COCOON 2013: Computing and Combinatorics pp 543-554 | Cite as
Parameterized Approximability of Maximizing the Spread of Influence in Networks
Abstract
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.
Keywords
Polynomial Time Bipartite Graph Regular Graph Decision Version Vertex SubsetPreview
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References
- 1.Aazami, A., Stilp, K.: Approximation algorithms and hardness for domination with propagation. SIAM J. Discrete Math. 23(3), 1382–1399 (2009)MathSciNetMATHCrossRefGoogle Scholar
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 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.Cai, L.: Parameterized complexity of cardinality constrained optimization problems. Comput. J. 51(1), 102–121 (2008)CrossRefGoogle Scholar
- 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.Chang, C.-L., Lyuu, Y.-D.: Spreading messages. Theor. Comput. Sci. 410(27-29), 2714–2724 (2009)MathSciNetMATHCrossRefGoogle Scholar
- 7.Chen, N.: On the approximability of influence in social networks. SIAM J. Discrete Math. 23(3), 1400–1415 (2009)MathSciNetMATHCrossRefGoogle Scholar
- 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.Dinur, I., Safra, S.: The importance of being biased. In: Proc. of STOC, pp. 33–42. ACM (2002)Google Scholar
- 10.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
- 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)MathSciNetMATHCrossRefGoogle Scholar
- 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.Marx, D.: Parameterized complexity and approximation algorithms. Comput. J. 51(1), 60–78 (2008)CrossRefGoogle Scholar
- 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.Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
- 16.Peleg, D.: Local majorities, coalitions and monopolies in graphs: a review. Theor. Comput. Sci. 282, 231–257 (2002)MathSciNetMATHCrossRefGoogle Scholar
- 17.Reddy, T.V.T., Rangan, C.P.: Variants of spreading messages. J. Graph Algorithms Appl. 15(5), 683–699 (2011)MathSciNetCrossRefGoogle Scholar