Constant Thresholds Can Make Target Set Selection Tractable

  • Morgan Chopin
  • André Nichterlein
  • Rolf Niedermeier
  • Mathias Weller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7659)


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.


Vertex Cover Input Graph Reduction Rule Constant Threshold Cover Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Morgan Chopin
    • 1
  • André Nichterlein
    • 2
  • Rolf Niedermeier
    • 2
  • Mathias Weller
    • 2
  1. 1.LAMSADEUniversité Paris-DauphineFrance
  2. 2.Institut für Softwaretechnik und Theoretische InformatikBerlinGermany

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