Let P be an undirected path graph of n vertices. Each edge of P has a positive length and a constant capacity. Every vertex has a nonnegative supply, which is an unknown value but is known to be in a given interval. The goal is to find a point on P to build a facility and move all vertex supplies to the facility such that the maximum regret is minimized. The previous best algorithm solves the problem in O ( n log 2 n ) time and O ( n log n ) space. In this paper, we present an O ( n log n ) time and O ( n ) space algorithm, and our approach is based on new observations and algorithmic techniques. 
Minmax regret 1-facility location on uncertain path networks