Before revision:   ]  Gawrychowski, Landau, Sung, and Weimann [ICALP'18] devise a greedy algorithm that runs in time O(n^{1.5}\log n) based on micro-macro decomposition .
After revision:  Given a rooted tree t and another tree T, one would like to incorporate compatible information from T to t. This problem is a subproblem in the tree refinement problem called the RF-Optimal Tree Refinement Problem defined by in Christensen, Molloy, Vachaspati and Warnow ] Gawrychowski, Landau, Sung, and Weimann [ICALP'18] devise a greedy algorithm that runs in time O(n^{1.5}\log n) based on micro-macro decomposition .