Hierarchical Facility Costs Optimal Methods Based on Disperse Move

In this paper, we study a variant of the facility location problem where facility cost depends on the set of clients assigned to the facility and the local search method. Consider the facility location problem with hierarchical facility costs, and give the first constant factor approximation algorithm for the problem independent of the number of levels in the hierarchy tree. By using the disperse moves to show that a constant factor approximation algorithm for the facility location problem with hierarchical facility costs, which a locally optimal solution is a 5-approximation for the problem. The algorithm for the problem independent of the number of levels in the hierarchy tree, for the case of identical costs on all facilities. We also propose a general model in which the facility costs are submodular functions of the set of clients assigned to the facility, where submodularity models a natural economy of scale. The generalization of our problem in which the facility costs are allowed to differ from each other by constant factors can model data gathering in sensor networks and data storage.