Straight-Line Orthogonal Drawings of Binary and Ternary Trees

  • Fabrizio Frati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)

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(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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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Fabrizio Frati
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità di Roma Tre 

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