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The Steiner Ratio of finite-dimensional Lp-spaces

  • Jens Albrecht
  • Dietmar Cieslik
Part of the Combinatorial Optimization book series (COOP, volume 6)

Abstract

Starting with the famous book “What is Mathematics” by Courant and Robbins the following problem has been popularized under the name of S t einer : For a given finite set of points in a metric space find a network which connects all points of the set with minimal length. Such a network must be a tree, which is called a Steiner Minimal Tree (SMT). It may contain vertices other than the points which are to be connected. Such points are called Steiner points.1 A classical survey of this problem in the Euclidean plane was given by Gilbert and Pollak [9]. An updated one can be found in [13].

Keywords

Minimum Span Tree Steiner Tree Euclidean Plane Steiner Point Isometric Embedding 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Jens Albrecht
    • 1
  • Dietmar Cieslik
    • 1
  1. 1.Institute of Mathematics and C.S.University of GreifswaldGermany

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