Abstract
The NP-hard Effectors problem on directed graphs is motivated by applications in network mining, particularly concerning the analysis of (random) information-propagation processes. In the corresponding model the arcs carry probabilities and there is a probabilistic diffusion process activating nodes by neighboring activated nodes with probabilities as specified by the arcs. The point is to explain a given network activation state best possible using a minimum number of “effector nodes”; these are selected before the activation process starts.
We complement and extend previous work from the data mining community by a more thorough computational complexity analysis of Effectors, identifying both tractable and intractable cases. To this end, we also exploit a parameterization measuring the “degree of randomness” (the number of ‘really’ probabilistic arcs) which might prove useful for analyzing other probabilistic network diffusion problems.
A full version is available at http://arxiv.org/abs/1411.7838.
Laurent Bulteau—Supported by the Alexander von Humboldt Foundation, Bonn, Germany.
Stefan Fafianie—Supported by the DFG Emmy Noether-program (KR 4286/1).
Vincent Froese—Supported by the DFG, project DAMM (NI 369/13).
Nimrod Talmon—Supported by DFG Research Training Group MDS (GRK 1408).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We conjecture that both models coincide if we have unlimited budget, that is, if the number of chosen effectors does not matter. On the contrary, they do not coincide if we have limited budget, see Sect. 2.
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Upper Saddle River (1993)
Askalidis, G., Berry, R.A., Subramanian, V.G.: Explaining snapshots of network diffusions: structural and hardness results. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds.) COCOON 2014. LNCS, vol. 8591, pp. 616–625. Springer, Heidelberg (2014)
Ben-Zwi, O., Hermelin, D., Lokshtanov, D., Newman, I.: Treewidth governs the complexity of target set selection. Discrete Optim. 8(1), 87–96 (2011)
Bharathi, S., Kempe, D., Salek, M.: Competitive influence maximization in social networks. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 306–311. Springer, Heidelberg (2007)
Chopin, M., Nichterlein, A., Niedermeier, R., Weller, M.: Constant thresholds can make target set selection tractable. Theory Comput. Syst. 55(1), 61–83 (2014)
Domingos, P., Richardson, M.: Mining the network value of customers. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 57–66. ACM (2001)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer, London (2013)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146. ACM (2003)
Lappas, T., Terzi, E., Gunopulos, D., Mannila, H.: Finding effectors in social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1059–1068. ACM (2010)
Nichterlein, A., Niedermeier, R., Uhlmann, J., Weller, M.: On tractable cases of target set selection. Soc. Netw. Anal. Min. 3(2), 233–256 (2013)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, New York (2006)
Wang, C., Chen, W., Wang, Y.: Scalable influence maximization for independent cascade model in large-scale social networks. Data Min. Knowl. Disc. 25(3), 545–576 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Bulteau, L., Fafianie, S., Froese, V., Niedermeier, R., Talmon, N. (2015). The Complexity of Finding Effectors. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-17142-5_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17141-8
Online ISBN: 978-3-319-17142-5
eBook Packages: Computer ScienceComputer Science (R0)