Gradient-Constrained Minimum Interconnection Networks

  • Marcus Brazil
  • Marcus G. Volz
Reference work entry


In two- or three-dimensional space, an embedded network is called gradient constrained if the absolute gradient of any differentiable point on the edges in the network is no more than a given value m. This chapter gives an overview of the properties of gradient-constrained networks that interconnect a given set of points and that minimize some property of the network, such as the total length of edges. The focus is particularly on geometric Steiner and Gilbert networks. These networks are of interest both mathematically and for their applications to the design of underground mines.


Vertical Plane Minkowski Space Steiner Tree Steiner Point Steiner 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.



The research for and writing of this chapter was supported by an ARC Linkage Grant. We gratefully acknowledge the contributions of our collaborators to much of the theory described in this chapter, particularly Professor Doreen Thomas at The University of Melbourne.

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringThe University of MelbourneParkvilleAustralia
  2. 2.TSG ConsultingMelbourneAustralia

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