Abstract
We consider a model of user engagement in social networks, where each player incurs a cost to remain engaged but derives a benefit proportional to the number of engaged neighbors. The natural equilibrium of this model corresponds to the k-core of the social network — the maximal induced subgraph with minimum degree at least k.
We study the problem of “anchoring” a small number of vertices to maximize the size of the corresponding anchored k-core — the maximal induced subgraph in which every non-anchored vertex has degree at least k. This problem corresponds to preventing “unraveling” — a cascade of iterated withdrawals. We provide polynomial-time algorithms for general graphs with k = 2, and for bounded-treewidth graphs with arbitrary k. We prove strong inapproximability results for general graphs and k ≥ 3.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brian Arthur, W.: Competing technologies, increasing returns, and lock-in by historical events. The Economic Journal 99(394), 116–131 (1989)
Blume, L.: The statistical mechanics of strategic interaction. Games and Economic Behavior 5, 387–424 (1993)
Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. Comput. J., 255–269 (2008)
Burke, M., Marlow, C., Lento, T.: Feed me: motivating newcomer contribution in social network sites. In: CHI (2009)
Chwe, M.S.-Y.: Structure and strategy in collective action. American Journal of Sociology 105(1), 128–156 (1999)
Chwe, M.S.-Y.: Communication and coordination in social networks. Review of Economic Studies 67, 1–16 (2000)
Downey, R.G., Fellows, M.R., McCartin, C., Rosamond, F.: Parameterized approximation of dominating set problems. Information Processing Letters 109, 68–70 (2008)
Ellison, G.: Learning, local interaction, and coordination. Econometrica 61, 1047–1071 (1993)
Ellison, N.B., Steinfield, C., Lampe, C.: The Benefits of Facebook Friends: Social Capital and College Students’ Use of Online Social Network Sites. Journal of Computer-Mediated Communication (2007)
Farzan, R., Dabbish, L.A., Kraut, R.E., Postmes, T.: Increasing commitment to online communities by designing for social presence. In: CSCW (2011)
Katz, M.L., Shapiro, C.: Network externalities, competition, and compatibility. American Economic Review 75(3), 424–440 (1985)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: KDD, pp. 137–146 (2003)
Kempe, D., Kleinberg, J., Tardos, É.: Influential Nodes in a Diffusion Model for Social Networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005)
Morris, S.: Contagion. Review of Economic Studies 67, 57–78 (2000)
Mossel, E., Roch, S.: On the submodularity of influence in social networks. In: STOC, pp. 128–134 (2007)
Saaskilahti, P.: Monopoly pricing of social goods. Technical report, University Library of Munich, Germany (2007)
Schelling, T.C.: Micromotives and Macrobehavior. Norton (1978)
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
Bhawalkar, K., Kleinberg, J., Lewi, K., Roughgarden, T., Sharma, A. (2012). Preventing Unraveling in Social Networks: The Anchored k-Core Problem. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-31585-5_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31584-8
Online ISBN: 978-3-642-31585-5
eBook Packages: Computer ScienceComputer Science (R0)