迫零及相关问题的计算方法
Computational Approaches for Zero Forcing and Related Problems
摘要：
在本文中，我们提出了计算方法的迫零问题，连接迫零问题，并迫使一个图在指定数量的时间步长的问题。我们的方法是基于整数规划模型和组合算法的组合，并包括配方迫零作为一个动态过程，并作为一个集覆盖问题。我们探索了这些模型的几种解决方案策略，在各种类型的图上进行测试，并表明它们与最先进的迫零算法具有竞争力。我们提出的算法连接迫零和控制迫零时间步的数量是这些问题的第一个通用的计算方法，并优于蛮力计算。
英文摘要：
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.
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