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On the addressing problem for directed graphs

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Abstract

The “distance” from vertexu to vertexv in a strongly connected digraph is the number of arcs in a shortest directed path fromu tov. The addressing problem, first formulated in the undirected case by Graham and Pollak, entails the assignment of a string of symbols to each vertex in such a way that the distances between vertices are equal to modified Hamming distances between corresponding strings.

A scheme for addressing digraphs is proposed, and the minimum address length is studied both in general and in certain special cases. The problem has some interesting reformulations in terms of matrix factorization and extremal set theory.

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References

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Author information

Authors and Affiliations

  1. Bell Communications Research, 07960, Morristown, NJ, USA

    F. R. K. Chung

  2. AT &T Bell Laboratories, 07974, Murray Hill, NJ, USA

    R. L. Graham

  3. Emory University, 30322, Atlanta, GA, USA

    P. M. Winkler

Authors
  1. F. R. K. Chung
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  2. R. L. Graham
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  3. P. M. Winkler
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Additional information

Supported by NSF grant MCS 84-02054.

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Chung, F.R.K., Graham, R.L. & Winkler, P.M. On the addressing problem for directed graphs. Graphs and Combinatorics 1, 41–50 (1985). https://doi.org/10.1007/BF02582927

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  • DOI: https://doi.org/10.1007/BF02582927

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