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Random exchanges of information

Published online by Cambridge University Press:  14 July 2016

John Haigh
John Haigh*
Affiliation:
University of Sussex
*
∗Postal address: Mathematics Division, School of Mathematical and Physical Sciences, The University of Sussex, Falmer, Brighton BN1 9QH, U.K.
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Abstract

Suppose that n persons each know a different piece of information, and that, whenever a pair of them talk on the telephone, each tells the other all the information he knows at that time. If the calls are made at random, we show that the expected number of calls required for everyone to know all n pieces of information is asymptotically 1.5 n log n + O(n). This sharpens an earlier result of D. W. Boyd and J. M. Steele. Some numerical comparisons are given.

Keywords

CONTAGIONRANDOM MATRIXTELEPHONE PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 743 - 746
Copyright
Copyright © Applied Probability Trust 

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References

Boyd, D. W. and Steele, J. M. (1979) Random exchanges of information. J. Appl. Prob. 16, 657–661.CrossRefGoogle Scholar
Moon, J. W. (1972) Random exchanges of information. Nieuw. Arch. Wisk. 20, 246–249.Google Scholar