Spreading of Messages in Random Graphs

Chang, C.-L. and Lyuu, Y.-D.

Chang and Lyuu study the spreading of a message in an Erdos-Renyi random graph G(n, p) starting from a set of vertices that are convinced of the message initially. In their strictmajority scenario, whenever more than half of the neighbors of a vertex v are convinced of a message, v itself also becomes convinced. The spreading proceeds asynchronously until no more vertices can be convinced. Following Chang and Lyuu, we derive lower bounds on the minimum number min-seed(n, p) of vertices that need to be convinced initially so that all vertices will be convinced at the end. For any sufficiently large constant d > 0 and any s <= n/(d ln n), we show that if one picks the set of seeds uniformly at random from the family of all s-sized sets, then with high probability, not all vertices will be convinced at the end.
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Cite as: Chang, C.-L. and Lyuu, Y.-D. (2009). Spreading of Messages in Random Graphs. In Proc. Fifteenth Computing: The Australasian Theory Symposium (CATS 2009), Wellington, New Zealand. CRPIT, 94. Downey, R. and Manyem, P., Eds. ACS. 3-7.

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