Abstract
We study the NP-complete Target Set Selection (TSS) problem occurring in social network analysis. Complementing results on its approximability and extending results for its restriction to trees and bounded treewidth graphs, we classify the influence of the parameters “diameter”, “cluster edge deletion number”, “vertex cover number”, and “feedback edge set number” of the underlying graph on the problem’s complexity, revealing both tractable and intractable cases. For instance, even for diameter-two split graphs TSS remains very hard. TSS can be efficiently solved on graphs with small feedback edge set number and also turns out to be fixed-parameter tractable when parameterized by the vertex cover number, both results contrasting known parameterized intractability results for the parameter treewidth. While these tractability results are relevant for sparse networks, we also show efficient fixed-parameter algorithms for the parameter cluster edge deletion number, yielding tractability for certain dense networks.
Supported by the DFG, research projects PABI, NI 369/7, and DARE, NI 369/11.
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
Preview
Unable to display preview. Download preview PDF.
References
Ben-Zwi, O., Hermelin, D., Lokshtanov, D., Newman, I.: An exact almost optimal algorithm for target set selection in social networks. In: Proc. 10th ACM EC, pp. 355–362. ACM Press, New York (2009)
Bodlaender, H.L.: Kernelization: New upper and lower bound techniques. In: IWPEC 2009. LNCS, vol. 5917, pp. 17–37. Springer, Heidelberg (2009)
Bodlaender, H.L., Thomassé, S., Yeo, A.: Analysis of data reduction: Transformations give evidence for non-existence of polynomial kernels. Technical Report UU-CS-2008-030, Department of Information and Computing Sciences, Utrecht University (2008)
Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications, vol. 3. SIAM, Philadelphia (1999)
Chen, N.: On the approximability of influence in social networks. SIAM Journal on Discrete Mathematics 23(3), 1400–1415 (2009)
Dom, M., Lokshtanov, D., Saurabh, S.: Incompressibility through colors and IDs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 378–389. Springer, Heidelberg (2009)
Domingos, P., Richardson, M.: Mining the network value of customers. In: Proc. 7th ACM KDD, pp. 57–66. ACM Press, New York (2001)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Fellows, M.R., Lokshtanov, D., Misra, N., Rosamond, F.A., Saurabh, S.: Graph layout problems parameterized by vertex cover. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 294–305. Springer, Heidelberg (2008)
Fiala, J., Golovach, P.A., Kratochvíl, J.: Parameterized complexity of coloring problems: Treewidth versus vertex cover. In: TAMC 2009. LNCS, vol. 5532, pp. 221–230. Springer, Heidelberg (2009)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Franks, D.W., Noble, J., Kaufmann, P., Stagl, S.: Extremism propagation in social networks with hubs. Adaptive Behavior 16(4), 264–274 (2008)
Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. ACM SIGACT News 38(1), 31–45 (2007)
Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proc. 9th ACM KDD, pp. 137–146. ACM Press, New York (2003)
McCartin, C., Rossmanith, P., Fellows, M.: Frontiers of intractability for dominating set (2007) (manuscript)
McConnell, R.M., Spinrad, J.: Linear-time modular decomposition and efficient transitive orientation of comparability graphs. In: Proc. 5th SODA, pp. 536–545. ACM/SIAM (1994)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)
Niedermeier, R.: Reflections on multivariate algorithmics and problem parameterization. In: Proc. 27th STACS. LIPIcs, vol. 5, pp. 17–32. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2010)
Potterat, J.J., Phillips-Plummer, L., Muth, S.Q., Rothenberg, R.B., Woodhouse, D.E., Maldonado-Long, T.S., Zimmerman, H.P., Muth, J.B.: Risk network structure in the early epidemic phase of HIV transmission in Colorado Springs. Sexually Transmitted Infections 78, 159–163 (2002)
Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Applied Mathematics 144(1-2), 173–182 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nichterlein, A., Niedermeier, R., Uhlmann, J., Weller, M. (2010). On Tractable Cases of Target Set Selection. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17517-6_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-17517-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17516-9
Online ISBN: 978-3-642-17517-6
eBook Packages: Computer ScienceComputer Science (R0)