Linear-time algorithm for the tree case

Determine whether the restricted inverse optimal value problem on shortest paths under the weighted l∞ norm on trees admits an O(n)-time algorithm, improving on the two O(n log n)-time algorithms developed in the paper.

Background

The paper presents two exact algorithms for the tree-based restricted inverse optimal value problem, and both have O(n log n) running time. The authors explicitly leave unresolved whether the problem can be solved in linear time.