Graph cut problems form a fundamental problem type in combinatorial optimization, and are a central object of study in both theory and practice. In addition, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed in a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different definitions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem modeling disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.

中文翻译：

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通过图形切割问题进行公平的灾难控制

图割问题是组合优化中的基本问题类型，是理论和实践中的核心研究对象。此外，算法设计和机器学习中的公平性研究最近受到了极大的关注，在各种背景下提出和分析了许多不同的概念。在本文中，我们通过给出第一个公平定义来启动图切割问题的公平性研究，随后我们展示了适当的算法技术，这些技术产生了严格的理论分析。具体来说，我们在特定的切割问题建模灾难控制场景中结合了两个不同的公平定义，即人口统计和概率个体公平。