In this paper we consider the edge ranking problem of weighted trees. We prove that a special instance of this problem, namely edge ranking of multitrees is NP-hard already for multitrees with diameter at most 10. Note that the same problem but for trees is linearly solvable. We give an O ( log n )-approximation polynomial time algorithm for edge ranking of weighted trees. © 2005 Elsevier B.V. All rights reserved.
Dereniowski, D. (2006). Edge ranking of weighted trees. Discrete Applied Mathematics, 154(8), 1198–1209. https://doi.org/10.1016/j.dam.2005.11.005