Before revision:  Eiben et al. (ESA 2019) improved the running time to O(8^tt^5n^2\log n)  . Moreover, they showed that there is no O(n^{2-\varepsilon})-time algorithm for trees under some reasonable complexity assumption.
After revision:  Eiben et al. (ESA 2019) improved the dependency of n in the running time by giving an O(8^tt^5n^2\log n) . Moreover, they showed that there is no O(n^{2-\varepsilon})-time algorithm for trees under some reasonable complexity assumption.