Robust location problems with pos/neg weights on a tree

In this paper we consider diierent aspects of robust 1-median problems on a tree network with uncertain or dynamically changing edge lengths and vertex weights which can also take negative values. The dynamic nature of a parameter is modeled by a linear function of time. A linear algorithm is designed for the absolute dynamic robust 1-median problem on a tree. The dynamic robust deviation 1-median problem on a tree with n vertices can be solved in O(n 2 (n) log n) time. Both problems possess optimal solutions which are not vertices of the graph (contradicting a statement of Kouvelis and Yu). The uncertainty is modeled by given intervals, in which each parameter can take a value randomly. The robust 1-median problem with interval data, where vertex weights might be negative, can be solved in linear time. The corresponding deviation problem can be solved in O(n 2) time.