Straight-Line Orthogonal Drawings of Binary and Ternary Trees

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


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.


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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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