Straight-Line Orthogonal Drawings of Binary and Ternary Trees
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(n1.5) area, straight-line orthogonal drawings of ternary trees in O(n1.631) area, and straight-line orthogonal drawings of complete ternary trees in O(n1.262) 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(n2) area lower bounds, that we also prove to be tight.
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