Facility location with hierarchical facility costs

摘要

We introduce a facility location problem with submodular facility cost functions, and give an O(log n) approximation algorithm for it. Then we focus on a special case of submodular costs, called hierarchical facility costs, and give a (4.237 + ε)-approximation algorithm using local search. The hierarchical facility costs model multilevel service installation. Shmoys et al. [2004] gave a constant factor approximation algorithm for a two-level version of the problem. Here we consider a multilevel problem, and give a constant factor approximation algorithm, independent of the number of levels, for the case of identical costs on all facilities.