【11-10】SKLCS Seminar on "Local Search for Clustering in Almost-linear Time"
文章来源： | 发布时间：2025-11-07 | 【打印】 【关闭】
| Title: | Local Search for Clustering in Almost-linear Time |
| Speaker: | 金耀楠, 华为泰勒实验室 |
| Time: | 2025年11月10日 上午10:00-11:00 |
| Venue: | 中国科学院软件研究所五号楼，334会议室 |
| Abstract: | We propose the first {\em local search} algorithm for Euclidean clustering that attains an $O(1)$-approximation in almost-linear time. Specifically, for Euclidean k-Means, our algorithm achieves an $O(c)$-approximation in $\tilde{O}(n^{1 + 1 / c})$ time, for any constant $c \ge 1$, maintaining the same running time as the previous (non-local-search-based) approach [la~Tour and Saulpic, arXiv'2407.11217] while improving the approximation factor from $O(c^{6})$ to $O(c)$. The algorithm generalizes to any metric space with sparse spanners,delivering efficient constant approximation in $\ell_p$ metrics,doubling metrics,Jaccard metrics,etc. This generality derives from our main technical contribution: a local search algorithm on general graphs that obtains an $O(1)$-approximation in almost-linear time. We establish this through a new $1$-swap local search framework featuring a novel swap selection rule. At a high level, this rule ``scores'' every possible swap, based on both its modification to the clustering and its improvement to the clustering objective, and then selects those high-scoring swaps. To implement this, we design a new data structure for maintaining approximate nearest neighbors with amortized guarantees tailored to our framework. |
| Bio: | Yaonan Jin is a full-time researcher at the Huawei TCS Lab (lead by Pinyan Lu). His research interests encompass Theoretical Computer Science, with an emphasis on Algorithmic Economics. Before joining Huawei,he obtained his PhD from Columbia University in 2023 (advised by Xi Chen and Rocco Servedio). Before that,he obtained his MPhil from Hong Kong University of Science and Technology in 2019 (advised by Qi Qi) and his BEng from Shanghai Jiao Tong University in 2017. |
