Randomized algorithms
Neural Networks: A Comprehensive Foundation
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Propagation of trust and distrust
Proceedings of the 13th international conference on World Wide Web
A survey of trust in computer science and the Semantic Web
Web Semantics: Science, Services and Agents on the World Wide Web
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
A survey of trust in internet applications
IEEE Communications Surveys & Tutorials
Dynamic monopolies with randomized starting configuration
Theoretical Computer Science
Variants of spreading messages
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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Chang and Lyuu [Chang and Lyuu, 2008] study the spreading of a message in an Erdős-Rényi random graph G(n, p) starting from a set of vertices that are convinced of the message initially. In their strict-majority 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, p2n2}) 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 vertices will be convinced at the end.