Computer Science – Social and Information Networks
Scientific paper
2011-05-12
Computer Science
Social and Information Networks
13 pages. Appeared in Proc. 4th International Symposium on Algorithmic Game Theory, (SAGT 2011), Lecture Notes in Computer Sci
Scientific paper
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize the graphs for which adoption of a product by the whole network is possible (respectively necessary) and the ones for which a unique outcome is guaranteed. These characterizations directly yield polynomial time algorithms that allow us to determine whether a given social network satisfies one of the above properties. We also study algorithmic questions for networks without unique outcomes. We show that the problem of computing the minimum possible spread of a product is NP-hard to approximate with an approximation ratio better than $\Omega(n)$, in contrast to the maximum spread, which is efficiently computable. We then move on to questions regarding the behavior of a node with respect to adopting some (resp. a given) product. We show that the problem of determining whether a given node has to adopt some (resp. a given) product in all final networks is co-NP-complete.
Apt Krzysztof R.
Markakis Evangelos
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