A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Mining the network value of customers
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Conductance and congestion in power law graphs
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Maximizing the spread of influence through a social network
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Cost-effective outbreak detection in networks
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
On the hardness of optimization in power-law graphs
Theoretical Computer Science
Primal-dual RNC approximation algorithms for (multi)-set (multi)-cover and covering integer programs
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Positive Influence Dominating Set in Online Social Networks
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Latency-Bounded Minimum Influential Node Selection in Social Networks
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
New dominating sets in social networks
Journal of Global Optimization
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Journal of Combinatorial Optimization
Cheap, easy, and massively effective viral marketing in social networks: truth or fiction?
Proceedings of the 23rd ACM conference on Hypertext and social media
Large Social Networks Can Be Targeted for Viral Marketing with Small Seed Sets
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
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In social networks, there is a tendency for connected users to match each other's behaviors. Moreover, a user likely adopts a behavior, if a certain fraction of his family and friends follows that behavior. Identifying people who have the most influential effect to the others is of great advantages, especially in politics, marketing, behavior correction, and so on. Under a graph-theoretical framework, we study the positive influence dominating set (PIDS) problem that seeks for a minimal set of nodes $\mathcal{P}$ such that all other nodes in the network have at least a fraction 驴0 of their neighbors in $\mathcal{P}$ . We also study a different formulation, called total positive influence dominating set (TPIDS), in which even nodes in $\mathcal{P}$ are required to have a fraction 驴 of neighbors inside $\mathcal{P}$ . We show that neither of these problems can be approximated within a factor of (1驴∈)lnmax{Δ,|V|1/2}, where Δ is the maximum degree. Moreover, we provide a simple proof that both problems can be approximated within a factor lnΔ+O(1). In power-law networks, where the degree sequence follows a power-law distribution, both problems admit constant factor approximation algorithms. Finally, we present a linear-time exact algorithms for trees.