NDLI: Preventing Unraveling in Social Networks: The Anchored $k$-Core Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sharma, Aneesh Kleinberg, Jon Lewi, Kevin Bhawalkar, Kshipra Roughgarden, Tim
Copyright Year	2015
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 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 $k \ge 3$.
Starting Page	1452
Ending Page	1475
Page Count	24
File Format	PDF
ISSN	08954801
DOI	10.1137/14097032X
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	29
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-08-11
Access Restriction	Subscribed
Subject Keyword	Nonnumerical algorithms $k$-core social networks Social networks Graph theory graph algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics

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