Parameterized Inapproximability of Target Set Selection and Generalizations
Bazgan, Cristina; Chopin, Morgan; Nichterlein, André; Sikora, Florian (2014), Parameterized Inapproximability of Target Set Selection and Generalizations, in Arnold Beckmann, Erzsébet Csuhaj-Varjú, Klaus Meer, Language, Life, Limits.10th Conference on Computability in Europe, CiE 2014, Budapest, Hungary, June 23-27, 2014. Proceedings, Springer : Berlin Heidelberg, p. 11-20. 10.1007/978-3-319-08019-2_2
TypeCommunication / Conférence
External document linkhttps://arxiv.org/abs/1403.3565v2
Book titleLanguage, Life, Limits.10th Conference on Computability in Europe, CiE 2014, Budapest, Hungary, June 23-27, 2014. Proceedings
Book authorArnold Beckmann, Erzsébet Csuhaj-Varjú, Klaus Meer
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Abstract (EN)In this paper, we consider the Target Set Selection problem: given a graph and a threshold value https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-08019-2_2/978-3-319-08019-2_2_IEq1_HTML.gif for each vertex v of the graph, find a minimum size vertex-subset to “activate” s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex v is activated during the propagation process if at least https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-08019-2_2/978-3-319-08019-2_2_IEq2_HTML.gif of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions f and ρ this problem cannot be approximated within a factor of ρ(k) in f(k) ·n O(1) time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results.
Subjects / KeywordsTarget Set Selection problem
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Bazgan, Cristina; Chopin, Morgan; Nichterlein, André; Sikora, Florian (2014) Article accepté pour publication ou publié