期刊
SIAM JOURNAL ON DISCRETE MATHEMATICS
卷 29, 期 3, 页码 1452-1475出版社
SIAM PUBLICATIONS
DOI: 10.1137/14097032X
关键词
social networks; graph algorithms; k-core
资金
- Stanford Graduate Fellowship
- NSF [CCF-1016885, IIS-0910664]
- Simons Investigator Award
- Google Research grant
- Facebook Faculty Research grant
- ARO MURI grant
- ONR PECASE Award
- AFOSR MURI grant
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1215965] Funding Source: National Science Foundation
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 introduce 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 nonanchored vertex has degree at least k. This problem corresponds to preventing unraveling-a cascade of iterated withdrawals-and it identifies the individuals whose participation is most crucial to the overall health of a social network. We classify the computational complexity of this problem as a function of k and of the graph structure. 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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