Yes, for , so case 3 might apply. There will be levels, with leaves at level l . In case 3 of the Master Theorem, the additive term dominates. In case 2, both parts contribute equally, which is why the log pops up. Since dwarfs , case 1 of the master theorem applies and .
Triangulation is an important first step in many geometric algorithms.
The simplest algorithm might be to try each pair of points and check if they see each other. If so, add the diagonal and recur on both halves, for a total of . However, Chazelle gave an algorithm which runs in time. Since , by case 1 of the Master Theorem, Chazelle's algorithm is linear, ie. Since but not , Case 2 of the Master Theorem applies and .