A polyhedral study of dynamic monopolies
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Spread of influence in a network can be modeled and studied within the concept of dynamic monopolies in graphs. We give an integer programming formulation for finding a minimum dynamic monopoly in an undirected graph. The corresponding 0–1 polytope and its facets are studied and several families of facet defining inequalities are introduced. Computational experiments have been performed to show the strength of the IP formulation and its facet defining inequalities.
KeywordsInteger programming Dynamic monopoly Facets
Mathematics Subject Classification90C10 05C69 90C57
- Chang, C. L., & Lyuu, Y. D. (2013). Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades. Theoretical Computer Science, 468, 37–49. https://doi.org/10.1016/j.tcs.2012.11.016, http://www.sciencedirect.com/science/article/pii/S0304397512010468.
- Flocchini, P., Lodi, E., Luccio, F., Pagli, L., & Santoro, N. (2004). Dynamic monopolies in Tori. Discrete Applied Mathematics 137(2):197–212. https://doi.org/10.1016/S0166-218X(03)00261-0, 1st international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN ’99)
- Günneç, D., Raghavan, S., & Zhang, R. (2017). Tailored incentives and least cost influence maximization on social networks. http://terpconnect.umd.edu/~raghavan/preprints/LCIP.pdf
- Khoshkhah, K., Soltani, H., & Zaker, M. (2012). On dynamic monopolies of graphs: the average and strict majority thresholds. Discrete Optimization 9(2):77–83. http://www.sciencedirect.com/science/article/pii/S1572528612000151
- Nemhauser, G., & Wolsey, L. (1999). Integer and combinatorial optimization. Wiley-interscience series in discrete mathematics and optimization. New York: Wiley, reprint of the 1988 original, A Wiley-Interscience PublicationGoogle Scholar