp contrast with the $(1+\varepsilon)$-approximation achievable in that case, when allowing randomization.In this paper, we provide deterministic sketches constructions for clustering, whose size bounds are close to the best-known randomized ones. We show how to compute a dimension reduction onto $\varepsilon^{-O(1)} \log k$ dimensions in time $k^{O\left(\varepsilon^{-O(1)}+\log \log k\right)}$ poly $(n d)$, and how to build a coreset of size $O\left(k^{2} \log ^{3} k \varepsilon^{-O(1)}\right)$ in time $2^{\varepsilon^{O(1)} k \log ^{3} k}+k^{O\left(\varepsilon^{-O(1)}+\log \log k\right)}$ poly $(n d)$. In the case where k is small, this answers an open question of [Feldman WIDM’20] and [Munteanu and Schwiegelshohn, Künstliche Intell. ’18] on whether it is possible to efficiently compute coresets deterministically.We also construct a deterministic algorithm for computing $(1+$ $\varepsilon)$-approximation to k-median and k-means in high dimensional Euclidean spaces in time $2^{k^{2} \log ^{3} k / \varepsilon^{O(1)}}$ poly $(n d)$, close to the best randomized complexity of $2^{(k / \varepsilon)^{O(1)}}$ nd (see [Kumar, Sabharwal, Sen, JACM 10] and [Bhattacharya, Jaiswal, Kumar, TCS’18]).Furthermore, our new insights on sketches also yield a randomized coreset construction that uses uniform sampling, that immediately improves over the recent results of [Braverman et al. FOCS ’22] by a factor k.},
  author       = {Cohen-Addad, Vincent and Saulpic, David and Schwiegelshohn, Chris},
  booktitle    = {2023 IEEE 64th Annual Symposium on Foundations of Computer Science},
  location     = {Santa Cruz, CA, United States},
  pages        = {1105--1130},
  publisher    = {IEEE},
  title        = {{Deterministic clustering in high dimensional spaces: Sketches and approximation}},
  doi          = {10.1109/focs57990.2023.00066},
  year         = {2023},
}