An improved PTAS approximation algorithm for k-means clustering problem

Abstract

This paper presented an improved (1+ε)-randomized approximation algorithm proposed by Ostrovsky. The running time of the improved algorithm is O(2(O(kα²/ε))nd), where d,n denote the dimension and the number of the input points respectively, and α(<;1) represents the separated coefficient. The successful probability is (1/2(1-e^(1/2ε)))k(1-O(√α)). Compared to the original algorithm, the improved algorithm runs more efficiency.