C-sensitive triangulations approximate the minmax length triangulation

  • Christos Levcopoulos
  • Andrzej Lingas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 652)


We introduce the notion of a c-sensitive triangulation based on the local notion of a c-sensitive triangulation edge. We show that any c-sensitive triangulation of a planar point set approximates the minmax length triangulation of the set within the factor 2(c+1). On the other hand we prove that the greedy triangulation and the Dclaunay triangulation of a planar straight-line graph are respectively 4-sensitive and 1-sensitive. We also generalize the relationship between c-sensitive triangulations and the minmax length triangulation to include appropriately augmented planar straight-line graphs. This enables us to obtain a O(n) log n)-time heuristic for the minmax length triangulation of an arbitrary planar straight-line graph with the approximation factor bounded by 3. A modification of the above heuristic for simple polygons runs in linear time.


Linear Time Voronoi Diagram Delaunay Triangulation Convex Polygon Simple Polygon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Christos Levcopoulos
    • 1
  • Andrzej Lingas
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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