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Total Positive Influence Domination on Weighted Networks

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Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 881))

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Abstract

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.

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Notes

  1. 1.

    http://perso.crans.org/aynaud/communities/.

  2. 2.

    https://www.gurobi.com.

  3. 3.

    https://github.com/dvgreetham/domset/.

References

  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)

    Chapter  Google Scholar 

  2. Blondel, V., Guillaume, J., Lambiotte, R., Mech, E.: Fast unfolding of communities in large networks. J. Stat. Mech. 2008, P10008 (2008)

    Article  Google Scholar 

  3. Bollobás, B.: Random Graphs, 2nd edn. Cambridge University Press (2001). https://doi.org/10.1017/CBO9780511814068

  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). https://doi.org/10.1561/2200000016

    Article  MATH  Google Scholar 

  5. Chen, N., Meng, J., Rong, J., Zhu, H.: Approximation for dominating set problem with measure functions. Comput. Inform. 23, 37–49 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Condon, A., Karp, R.: Algorithms for graph partitioning on the planted partition model. Random Struct. Algor. 18, 116–140 (2001)

    Article  MathSciNet  Google Scholar 

  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 2015

    Google Scholar 

  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). https://doi.org/10.1007/s10878-012-9530-7

    Article  MathSciNet  MATH  Google Scholar 

  9. Dunbar, J., Hoffman, D., Laskar, R., Markus, L.: \(\alpha \)-domination. Discrete Math. 211, 11–26 (2000)

    Article  MathSciNet  Google Scholar 

  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). http://www.sciencedirect.com/science/article/pii/S0166218X11002423

    Article  MathSciNet  Google Scholar 

  11. Gagarin, A., Poghosyan, A., Zverovich, V.E.: Upper bounds for alpha-domination parameters. Graphs Comb. 25(4), 513–520 (2009)

    Article  Google Scholar 

  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)

    MATH  Google Scholar 

  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. 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 2008

    Google Scholar 

  15. Holme, P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65, 026107 (2002)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  17. Klasing, R., Laforest, C.: Hardness results and approximation algorithms of k-tuple domination in graphs. Inf. Process. Lett. 89(2), 75–83 (2004). https://doi.org/10.1016/j.ipl.2003.10.004

    Article  MathSciNet  MATH  Google Scholar 

  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 2015

    Google Scholar 

  19. Leskovec, J., Krevl, A.: SNAP datasets: stanford large network dataset collection, June 2014. http://snap.stanford.edu/data

  20. Lewandowski, G., Condon, A.: Experiments with parallel graph coloring heuristics and applications of graph coloring (1994)

    Google Scholar 

  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). http://www.sciencedirect.com/science/article/pii/S0378437118302218

    Article  MathSciNet  Google Scholar 

  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). http://www.nature.com/srep/2014/140909/srep06308/full/srep06308.html

  23. Nguyen, T.H.: Graph coloring benchmark instances. https://turing.cs.hbg.psu.edu/txn131/graphcoloring.html. Accessed 14 Oct 2018

  24. Porumbel, D.: DIMACS graphs: benchmark instances and best upper bounds (2011). http://www.info.univ-angers.fr/pub/porumbel/graphs/

  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). http://networkrepository.com

  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). http://www.mdpi.com/1099-4300/20/2/87

    Article  MathSciNet  Google Scholar 

  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 2014

    Google Scholar 

  28. Wang, F., et al.: On positive influence dominating sets in social networks. Theor. Comput. Sci. 412(3), 265–269 (2011). http://www.sciencedirect.com/science/article/pii/S0304397509007221

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Knowledge Media Institute, The Open University, Milton Keynes, UK

    Danica Vukadinović Greetham

  2. CountingLab Ltd., Reading, UK

    Nathaniel Charlton

  3. University of Bath, Bath, UK

    Anush Poghosyan

Authors
  1. Danica Vukadinović Greetham
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  2. Nathaniel Charlton
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  3. Anush Poghosyan
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Corresponding author

Correspondence to Danica Vukadinović Greetham .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

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Vukadinović Greetham, D., Charlton, N., Poghosyan, A. (2020). Total Positive Influence Domination on Weighted Networks. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_27

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