SMT and MST in Metric Spaces — A Survey

  • Dietmar Cieslik
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 23)


Here, we describe several basic facts about the combinatorial and computational structure of SMT’s and MST’s. Since we first consider arbitrary metric spaces we state only some general facts, namely
  1. (i)

    An SMT for n given points has at most n — 2 Steiner points.

  2. (ii)

    For any finite set N of points in a metric space the length of an MST for N is less than two times of the length of an SMT for N.

  3. (iii)

    Isometric spaces are not distinguished in the sense of Steiner’s Problem.



Short Path Span Tree Minimum Span Tree Voronoi Diagram Delaunay Triangulation 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Dietmar Cieslik
    • 1
  1. 1.Ernst-Moritz-Arndt UniversityGreifswaldGermany

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