Spreading of Messages in Random Graphs

Chang and Lyuu [Chang and Lyuu, 2008] study the spreading of a message in an Erd˝os-R´enyi 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 [Chang and Lyuu, 2008], 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. Our main results are that min-seed(n, p) = Ω min n, p2 n2 and min-seed(n, p) = Ω n2/3 hold with high probability. We also consider the case of random seeds. 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 ver...

• Type: Journal
• Year: 2011
• Where: MST
• Authors: Ching-Lueh Chang, Yuh-Dauh Lyuu
• Keywords: Erd˝os-R´enyi Random Graph, Hardware, MST 2011, Random, Strictmajority Scenario