Total Positive Influence Domination on Weighted Networks

  • Danica Vukadinović GreethamEmail author
  • Nathaniel Charlton
  • Anush Poghosyan
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)


We are proposing two greedy and a new linear programming based approximation algorithm for the total positive influence dominating set problem in weighted networks. Applications of this problem in weighted settings include finding: a minimum cost set of nodes to broadcast a message in social networks, such that each node has majority of neighbours broadcasting that message; a maximum trusted set in bitcoin network; an optimal set of hosts when running distributed apps etc.. Extensive experiments on different generated and real networks highlight advantages and potential issues for each algorithm.


Domination sets Total positive influence Vertex-weighted networks Network communities 


  1. 1.
    Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pp. 3–14. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Blondel, V., Guillaume, J., Lambiotte, R., Mech, E.: Fast unfolding of communities in large networks. J. Stat. Mech. 2008, P10008 (2008)CrossRefGoogle Scholar
  3. 3.
    Bollobás, B.: Random Graphs, 2nd edn. Cambridge University Press (2001).
  4. 4.
    Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011). Scholar
  5. 5.
    Chen, N., Meng, J., Rong, J., Zhu, H.: Approximation for dominating set problem with measure functions. Comput. Inform. 23, 37–49 (2004)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Condon, A., Karp, R.: Algorithms for graph partitioning on the planted partition model. Random Struct. Algor. 18, 116–140 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dhawan, A., Rink, M.: Positive influence dominating set generation in social networks. In: 2015 International Conference on Computing and Network Communications (CoCoNet), pp. 112–117, December 2015Google Scholar
  8. 8.
    Dinh, T., Shen, Y., Nguyen, D., Thai, M.: On the approximability of positive influence dominating set in social networks. J. Comb. Optim. 27(3), 487–503 (2014). Scholar
  9. 9.
    Dunbar, J., Hoffman, D., Laskar, R., Markus, L.: \(\alpha \)-domination. Discrete Math. 211, 11–26 (2000)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gagarin, A., Poghosyan, A., Zverovich, V.: Randomized algorithms and upper bounds for multiple domination in graphs and networks. Discrete Appl. Math. 161(4-5), 604 – 611 (2013). Scholar
  11. 11.
    Gagarin, A., Poghosyan, A., Zverovich, V.E.: Upper bounds for alpha-domination parameters. Graphs Comb. 25(4), 513–520 (2009)CrossRefGoogle Scholar
  12. 12.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)zbMATHGoogle Scholar
  13. 13.
    Greaves, C., Reddy, P., Sheppard, K.: Supporting behaviour change for diabetes prevention. In: Schwarz, P., Reddy, P., Greaves, C., Dunbar, J. (eds.) Diabetes Prevention in Practice, pp. 19–29. Tumaini Institute for Prevention Management, Dresden (2010)Google Scholar
  14. 14.
    Hagberg, A., Schult, D., Swart, P.: Exploring network structure, dynamics, and function using networkX. In: Proceedings of the 7th Python in Science Conference (SciPy2008), Passadena, CA, USA, pp. 11–15, August 2008Google Scholar
  15. 15.
    Holme, P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65, 026107 (2002)CrossRefGoogle Scholar
  16. 16.
    Johnson, D.S., Aragon, C.R., Mcgeoch, L.A., Schevon, C.: Optimization by simulated annealing: an experimental evaluation; part II, graph coloring and number partitioning. Oper. Res. 39, 378–406 (1991)CrossRefGoogle Scholar
  17. 17.
    Klasing, R., Laforest, C.: Hardness results and approximation algorithms of k-tuple domination in graphs. Inf. Process. Lett. 89(2), 75–83 (2004). Scholar
  18. 18.
    Lee, Y.T., Sidford, A.: Efficient inverse maintenance and faster algorithms for linear programming. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, pp. 230–249, October 2015Google Scholar
  19. 19.
    Leskovec, J., Krevl, A.: SNAP datasets: stanford large network dataset collection, June 2014.
  20. 20.
    Lewandowski, G., Condon, A.: Experiments with parallel graph coloring heuristics and applications of graph coloring (1994)Google Scholar
  21. 21.
    Lin, G., Guan, J., Feng, H.: An ILP based memetic algorithm for finding minimum positive influence dominating sets in social networks. Phys. A: Stat. Mech. Appl. 500, 199–209 (2018). Scholar
  22. 22.
    Molnàr Jr., F., Derzsy, N., Czabarka, E., Székely, L., Szymanski, B.K., Korniss, G.: Dominating scale-free networks using generalized probabilistic methods. Sci. Rep. 4(6308) (2014).
  23. 23.
    Nguyen, T.H.: Graph coloring benchmark instances. Accessed 14 Oct 2018
  24. 24.
    Porumbel, D.: DIMACS graphs: benchmark instances and best upper bounds (2011).
  25. 25.
    Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (2015).
  26. 26.
    Vazquez-Araujo, F., Dapena, A., Souto-Salorio, M.J., Castro, P.M.: Calculation of the connected dominating set considering vertex importance metrics. Entropy 20(2) (2018). Scholar
  27. 27.
    Vukadinovic Greetham, D., Poghosyan, A., Charlton, N.: Weighted alpha-rate dominating sets in social networks. In: Tenth International Conference on Signal-Image Technology and Internet-Based Systems (SITIS), Marrakech, Morocco, pp. 369–375, 23–27 November 2014Google Scholar
  28. 28.
    Wang, F., et al.: On positive influence dominating sets in social networks. Theor. Comput. Sci. 412(3), 265–269 (2011). Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Danica Vukadinović Greetham
    • 1
    Email author
  • Nathaniel Charlton
    • 2
  • Anush Poghosyan
    • 3
  1. 1.Knowledge Media InstituteThe Open UniversityMilton KeynesUK
  2. 2.CountingLab Ltd.ReadingUK
  3. 3.University of BathBathUK

Personalised recommendations