Discrete & Computational Geometry

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

On optimal realizations of finite metric spaces by graphs

  • Ingo Althöfer


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.


Short Path Discrete Comput Geom Weighted Graph Common Endpoint Unweighted Graph 
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

© 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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