Minimax regret 1-sink location problem in dynamic cycle networks

In this paper, we consider the minimax regret 1-sink location problem in a dynamic cycle network with positive edge lengths and uniform edge capacity. Let C be an undirected cycle graph of n vertices and n edges. Each edge has a positive edge length and a uniform edge capacity. Each vertex has a weight which is not known exactly but we know the interval it belongs to. The problem is to find a point x as the sink on the cycle and all weights evacuate to x such that the maximum regret for all possible weight distributions is minimized. This paper presents an O(ⁿ³ logn) time algorithm.