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Geometric Conditions for Euclidean Steiner Trees in d Jon W. Van Laarhoven
 

Summary: Geometric Conditions for Euclidean Steiner Trees in d
Jon W. Van Laarhoven
Department of Applied Mathematics and Computational Sciences
University of Iowa, Iowa City, IA 52242
jon-vanlaarhoven@uiowa.edu
Kurt M. Anstreicher
Department of Management Sciences
University of Iowa, Iowa City, IA 52242
kurt-anstreicher@uiowa.edu
July 1, 2010
Abstract
We present geometric conditions that can be used to restrict or eliminate candidate topologes for
Euclidean Steiner minimal trees in d
, d 2. Our emphasis is on conditions that are not restricted
to the planar case (d = 2). For trees with a Steiner topology we give restrictions on terminal-Steiner
connections that are based on the Voronoi diagram associated with the set of terminal nodes. We then
describe more restrictive conditions for trees with a full Steiner topology and show how these conditions
can be used to improve implicit enumeration algorithms for finding Euclidean Steiner minimal trees with
d > 2.
Keywords: Euclidean Steiner tree, branch and bound, Voronoi diagram, Delaunay trian-

  

Source: Anstreicher, Kurt M. - Department of Computer Science, University of Iowa

 

Collections: Computer Technologies and Information Sciences