A Note on Optimal Area Algorithms for Upward Drawings of Binary Trees

Crescenzi, P., G. Di Battista and A. Piperno, A note on optimal area algorithms for upward drawings of binary trees, Computational Geometry: Theory and Applications 2 (1992) 187-200. The goal of this paper is to investigate the area requirements for upward grid drawings of binary trees. First, we show that there is a family of binary trees with n vertices that require Q(n logn) area; this bound is tight to within a costant factor, i.e. any binary tree with n vertices can be drawn in O(n logn) area. Then we present an algorithm for constructing an upward drawing of a complete binary tree with n vertices in O(n) area, and, finally, we extend this result to the drawings of Fibonacci trees.