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Journal of Combinatorial Optimization

, Volume 27, Issue 3, pp 487–503 | Cite as

On the approximability of positive influence dominating set in social networks

  • Thang N. Dinh
  • Yilin Shen
  • Dung T. Nguyen
  • My T. Thai
Article

Abstract

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 ρ>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 ρ of neighbors inside \(\mathcal{P}\). We show that neither of these problems can be approximated within a factor of (1−ϵ)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.

Keywords

Hardness of approximation Approximation algorithm Social networks Information diffusion 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Thang N. Dinh
    • 1
  • Yilin Shen
    • 1
  • Dung T. Nguyen
    • 1
  • My T. Thai
    • 1
  1. 1.Department of Computer & Information Science & EngineeringUniversity of FloridaGainesvilleUSA

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