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Computational approaches for zero forcing and related problems

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  • Brimkov, Boris
  • Fast, Caleb C.
  • Hicks, Illya V.

Abstract

In this paper, we propose computational approaches for the zero forcing problem, the connected zero forcing problem, and the problem of forcing a graph within a specified number of timesteps. Our approaches are based on a combination of integer programming models and combinatorial algorithms, and include formulations for zero forcing as a dynamic process, and as a set-covering problem. We explore several solution strategies for these models, test them on various types of graphs, and show that they are competitive with the state-of-the-art algorithm for zero forcing. Our proposed algorithms for connected zero forcing and for controlling the number of zero forcing timesteps are the first general-purpose computational methods for these problems, and are superior to brute force computation.

Suggested Citation

  • Brimkov, Boris & Fast, Caleb C. & Hicks, Illya V., 2019. "Computational approaches for zero forcing and related problems," European Journal of Operational Research, Elsevier, vol. 273(3), pages 889-903.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:3:p:889-903
    DOI: 10.1016/j.ejor.2018.09.030
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    1. Mariana O. Da Silva & Gustavo A. Gimenez-Lugo & Murilo V. G. Da Silva, 2013. "Vertex Cover In Complex Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(11), pages 1-9.
    2. Chun-Ying Chiang & Liang-Hao Huang & Bo-Jr Li & Jiaojiao Wu & Hong-Gwa Yeh, 2013. "Some results on the target set selection problem," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 702-715, May.
    3. Oecd, 2013. "Broadband Networks and Open Access," OECD Digital Economy Papers 218, OECD Publishing.
    4. Ball, Brian & Newman, M.E.J., 2013. "Friendship networks and social status," Network Science, Cambridge University Press, vol. 1(1), pages 16-30, April.
    5. ., 2013. "The network nature of the Internet infrastructure," Chapters, in: The Geography of the Internet, chapter 4, pages 81-133, Edward Elgar Publishing.
    6. Oecd, 2013. "Building Blocks for Smart Networks," OECD Digital Economy Papers 215, OECD Publishing.
    7. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    8. Ashkan Aazami, 2010. "Domination in graphs with bounded propagation: algorithms, formulations and hardness results," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 429-456, May.
    9. Oecd, 2013. "Knowledge Networks and Markets," OECD Science, Technology and Industry Policy Papers 7, OECD Publishing.
    10. Thomas Y.S. Lee, 2013. "Performance analysis of mobile communication networks," International Journal of Information and Decision Sciences, Inderscience Enterprises Ltd, vol. 5(1), pages 1-24.
    11. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
    12. Maguy TREFOIS & Jean-Charles DELVENNE, 2015. "Zero forcing number, constrained matchings and strong structural controllability," LIDAM Reprints CORE 2785, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Rodolfo Carvajal & Miguel Constantino & Marcos Goycoolea & Juan Pablo Vielma & Andrés Weintraub, 2013. "Imposing Connectivity Constraints in Forest Planning Models," Operations Research, INFORMS, vol. 61(4), pages 824-836, August.
    14. L. C. G. Rogers & L. A. M. Veraart, 2013. "Failure and Rescue in an Interbank Network," Management Science, INFORMS, vol. 59(4), pages 882-898, April.
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