On the Factor Revealing LP Approach for Facility Location with Penalties
We consider the uncapacitated facility location problem with (linear) penalty function and show that a modified JMS algorithm, combined with a randomized LP rounding technique due to Byrka-Aardal, Li and Li et al. yields 1.488 approximation, improving the factor 1.5148 due to Li et al.. This closes the current gap between the classical facility location problem and this penalized variant. Main ingredient is a straightforward adaptation of the JMS algorithm to the penalty setting plus a consistent use of the upper bounding technique for factor revealing LPs due to Fernandes et al.. In contrast to the bounds in , our factor revealing LP is monotone.