Discrete & Computational Geometry

, Volume 3, Issue 2, pp 103–122 | Cite as

On optimal realizations of finite metric spaces by graphs

  • Ingo Althöfer
Article

Abstract

Graph realizations of finite metric spaces have widespread applications, for example, in biology, economics, and information theory. The main results of this paper are:
  1. 1.

    Finding optimal realizations of integral metrics (which means all distances are integral) is NP-complete.

     
  2. 2.

    There exist metric spaces with a continuum of optimal realizations.

     

Furthermore, two conditions necessary for a weighted graph to be an optimal realization are given and an extremal problem arising in connection with the realization problem is investigated.

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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Ingo Althöfer
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldFederal Republic of Germany

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