Parameterized Inapproximability of Target Set Selection and Generalizations

  • Cristina Bazgan
  • Morgan Chopin
  • André Nichterlein
  • Florian Sikora
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8493)


In this paper, we consider the Target Set Selection problem: given a graph and a threshold value Open image in new window 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 Open image in new window 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.


Bipartite Graph Vertex Cover Input Node Computable Function Satisfying Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Cristina Bazgan
    • 1
    • 4
  • Morgan Chopin
    • 2
  • André Nichterlein
    • 3
  • Florian Sikora
    • 1
  1. 1.LAMSADE UMR CNRS 7243PSL, Université Paris-DauphineFrance
  2. 2.Institut für Optimierung und Operations ResearchUniversität UlmGermany
  3. 3.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  4. 4.Institut Universitaire de FranceFrance

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