Trees with Convex Faces and Optimal Angles

  • Josiah Carlson
  • David Eppstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)


We consider drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons. Among all such drawings we seek the one maximizing the angular resolution of the drawing. We find linear time algorithms for solving this problem, both for plane trees and for trees without a fixed embedding. In any such drawing, the edge lengths may be set independently of the angles, without crossing; we describe multiple strategies for setting these lengths.


Edge Length Voronoi Diagram Angular Resolution Optimal Angle Root Edge 
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  1. 1.
    Liotta, G., Meijer, H.: Voronoi drawings of trees. Computational Geometry: Theory and Applications 24(3), 147–178 (2003)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Malitz, S.: On the angular resolution of planar graphs. In: Proc. 24th ACM Symp. Theory of Computing, pp. 527–538. ACM Press, New York (1992)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Josiah Carlson
    • 1
  • David Eppstein
    • 1
  1. 1.Computer Science Department, University of California, Irvine 

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