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Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems

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  • S. L. Hakimi

    (The Technological Institute, Northwestern University, Evanston, Illinois)

Abstract

The concept of a median in a weighted graph is generalized to a multimedian. Then, it is shown that the optimum distribution of p switching centers in a communication network is at a p -median of the corresponding weighted graph. The following related problem in highway networks is also considered: What is a minimum number of policemen that can be distributed in a highway network so that no one is farther away from a policeman than a given distance d ? This problem is attacked by generating all vertex-coverings (externally stable sets) of a graph by means of a Boolean function defined over the vertices of a graph. Then this idea is extended to Boolean functions that generate all matchings, all factors, and all possible subgraphs of G with given degrees.

Suggested Citation

  • S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    • Handle: RePEc:inm:oropre:v:13:y:1965:i:3:p:462-475
    DOI: 10.1287/opre.13.3.462
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