An LP-Rounding Based Algorithm for a Uniform Capacitated Facility Location Problem with Penalties

Abstract

The capacitated constraint is a common variant in the field of combinatorial optimization. In the capcitated facility location problem, there is a limitation of service for each facility, that is, capacity. From the view of the approximation algorithm, this variant makes the algorithm difficult to design. Actually, the integral gap of the standard linear program for the capacitated facility location problem is infinite. That is, there is no LP-based constant approximation algorithm. In this work, we consider a special case of the uniform open cost for the capacitated facility location problem. Moreover, all clients are needed to be served. There is another variant of facility location problem called as “robust”. In this paper, we also consider one of the robust forms, named cpacitated facility location problem with penalties. We obtain an LP-based 5.732-approximation algorithm for a uniform capacitated facility location problem with penalties.