A Linear Time Algorithm for Computing Minmax Regret 1-Median on a Tree

In a model of facility location problem, the uncertainty in the weight of a vertex is represented by an interval of weights, and minimizing the maximum “regret” is the goal. The most efficient previously known algorithm for finding the minmax regret 1-median on trees with positive vertex weights takes O(nlogn) time. We improve it to O(n), solving the open problem posed by Brodal et al. in [3].