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Random exchanges of information

Published online by Cambridge University Press:  14 July 2016

David W. Boyd  and
J. Michael Steele
David W. Boyd
Affiliation:
The University of British Columbia
J. Michael Steele*
Affiliation:
The University of British Columbia
*
∗ Postal address: Department of Mathematics, The University of British Columbia, 2075 Wesbrook Mall, Vancouver, B.C. Canada V6T 1W5.
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Abstract

Suppose that n persons each know a different piece of information, and that whenever a pair of persons talk on the telephone each tells the other all the information that he knows at the time. If calls are made at random, we show that the expected number of calls necessary until everyone knows all n pieces of information is asymptotically 1.5 n log n. This sharpens an earlier result of J. W. Moon.

Keywords

CONTAGIONRANDOM MATRIXTELEPHONE PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 657 - 661
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

∗∗

Present address: Department of Statistics, Stanford University, Stanford, CA 94305, U.S.A. Research supported in part by the National Research Council of Canada.

References

[1] Bumby, R. T. and Spencer, J. Unpublished paper cited in [2].Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Wiley, New York.Google Scholar
[3] Hajnal, A., Milner, E. C. and Szemeredi, E. (1972) A cure for the telephone disease. Canad. Math. Bull. 15, 447–450.Google Scholar
[4] Moon, J. W. (1972) Random exchanges of information. Nieuw Arch. Wisk. 20, 246–249.Google Scholar
[5] Tijdeman, R. (1971) On a telephone problem. Nieuw Arch. Wisk. 19, 188–192.Google Scholar