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The Complexity Of The Network Design Problem

Author

Listed:
  • Johnson, D. S.
  • Lenstra, J. K.
  • Rinnooy Kan, A. H. G.

Abstract

In the network design problem we are given a weighted undirected graph. We wish to find a subgraph which connects all the original vertices and minimizes the sum of the shortest path weights between all vertex pairs, subject to a budget constraint on the sum of its edge weights. In this note we establish NP-completeness for the network design problem, even for the simple case where all edge weights are equal and the budget restricts the choice to spanning trees. This result justifies the development of enumerative optimization methods and of approximation algorithms, such as those described in a recent paper by R. Dionne and M. Florian.

Suggested Citation

  • Johnson, D. S. & Lenstra, J. K. & Rinnooy Kan, A. H. G., 1977. "The Complexity Of The Network Design Problem," Econometric Institute Archives 272157, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272157
    DOI: 10.22004/ag.econ.272157
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