On gossiping with faulty telephone lines.

*(English)*Zbl 0626.05033In the well-known gossip problem, each of n gossips initially has a unique piece of information. The gossips can make a sequence of two-party telephone calls in which the two participants exchange every piece of information they have at the time of the call. The problem is to determine a minimum length sequence of telephone calls such that, by the end, everyone knows everyone else’s information. We consider K. A. Berman and M. Hawrylycz’s variation on this problem [ibid. 7, 13- 17 (1986; Zbl 0578.05059)]. They introduce the additional feature that as many as k of the calls may fail in the sense that no information is exchanged, where k is a second parameter of the problem. We improve upon their upper bound on the minimum number of calls needed. This disproves a conjecture in the same paper. We also briefly consider the parallel complexity of this problem.

##### Keywords:

telephone problem; fault-tolerant communication; gossip problem; minimum length sequence; telephone calls
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\textit{R. W. Haddad} et al., SIAM J. Algebraic Discrete Methods 8, 439--445 (1987; Zbl 0626.05033)

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