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Parameterized Inapproximability of Target Set Selection and Generalizations

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Language, Life, Limits (CiE 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8493))

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Abstract

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value 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 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.

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References

  1. Aazami, A., Stilp, K.: Approximation algorithms and hardness for domination with propagation. SIAM J. Discrete Math. 23(3), 1382–1399 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arora, S., Lund, C.: Hardness of approximations. In: Approximation Algorithms for NP-Hard Problems, pp. 399–446. PWS Publishing Company (1996)

    Google Scholar 

  3. Bazgan, C., Chopin, M., Nichterlein, A., Sikora, F.: Parameterized approximability of maximizing the spread of influence in networks. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 543–554. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Ben-Zwi, O., Hermelin, D., Lokshtanov, D., Newman, I.: Treewidth governs the complexity of target set selection. Discrete Optim. 8(1), 87–96 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cai, L., Huang, X.: Fixed-parameter approximation: Conceptual framework and approximability results. Algorithmica 57(2), 398–412 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chang, C.-L., Lyuu, Y.-D.: Spreading messages. Theor. Comput. Sci. 410(27-29), 2714–2724 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen, N.: On the approximability of influence in social networks. SIAM J. Discrete Math. 23(3), 1400–1415 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, Y., Grohe, M., Grüber, M.: On parameterized approximability. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 109–120. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Chopin, M., Nichterlein, A., Niedermeier, R., Weller, M.: Constant thresholds can make target set selection tractable. In: Even, G., Rawitz, D. (eds.) MedAlg 2012. LNCS, vol. 7659, pp. 120–133. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. Cicalese, F., Cordasco, G., Gargano, L., Milanič, M., Vaccaro, U.: Latency-bounded target set selection in social networks. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 65–77. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Dinur, I., Safra, S.: The importance of being biased. In: Proc. of STOC 2002, pp. 33–42. ACM (2002)

    Google Scholar 

  12. Downey, R.G., Fellows, M.R., McCartin, C.: Parameterized approximation algorithms. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 121–129. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer (2013)

    Google Scholar 

  14. Dreyer, P.A., Roberts, F.S.: Irreversible k-threshold processes: Graph-theoretical threshold models of the spread of disease and of opinion. Discrete Appl. Math. 157(7), 1615–1627 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)

    Google Scholar 

  16. Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proc. of KDD 2003, pp. 137–146. ACM (2003)

    Google Scholar 

  17. Marx, D.: Parameterized complexity and approximation algorithms. Comput. J. 51(1), 60–78 (2008)

    Article  Google Scholar 

  18. Marx, D.: Completely inapproximable monotone and antimonotone parameterized problems. J. Comput. Syst. Sci. 79(1), 144–151 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  19. Nichterlein, A., Niedermeier, R., Uhlmann, J., Weller, M.: On tractable cases of target set selection. Soc. Network Anal. Mining 3(2), 233–256 (1869) ISSN 1869-5450

    Google Scholar 

  20. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)

    Google Scholar 

  21. Peleg, D.: Local majorities, coalitions and monopolies in graphs: a review. Theor. Comput. Sci. 282(2), 231–257 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  22. Reddy, T.V.T., Rangan, C.P.: Variants of spreading messages. J. Graph Algorithms Appl. 15(5), 683–699 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. LAMSADE UMR CNRS 7243, PSL, Université Paris-Dauphine, France

    Cristina Bazgan & Florian Sikora

  2. Institut für Optimierung und Operations Research, Universität Ulm, Germany

    Morgan Chopin

  3. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany

    André Nichterlein

  4. Institut Universitaire de France, France

    Cristina Bazgan

Authors
  1. Cristina Bazgan
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  2. Morgan Chopin
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  3. André Nichterlein
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  4. Florian Sikora
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Editor information

Editors and Affiliations

  1. College of Science, Department of Computer Science, Swansea University, SA2 8PP, Swansea, UK

    Arnold Beckmann

  2. Department of Algorithms and Their Applications, Eötvös Loránd University, Pázmány Péter sétány 1/c,, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  3. Computer Science Institute, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Bazgan, C., Chopin, M., Nichterlein, A., Sikora, F. (2014). Parameterized Inapproximability of Target Set Selection and Generalizations. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds) Language, Life, Limits. CiE 2014. Lecture Notes in Computer Science, vol 8493. Springer, Cham. https://doi.org/10.1007/978-3-319-08019-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-08019-2_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08018-5

  • Online ISBN: 978-3-319-08019-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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