In this paper, we study the linear space structure necessary to perform planar point location for connected planar subdivisions in near-logarithmic query and update time. The paper is decomposed into non-recursive and recursive descriptions. Due to the paper's length and density we will only explore the non-recursive description which details the process of building a linear-space multi-colored segment tree that achieves O(logn(loglogn)2) query time and O(lognloglogn) update time.
(Based on a paper by T. Chan and Y. Nekrich from FOCS 2015.)