Pointed Binary Encompassing Trees

  • Michael Hoffmann
  • Bettina Speckmann
  • Csaba D. Tóth
Conference paper

DOI: 10.1007/978-3-540-27810-8_38

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3111)
Cite this paper as:
Hoffmann M., Speckmann B., Tóth C.D. (2004) Pointed Binary Encompassing Trees. In: Hagerup T., Katajainen J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg


We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing treeT, that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex vT is pointed, that is, v has an incident angle greater than π. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follows that every set of disjoint line segments has a minimum pseudo-triangulation of bounded vertex degree.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michael Hoffmann
    • 1
  • Bettina Speckmann
    • 2
  • Csaba D. Tóth
    • 3
  1. 1.Institute of Theoretical Computer ScienceETH Zürich 
  2. 2.Department of Mathematics and Computer ScienceTU Eindhoven 
  3. 3.Department of Computer ScienceUniversity of California at Santa Barbara 

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