We consider the problem of fair allocation of indivisible chores under additive valuations. We assume that the chores are divided into two types and under this scenario, we present several results. Our first result is a new characterization of Pareto optimal allocations in our setting, and a polynomial-time algorithm to compute an envy-free up to one item (EF1) and Pareto optimal allocation. We then turn to the question of whether we can achieve a stronger fairness concept called envy-free up any item (EFX). We present a polynomial-time algorithm that returns an EFX allocation. Finally, we show that for our setting, it can be checked in polynomial time whether an envy-free allocation exists or not.

翻译：我们考虑了在添加值下公平分配不可分割的家务的问题。我们假设这些家务分为两类,在这种假设下,我们提出若干结果。我们的第一个结果是,对在我们所处的环境中的Pareto最佳分配进行新的定性,以及计算一个无嫉妒的物品(EF1)和Pareto最佳分配的多元时间算法。然后我们讨论我们是否能够实现一个更强有力的公平概念,称为无嫉妒的物品(EFX)的问题。我们提出了一种返回EFX分配的多元时间算法。最后,我们表明,在我们所处的环境中,无论是否存在无嫉妒的分配,都可以在多婚时间里加以检查。