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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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