Nearly optimal monotone drawing of trees

The problem of finding monotone drawings for trees has been studied in several recent papers. The main focus is to reduce the size of the drawing. Currently, the smallest drawing size is O(n1.205)×O(n1.205). In this paper, we present an algorithm for constructing monotone drawing of trees on a grid of size at most O(nlog⁡n)×O(nlog⁡n).