Journal of Global Optimization

, Volume 35, Issue 4, pp 573–592 | Cite as

Approximations and Lower Bounds for the Length of Minimal Euclidean Steiner Trees

  • J. H. Rubinstein
  • J. Weng
  • N. WormaldEmail author


We give a new lower bound on the length of the minimal Steiner tree with a given topology joining given terminals in Euclidean space, in terms of toroidal images. The lower bound is equal to the length when the topology is full. We use the lower bound to prove bounds on the “error” e in the length of an approximate Steiner tree, in terms of the maximum deviation d of an interior angle of the tree from 120°. Such bounds are useful for validating algorithms computing minimal Steiner trees. In addition we give a number of examples illustrating features of the relationship between e and d, and make a conjecture which, if true, would somewhat strengthen our bounds on the error.


Equilateral Triangle Steiner Tree Steiner Point Angle Error Steiner Tree Problem 
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 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneAustralia
  2. 2.ARC Special Research Center for Ultra-Broadband Information Networks (CUBIN) Department of Electrical and Electronic EngineeringUniversity of MelbourneAustralia
  3. 3.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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