Approximation Algorithms for p-Hub Center Problems

We study the 3 p-hub center problems for which no approximation algorithm is known. The p-hub center problems are one of the four hub location problems defined by Campbell (1994). Hub location problems consider combined location and routing decisions. They model the location problems of logistics providers, especially for intermodal freight transport. Hub center problems are a subpart and focus on minimizing the maximal cost of a hub location objective. There are three variants of hub center problems with different objectives. In this paper, an approximation algorithm is constructed for the third p-hub center problem, which is a generalization of a k-center algorithm. In addition, this paper develops a reduction from the first and second p-hub center problems to the third p-hub center problem. Both results combined lead to a constant factor approximation algorithm for any phub center problem. In addition, this paper further improves these bounds for the problems' multi-allocation variant.