Graph cut problems are fundamental in Combinatorial Optimization, and are a central object of study in both theory and practice. Furthermore, the study of \emph{fairness} in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed for 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 notions of fairness, namely \emph{demographic} and \emph{probabilistic individual} fairness, in a particular cut problem that models disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees.

翻译：图形切除问题在组合优化中具有根本意义,并且是理论和实践研究的中心对象。此外,最近,对算术设计和机器学习中的\emph{公平性的研究受到极大关注,并针对各种背景提出了许多不同的概念并进行了分析。在本文中,我们通过给图表切除问题给出第一个公平定义,开始对图的公平性进行研究,随后我们展示了适当的算法技术,从而产生严格的理论分析。具体地说,我们纳入了两个不同的公平性概念,即:\emph{人口学}和\emph{概率个体}公平性,这在模拟灾害遏制情景的特定问题中。我们的结果包括了各种近似算法,并提供了可行的理论保障。