An approximation algorithm for lower-bounded k-median with constant factor

Xiaoliang Wu, Feng Shi, Yutian Guo, Zhen Zhang, Junyu Huang, Jianxin Wang

Abstract: The lower-bounded k-median problem plays a key role in many applications related to privacy protection, which requires that the amount of assigned client to each facility should not be less than the requirement. Unfortunately, the lower-bounded clustering problem remains elusive under the widely studied k-median objective. Within this paper, we convert this problem to the capacitated facility location problem and successfully give a (516 + ϵ-approximation for this problem.