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. Note that some of equations in this abstract may have been omitted or may be displayed incorrectly.

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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