Improved Approximation Algorithm for the Distributed Lower-Bounded k-Center Problem

Ting Liang, Qilong Feng, Xiaoliang Wu, Jinhui Xu, Jianxin Wang

Abstract: Clustering large data is a fundamental task with widespread applications. The distributed computation methods have received greatly attention in recent years due to the increasing size of data. In this paper, we consider a variant of the widely used k-center problem, i.e., the lower-bounded k-center problem, and study the lower-bounded k-center problem in the Massively Parallel Computation (MPC) model. The lower-bounded k-center problem takes as input a set C of points in a metric space, the desired number k of centers, and a lower bound L. The goal is to partition the set C into at most k clusters such that the number of points in each cluster is at least L, and the k-center clustering objective is minimized. The current best result for the above problem in the MPC model is 16-approximation algorithm with 4 rounds. In this paper, we obtain a 2-round \((7+\epsilon )\)-approximation algorithm for this problem in the MPC model.