2020/02/18 by Davin Choo, Choo, Davin, Christoph Grunau +5 · 2 citations
Computer Science · #Complexity and Algorithms in Graphs #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.2002.07784
openalex publication_date 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The k-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is a state-of-the-art algorithm for solving the k-means clustering problem and is known to give an O(log k)-approximation in expectation. Recently, Lattanzi and Sohler (ICML 2019) proposed augmenting k-means++ with O(k log log k) local search steps to yield a constant approximation (in expectation) to the k-means clustering problem. In this paper, we improve their analysis to show that, for any arbitrarily small constant \eps > 0, with only \eps k additional local search steps, one can achieve a constant approximation guarantee (with high probability in k), resolving an open problem in their paper.