Straight Line Orthogonal Drawings of Complete Ternery Trees

In this paper we study embeddings of complete ternary trees in a 2-D lattice. Suppose we are given an n-node complete ternary tree Tn with height h. We can construct an embedding of Th on a 2-D lattice L so that every node in Th corresponds to a vertex in L, and every edge in Th corresponds to a horizontal or vertical path in the lattice. We provide a better upper bound on the area requirement of straight-line orthogonal drawings of ternery trees, namely O(n) area. Further, we consider abstract configurations of ternary trees, where subtrees of level h − k for an integer h < k are modeled by disjoint boxes, providing lower bounds on the space requirements for Th.