Abstract
We model a network in which messages spread by a simple directed graph G = (V,E) [8] and a function α: V→ℕ mapping each v ∈ V to a positive integer less than or equal to the indegree of v. The graph G represents the individuals in the network and the communication channels between them. An individual v ∈ V will be convinced of a message when at least α(v) of its in-neighbors are convinced. Suppose we are to convince a message to all individuals by convincing a subset S ⊆ V of individuals at the beginning and then let the message spread. We study minimum-sized sets S needed to convince all individuals at the end. In particular, our results include a lower bound on the size of a minimum S and the NP-completeness of computing a minimum S. Our lower bound utilizes a technique in [9]. Finally, we analyze the special case where each individual is convinced of a message when more than half of its in-neighbors are convinced.
The authors are supported in part by NSC grant 96-2213-E-002-024.
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Chang, CL., Lyuu, YD. (2008). Spreading Messages. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_58
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DOI: https://doi.org/10.1007/978-3-540-69733-6_58
Publisher Name: Springer, Berlin, Heidelberg
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