Minimax regret vertex centdian location problem in general dynamic networks

In this paper, we consider the minimax regret centdian location problem in general dynamic networks with positive edge lengths and interval vertex weights, where the centdian point should be located on a vertex only. Let G=(V,E) be an undirected connected simple graph with n vertices. Each vertex has a weight that is not known precisely, but the interval to which it belongs is given. A particular assignment of a weight to each vertex is called a scenario. The problem requires that a vertex x should be determined as the minimax regret centdian on the graph, such that the maximum regret of the objective function for all possible scenarios is minimized. We present an O(n3log n) time algorithm for solving this problem. Several computational experiments are also discussed.