Abstract
We consider the following multi–level opinion spreading model on networks. Initially, each node gets a weight from the set {0,…,k − 1}, where such a weight stands for the individuals conviction of a new idea or product. Then, by proceeding to rounds, each node updates its weight according to the weights of its neighbors. We are interested in the initial assignments of weights leading each node to get the value k − 1 –e.g. unanimous maximum level acceptance– within a given number of rounds. We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules, where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bermond, J.C., Bond, J., Peleg, D., Perennes, S.: Tight bounds on the size of 2-monopolies. In: SIROCCO, pp. 170–179 (1996)
Bermond, J.C., Bond, J., Peleg, D., Perennes, S.: The power of small coalitions in graphs. Discrete Applied Mathematics 127(3), 399–414 (2003)
Bermond, J.C., Gargano, L., Rescigno, A.A., Vaccaro, U.: Fast Gossiping by Short Messages. SIAM J. on Computing 27(4), 917–941 (1998)
Brunetti, S., Lodi, E., Quattrociocchi, W.: Dynamic monopolies in colored tori. In: IPDPS Workshops, pp. 626–631 (2011)
Chen, N.: On the approximability of influence in social networks. SIAM J. Discret. Math. 23, 1400–1415 (2009)
Domingos, P., Richardson, M.: Mining the network value of customers. In: KDD 2001: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA, pp. 57–66 (2001)
Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press (2010)
Flocchini, P., Královič, R., Ružička, P., Roncato, A., Santoro, N.: On time versus size for monotone dynamic monopolies in regular topologies. J. of Discrete Algorithms 1(2), 129–150 (2003)
Granovetter, M.: Economic action and social structure: the problem of embeddedness. American Journal of Sociology 91 (1985)
Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: KDD 2003: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146. ACM, New York (2003)
Kulich, T.: Dynamic monopolies with randomized starting configuration. Theor. Comput. Sci. 412(45), 6371–6381 (2011)
Linial, N., Peleg, D., Rabinovich, Y., Saks, M.: Sphere packing and local majorities in graphs. In: ISTCS, pp. 141–149. IEEE Computer Soc. Press (1993)
Mishra, S., Rao, S.B.: Minimum monopoly in regular and tree graphs. Electronic Notes in Discrete Mathematics 15(0), 126 (2003)
Nayak, A., Pagli, L., Santoro, N.: Efficient construction of catastrophic patterns for vlsi reconfigurable arrays with bidirectional links. In: ICCI, pp. 79–83 (1992)
Peleg, D.: Size bounds for dynamic monopolies. Discrete Applied Mathematics 86(2-3), 263–273 (1998)
Peleg, D.: Local majorities, coalitions and monopolies in graphs: a review. Theor. Comput. Sci. 282(2), 231–257 (2002)
Valente, T.W.: Network models of the diffusion of innovations. Hampton Press (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brunetti, S., Cordasco, G., Gargano, L., Lodi, E., Quattrociocchi, W. (2012). Minimum Weight Dynamo and Fast Opinion Spreading. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-34611-8_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34610-1
Online ISBN: 978-3-642-34611-8
eBook Packages: Computer ScienceComputer Science (R0)