On the submodularity of influence in social networks

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On the submodularity of influence in social networks
We prove and extend a conjecture of Kempe, Kleinberg, and Tardos (KKT) on the spread of influence in social networks. A social network can be represented by a directed graph where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or "word-of-mouth" effects on such a graph is to consider an increasing process of "infected" (or active) nodes: each node becomes infected once an activation function of the set of its infected neighbors crosses a certain threshold value. Such a model was introduced by KKT in [7, 8] where the authors also impose several natural assumptions: the threshold values are (uniformly) random to account for our lack of knowledge of the true values; and the activation functions are monotone and submodular, i.e. have "diminishing returns." The monotonicity condition indicates that a node is more likely to become active if more of its neighbors ...
Elchanan Mossel, Sébastien Roch
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2007
Where STOC
Authors Elchanan Mossel, Sébastien Roch
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