Constant Thresholds Can Make Target Set Selection Tractable
Target Set Selection, which is a prominent NP-hard problem occurring in social network analysis and distributed computing, is notoriously hard both in terms of achieving useful approximation as well as fixed-parameter algorithms. The task is to select a minimum number of vertices into a “target set” such that all other vertices will become active in course of a dynamic process (which may go through several activation rounds). A vertex, which is equipped with a threshold value t, becomes active once at least t of its neighbors are active; initially, only the target set vertices are active. We contribute further insights into islands of tractability for Target Set Selection by spotting new parameterizations characterizing some sparse graphs as well as some “cliquish” graphs and developing corresponding fixed-parameter tractability and (parameterized) hardness results. In particular, we demonstrate that upper-bounding the thresholds by a constant may significantly alleviate the search for efficiently solvable, but still meaningful special cases of Target Set Selection.
Unable to display preview. Download preview PDF.
- 6.Chiang, C.-Y., Huang, L.-H., Li, B.-J., Wu, J., Yeh, H.-G.: Some results on the target set selection problem. Journal of Combinatorial Optimization (2012)Google Scholar
- 7.Diestel, R.: Graph Theory, 4th edn. Graduate Texts in Mathematics, vol. 173. Springer (2010)Google Scholar
- 9.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
- 11.Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press (2010)Google Scholar
- 12.Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)Google Scholar
- 16.Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)Google Scholar
- 17.Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proc. 9th ACM KDD, pp. 137–146. ACM Press (2003)Google Scholar
- 21.Nichterlein, A., Niedermeier, R., Uhlmann, J., Weller, M.: On tractable cases of target set selection. Social Network Analysis and Mining (2012)Google Scholar
- 22.Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar