Facility Leasing with Penalties
  In this paper we study the facility leasing problem with penalties. We present a primal-dual algorithm which is a 3-approximation, based on the algorithm by Nagarajan and Williamson for the facility leasing problem and on the algorithm by Charikar et al. for the facility location problem with penalties. 
Murilo S. de Lima, M\'ario C. San Felice, Orlando Lee
cs.DS