Shortest Networks for One Line and Two Points in Space

  • R. S. Booth
  • D. A. Thomas
  • J. F. Weng
Part of the Combinatorial Optimization book series (COOP, volume 6)


In this paper we study a new generalization of the Steiner tree problem: the shortest network interconnecting two points and a straight line in space. We prove that this shortest network, either with one access point on the line or the line being multi-accessible, can be computed exactly by solving a certain quartic equation. Moreover, we will show how Euclidean 3D-space can be partitioned into regions (point sets in space) which are defined by the topology of the Steiner minimal tree.


Access Point Steiner Tree Steiner Point Optimal Region Steiner Tree Problem 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • R. S. Booth
    • 1
  • D. A. Thomas
    • 2
  • J. F. Weng
    • 2
  1. 1.Department of Mathematics and StatisticsThe Flinders University of South AustraliaAdelaideAustralia
  2. 2.Department of Electrical and Electronic EngineeringThe University of MelbourneAustralia

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