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.
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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
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DOI: https://doi.org/10.1007/978-3-642-31585-5_40
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