Computational Approaches for Zero Forcing and Related Problems

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, and numerically compare them to the well-known Wavefront algorithm for zero forcing developed by Grout et al. Our proposed algorithms for connected zero forcing and for controlling the propagation time are the first general-purpose computational methods for these problems; they are comparable in performance to Wavefront and superior to brute force computation.