The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would allow multi-parameter persistent homology to be a viable option for data analysis. In this paper, we provide theoretical results for the computation of the matching distance in two dimensions along with a geometric interpretation of the lines through parameter space realizing this distance. The crucial point of the method we propose is that it can be easily implemented.

翻译：多参数持久性模块匹配距离的确切计算是计算表层研究的一个活跃领域。 实现这一距离的简单精确计算将使多参数持久性同质学成为数据分析的一个可行选项。 在本文中,我们提供理论结果,用于计算两个维度的匹配距离,并通过实现这一距离的参数空间对线条进行几何判读。 我们建议的方法的关键点是,它很容易实施。