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

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.