Variants of Spreading Messages

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In a distributed computing environment a faulty node could lead other nodes in the system to behave in a faulty manor. An initial set of faults could make all the nodes in the system become faulty. Such a set is called an irreversible dynamo. This is modelled as spreading a message among individuals V in a community \(G=\left( V,E\right) \) where E represents the acquaintance relation. A particular individual will believe a message if some of the individual’s acquaintances believe the same and forward the believed messages to its neighbours. We are interested in finding the minimum set of initial individuals to be considered as convinced, called the min-seed, such that every individual in the community is finally convinced. We solve for min-seed on some special classes of graphs and then give an upper bound on the cardinality of the min-seed for arbitrary undirected graphs. We consider some interesting variants of the problem and analyse their complexities and give some approximate algorithms.