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Improved approximation algorithm for k-level UFL with penalties, a simplistic view on randomizing the scaling parameter
The state of the art in approximation algorithms for facility location
problems are complicated combinations of various techniques. In particular, the
currently best 1.488-approximation algorithm for the uncapacitated facility
location (UFL) problem by Shi Li is presented as a result of a non-trivial
randomization of a certain scaling parameter in the LP-rounding algorithm by
Chudak and Shmoys combined with a primal-dual algorithm of Jain et al. In this
paper we first give a simple interpretation of this randomization process in
terms of solving an aux- iliary (factor revealing) LP. Then, armed with this
simple view point, Abstract. we exercise the randomization on a more
complicated algorithm for the k-level version of the problem with penalties in
which the planner has the option to pay a penalty instead of connecting chosen
clients, which results in an improved approximation algorithm