2 research outputs found
Tighter Upper Bounds for the Minimum Number of Calls and Rigorous Minimal Time in Fault-Tolerant Gossip Schemes
The gossip problem (telephone problem) is an information dissemination
problem in which each of nodes of a communication network has a unique
piece of information that must be transmitted to all the other nodes using
two-way communications (telephone calls) between the pairs of nodes. During a
call between the given two nodes, they exchange the whole information known to
them at that moment. In this paper we investigate the -fault-tolerant gossip
problem, which is a generalization of the gossip problem, where at most
arbitrary faults of calls are allowed. The problem is to find the minimal
number of calls needed to guarantee the -fault-tolerance. We
construct two classes of -fault-tolerant gossip schemes (sequences of calls)
and found two upper bounds of , which improve the previously known
results. The first upper bound for general even is . This result is used to obtain the upper bound
for general odd . From the expressions for the second upper bound it follows
that for large . Assuming that the calls can
take place simultaneously, it is also of interest to find -fault-tolerant
gossip schemes, which can spread the full information in minimal time. For even
we showed that the minimal time is .Comment: 19 pages, 5 figure