On the minmax regret path median problem on trees

This paper studies the problem of finding the path median on a tree in which vertex weights are uncertain and the uncertainty is characterized by given intervals. It is required to find a minmax regret solution, which minimizes the worst-case loss in the objective function. An O ( n 2 ) -time algorithm is presented, improving the previous upper bound from O ( n 4 ) . We study the minmax regret path median problem on a tree.The weight of each vertex is uncertain and is characterized by an interval.It is required to find a solution minimizing the worst-case loss.An improved O ( n 2 ) -time algorithm is presented.