Discrete & Computational Geometry

, Volume 11, Issue 2, pp 163–191

Approximating the minimum weight steiner triangulation

  • David Eppstein

DOI: 10.1007/BF02574002

Cite this article as:
Eppstein, D. Discrete Comput Geom (1994) 11: 163. doi:10.1007/BF02574002


We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. InO(n logn) time we can compute a triangulation withO(n) new points, and no obtuse triangles, that approximates the MWST. We can also approximate the MWST with triangulations having no sharp angles. We generalize some of our results to higher-dimensional triangulation problems. No previous polynomial-time triangulation algorithm was known to approximate the MWST within a factor better thanO(logn).

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • David Eppstein
    • 1
  1. 1.Department of Information and Computer ScienceUniversity of CaliforniaIrvineUSA