Parameterized Approximability of Maximizing the Spread of Influence in Networks

  • Cristina Bazgan
  • Morgan Chopin
  • André Nichterlein
  • Florian Sikora
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7936)


In this paper, we consider the problem of maximizing the spread of influence through a social network. Here, we are given a graph G = (V,E), a positive integer k and a threshold value thr(v) attached to each vertex v ∈ V. The objective is then to find a subset of k vertices to “activate” such that the number of activated vertices at the end of a propagation process is maximum. A vertex v gets activated if at least thr(v) of its neighbors are. We show that this problem is strongly inapproximable in fpt-time with respect to (w.r.t.) parameter k even for very restrictive thresholds. For unanimity thresholds, we prove that the problem is inapproximable in polynomial time and the decision version is W[1]-hard w.r.t. parameter k. On the positive side, it becomes r(n)-approximable in fpt-time w.r.t. parameter k for any strictly increasing function r. Moreover, we give an fpt-time algorithm to solve the decision version for bounded degree graphs.


Polynomial Time Bipartite Graph Regular Graph Decision Version Vertex Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aazami, A., Stilp, K.: Approximation algorithms and hardness for domination with propagation. SIAM J. Discrete Math. 23(3), 1382–1399 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Ben-Zwi, O., Hermelin, D., Lokshtanov, D., Newman, I.: Treewidth governs the complexity of target set selection. Discrete Optim. 8(1), 87–96 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bourgeois, N., Giannakos, A., Lucarelli, G., Milis, I., Paschos, V.T.: Exact and approximation algorithms for densest k-subgraph. In: Ghosh, S.K., Tokuyama, T. (eds.) WALCOM 2013. LNCS, vol. 7748, pp. 114–125. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Cai, L.: Parameterized complexity of cardinality constrained optimization problems. Comput. J. 51(1), 102–121 (2008)CrossRefGoogle Scholar
  5. 5.
    Cai, L., Chan, S.M., Chan, S.O.: Random separation: A new method for solving fixed-cardinality optimization problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 239–250. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Chang, C.-L., Lyuu, Y.-D.: Spreading messages. Theor. Comput. Sci. 410(27-29), 2714–2724 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Chen, N.: On the approximability of influence in social networks. SIAM J. Discrete Math. 23(3), 1400–1415 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Chopin, M., Nichterlein, A., Niedermeier, R., Weller, M.: Constant thresholds can make target set selection tractable. In: Even, G., Rawitz, D. (eds.) MedAlg 2012. LNCS, vol. 7659, pp. 120–133. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Dinur, I., Safra, S.: The importance of being biased. In: Proc. of STOC, pp. 33–42. ACM (2002)Google Scholar
  10. 10.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
  11. 11.
    Dreyer, P.A., Roberts, F.S.: Irreversible k-threshold processes: Graph-theoretical threshold models of the spread of disease and of opinion. Discrete Appl. Math. 157(7), 1615–1627 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proc. of KDD, pp. 137–146. ACM (2003)Google Scholar
  13. 13.
    Marx, D.: Parameterized complexity and approximation algorithms. Comput. J. 51(1), 60–78 (2008)CrossRefGoogle Scholar
  14. 14.
    Nichterlein, A., Niedermeier, R., Uhlmann, J., Weller, M.: On tractable cases of target set selection. Soc. Network Anal. Mining (2012) (online available)Google Scholar
  15. 15.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
  16. 16.
    Peleg, D.: Local majorities, coalitions and monopolies in graphs: a review. Theor. Comput. Sci. 282, 231–257 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Reddy, T.V.T., Rangan, C.P.: Variants of spreading messages. J. Graph Algorithms Appl. 15(5), 683–699 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Cristina Bazgan
    • 1
    • 3
  • Morgan Chopin
    • 1
  • André Nichterlein
    • 2
  • Florian Sikora
    • 1
  1. 1.LAMSADE UMR CNRS 7243PSL, Université Paris-DauphineFrance
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  3. 3.Institut Universitaire de FranceFrance

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