Shortest Networks on Surfaces

  • J. F. Weng


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.


Minimal Span Tree Steiner Tree Euclidean Plane Steiner Point Steiner Tree Problem 
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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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