Pointed binary encompassing trees: Simple and optimal

For n disjoint line segments in the plane we construct in optimal O(n log n) time and linear space an encompassing tree of maximum degree three such that at every vertex all incident edges lie in a halfplane defined by the incident input segment. In particular, this tree is pointed since every vertex has an incident angle greater than . Such a pointed binary tree can be augmented to a minimum pseudo-triangulation. It follows that every set of disjoint line segments in the plane has a constrained minimum pseudo-triangulation whose maximum vertex degree is bounded by a constant.

• Type: Journal
• Year: 2010
• Where: COMGEO
• Authors: Michael Hoffmann, Bettina Speckmann, Csaba D. Tóth
• Keywords: Applied Computing, COMGEO 2010, Disjoint Line Segments, Incident Input Segment, Minimum Pseudo-triangulation