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Shortest Networks on Surfaces

  • J. F. Weng
Chapter

Abstract

Suppose A = {a l, a 2, ... , a n } is a point set in a metric space M. The shortest network problem asks for a minimum length network S(A) that interconnects all points of A (called terminals), possibly with some additional points to shorten the network. S(A) must be a tree since it cannot contain any cycle for minimality. In the literature this problem is called the Steiner tree problem, and S(A) is called a Steiner minimal tree for A [9]. If no additional points are added, then the network, denoted by T(A), is called a minimal spanning tree on A. Sometimes these networks are simply denoted by S and T if no confusion is caused.

Keywords

Minimal Span Tree Steiner Tree Euclidean Plane Steiner Point 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

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • J. F. Weng
    • 1
  1. 1.Department of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia

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