Skip to main content
SpringerLink
Log in

Efficient approaches for the Flooding Problem on graphs

  • S.I.: CLAIO 2016
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper deals with the Flooding Problem on graphs. This problem consists in finding the shortest sequence of flooding moves that turns a colored graph into a monochromatic one. The problem has applications in some areas as disease propagation, for example. Three metaheuristics versions are proposed and compared with the literature results. A new integer programming formulation is also proposed and tested with the only formulation known. The obtained results indicate that both the proposed formulation and the Evolutionary Algorithm are, respectively, the best exact and heuristic approaches for the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Adriaen, M., De Causmaecker, P., Demeester, P., & Vanden Berghe, G. (2004). Spatial simulation model for infectious viral disease with focus on SARS and the common flu. In 37th annual Hawaii international conference on system sciences. IEEE Computer Society. ISBN: 0-7695-2056-1.

  • Aiex, R. M., Resende, M. G. C., & Ribeiro, C. C. (2002). Probability distribution of solution time in GRASP: An experimental investigation. Journal of Heuristics, 8, 343–373.

    Article  Google Scholar 

  • Barone, P., Bonizzoni, P., Vedova, G. D., & Mauri, G. (2001). An approximation algorithm for the shortest common supersequence problem: An experimental analysis. In ACM symposium on applied computing (pp. 56–60).

  • Barros, B. J. S., Pinheiro, R. G. S., & Souza, U. S. (2015). Métodos heurísticos e exatos para o Problema de Inundação em Grafos. In Anais do XLVII Simpósio Brasileiro de Pesquisa Operacional (SBPO2015), Salvador/Brasil.

  • Clifford, R., Jalsenius, M., Montanaro, A., & Sach, B. (2012). The complexity of flood filling game. Theory of Computing Systems, 50, 72–92. https://doi.org/10.1007/s00224-011-9339-2.

    Article  Google Scholar 

  • Contreras, I., Tanash, M., & Vidyarthi, N. (2016). Exact and heuristic approaches for the cycle hub location problem. Annals of Operations Research, 1–23. https://doi.org/10.1007/s10479-015-2091-2.

    Article  Google Scholar 

  • da Fonseca, G. H. G., Santos, H. G., Toffolo, T. A. M., Brito, S. S., & Souza, M. J. F. (2016). GOAL solver: A hybrid local search based solver for high school timetabling. Annals of Operations Research, 239(1), 77–97. https://doi.org/10.1007/s10479-014-1685-4.

    Article  Google Scholar 

  • da Silva, C. T. L., Arenales, M. N., & Silveira, R. (2007). Métodos tipo dual simplex para problemas de otimização linear canalizados e esparsos. Pesquisa Operacional, 27, 457–486. https://doi.org/10.1590/S0101-74382007000300004.

    Article  Google Scholar 

  • Davis, T., Rajamanickam, S., & Sid-Lakhdar, W. (2016). A survey of direct methods for sparse linear systems. Acta Numerica, 25, 383–566. https://doi.org/10.1017/S0962492916000076.

    Article  Google Scholar 

  • Feo, T. A., & Resende, M. G. C. (1995). Greedy randomized adaptive search procedures. Journal of Global Optimization, 6, 109–133.

    Article  Google Scholar 

  • Festa, P., & Resende, M. G. C. (2002). GRASP: An annotated bibliography. In C. C. Ribeiro & P. Hansen (Eds.), Essays and surveys on metaheuristics (pp. 325–367). Boston: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Fleischer, R., & Woeginger, G. J. (2010). An algorithmic analysis of the Honey-Bee game. In P. Boldi, & L. Gargano (Eds.), FUN. Lecture notes in computer science (Vol. 6099, pp. 178-189). Berlin: Springer. ISBN: 978-3-642-13121-9.

  • Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Boston, MA: Addison-Wesley Longman Publishing Co. Inc.

    Google Scholar 

  • Gonçalves, J. F., Resende, M. G. C., & Costa, M. D. (2016). A biased random-key genetic algorithm for the minimization of open stacks problem. International Transactions in Operational Research, 23, 25–46.

    Article  Google Scholar 

  • Holland, J. H. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press.

    Google Scholar 

  • LabPixies. (2015). Labpixies—The coolest games! Avaiable at http://www.labpixies.com. Access on 04/27/2015.

  • Lagoutte, A., & Tavenas, S. (2013). The complexity of shortest common supersequence for inputs with no identical consecutive letters. arXiv:1309.0422 [cs.DM].

  • Lagoutte, A., Noual, M., & Thierry, E. (2014). Flooding games on graphs. Discrete Applied Mathematics, 164(2), 532–538.

    Article  Google Scholar 

  • López-Ibáñez, M., Dubois-Lacoste, J., Cáceres, L. P., Stützle, T., & Birattari, M. (2016). The irace package: Iterated racing for automatic algorithm configuration. Operations Research Perspectives, 3, 43–58.

