Straight-line orthogonal drawings of binary and ternary trees

Abstract

In this paper we provide upper and lower bounds on the area requirement of straight-line orthogonal drawings of n-node binary and ternary trees. Namely, we show algorithms for constructing order-preserving straight-line orthogonal drawings of binary trees in O(n 1.5) area, straight-line orthogonal drawings of ternary trees in O(n 1.631) area, and straight-line orthogonal drawings of complete ternary trees in O(n 1.262) area. As far as we know, the ones we present are the first algorithms achieving sub-quadratic area for these problems. Further, for upward order-preserving straight-line orthogonal drawings of binary trees and for order-preserving straight-line orthogonal drawings of ternary trees we provide Ω(n 2) area lower bounds, that we also prove to be tight. © 2008 Springer-Verlag Berlin Heidelberg.