Computational approaches for zero forcing and related problems

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

European Journal of Operational Research, 2019, vol. 273, issue 3, 889-903

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.

Keywords: Combinatorial optimization; Zero forcing; Integer programming; Set-covering (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:273:y:2019:i:3:p:889-903

DOI: 10.1016/j.ejor.2018.09.030

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