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, Computability, 3, 2, p. 135-145. 10.3233/COM-140030
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1403.3565v2
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Abstract (EN)In this paper, we consider the TARGET SET SELECTION problem: given a graph and a threshold value thr(v) for each vertex v of the graph, find a minimum size vertex-subset to “activate” such that all 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 thr(v) 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)·nO(1) time, unless FPT=W[P], even for restricted thresholds (namely constant and majority thresholds), where k is the number of vertices to activate in the beginning. We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results.
Subjects / Keywordsparameterized complexity; parameterized approximation; target set selection; spread of information
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Bazgan, Cristina; Chopin, Morgan; Nichterlein, André; Sikora, Florian (2014) Article accepté pour publication ou publié