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On gossiping with faulty telephone lines. (English) Zbl 0626.05033
In 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.

MSC:
05C38 Paths and cycles
94C15 Applications of graph theory to circuits and networks
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