Geometric conditions for Euclidean Steiner trees in Rd

Authors:
Jon W. Van Laarhoven;Kurt M. Anstreicher
Affiliations:
Daniel H. Wagner Associates, 2 Eaton Street, Suite 500, Hampton, VA 23669, United States;Department of Management Sciences, University of Iowa, Iowa City, IA 52242, United States
Venue:
Computational Geometry: Theory and Applications
Year:
2013

Citing 5
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Abstract

We present geometric conditions that can be used to restrict or eliminate candidate topologies 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 d2.