    Article  Google Scholar 

  • Lourenço, H. R., Martin, O. C., & Stutzle, T. (2003). Iterated local search. In F. Glover & G. A. Kochenberger (Eds.), Handbook of metaheuristics (pp. 321–353). Norwell: Kluwer Academic Publishers.

    Google Scholar 

  • Meeks, K., & Scott, A. (2011). The complexity of flood-filling games on graphs. Discrete Applied Mathematics, 160, 959–969. https://doi.org/10.1016/j.dam.2011.09.001.

    Article  Google Scholar 

  • Meeks, K., & Scott, A. (2013). The complexity of free-flood-it on \(2\times n\) boards. Theoretical Computer Science, 500, 25–43. https://doi.org/10.1016/j.tcs.2013.06.010.

    Article  Google Scholar 

  • Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2013). An iterated local search heuristic for the heterogeneous fleet vehicle routing problem. Journal of Heuristics, 19(2), 201–232. https://doi.org/10.1007/s10732-011-9186-y.

    Article  Google Scholar 

  • Rahmann, S. (2003). The shortest common supersequence problem in a microarray production setting. Bioinformatics, 19(2), 156–161.

    Google Scholar 

  • Sabar, N. R., & Kendall, G. (2015). An iterated local search with multiple perturbation operators and time varying perturbation strength for the aircraft landing problem. Omega, 56(Supplement C), 88–98. https://doi.org/10.1016/j.omega.2015.03.007.

    Article  Google Scholar 

  • Silva, A. R. V., & Ochi, L. S. (2010). Hybrid heuristics for dynamic resource-constrained project scheduling problem. In Hybrid metaheuristics: 7th international workshop, HM 2010, Vienna, Austria (pp. 73–87). https://doi.org/10.1007/978-3-642-16054-7-6.

  • Silva, A. R. V., & Ochi, L. S. (2016). An efficient hybrid algorithm for the traveling car renter problem. Expert Systems with Applications, 64, 132–140. https://doi.org/10.1016/j.eswa.2016.07.038.

    Article  Google Scholar 

  • Sim, J., & Park, K. (2003). The consensus string problem for a metric is NP-complete. Journal of Discrete Algorithms, 1(1), 111–117.

    Article  Google Scholar 

  • Souza, U. S., Protti, F., & Dantas da Silva, M. (2014). An algorithmic analysis of flood-it and free-flood-it on graph powers. Discrete Mathematics and Theoretical Computer Science, 16, 279–290.

    Google Scholar 

  • Souza, U. S., Protti, F., & Silva, M. D. (2013). Parameterized complexity of flood-filling games on trees. In D. Z. Du & G. Zhang (Eds.), Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science (Vol. 7936). Berlin: Springer. https://link.springer.com/chapter/10.1007/978-3-642-38768-5_47.

  • Stefanello, F., Buriol, L. S., Hirsch, M. J., Pardalos, P. M., Querido, T., Resende, M. G. C., et al. (2017). On the minimization of traffic congestion in road networks with tolls. Annals of Operations Research, 249(1), 119–139. https://doi.org/10.1007/s10479-015-1800-1.

    Article  Google Scholar 

  • Yevseyeva, I., Basto-Fernandes, V., Ruano-Ordás, D., & Méendez, J. R. (2013). Optimising anti-spam filters with evolutionary algorithms. Expert Systems with Applications, 40(1), 4010–4021. https://doi.org/10.1016/j.eswa.2013.01.008.

    Article  Google Scholar 

Download references

Acknowledgements

We thank the partial support given by FAPERJ, CNPq and CAPES.

Author information

Authors and Affiliations

  1. Universidade Federal Fluminense - Instituto de Ciência e Tecnologia, R. Recife s/n, Jardim Bela Vista, Rio das Ostras, RJ, 28895-532, Brazil

    André Renato Villela da Silva

  2. Universidade Federal Fluminense - Instituto de Computação, Av. Gal. Milton Tavares de Souza, s/n - São Domingos, Niterói, RJ, 24210-310, Brazil

    Luiz Satoru Ochi

  3. Universidade Federal Rural de Pernambuco - Unidade Acadêmica de Garanhuns, Av. Bom Pastor, s/n, Boa Vista, Garanhuns, PE, 55296-901, Brazil

    Bruno José da Silva Barros & Rian Gabriel S. Pinheiro

Authors
  1. André Renato Villela da Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luiz Satoru Ochi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bruno José da Silva Barros
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rian Gabriel S. Pinheiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to André Renato Villela da Silva.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

da Silva, A.R.V., Ochi, L.S., Barros, B.J.d.S. et al. Efficient approaches for the Flooding Problem on graphs. Ann Oper Res 286, 33–54 (2020). https://doi.org/10.1007/s10479-018-2796-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-018-2796-0

Keywords

Search

Navigation