One of the most important topics in discrete fair division is whether an EFX allocation exists for any instance. Although the existence of EFX allocations is a standing open problem for both goods and chores, the understanding of the existence of EFX allocations for chores is less established compared to goods. We study the existence of EFX allocation for chores under the assumption that all agent's cost functions are additive. Specifically, we show the existence of EFX allocations for the following three cases: (i) the number of chores is at most twice the number of agents, (ii) the cost functions of all agents except for one are identical ordering, and (iii) the number of agents is three and each agent has a personalized bi-valued cost function. Furthermore, we provide a polynomial time algorithm to find an EFX allocation for each case.

翻译：离散公平分配中最重要的课题之一是对于任意实例是否存在EFX分配。尽管EFX分配的存在性对于物品和家务而言都是一个尚未解决的开放问题，但与物品相比，人们对家务的EFX分配存在性的理解尚不充分。我们在所有代理的成本函数均为可加性的假设下研究了家务的EFX分配存在性。具体而言，我们证明了以下三种情况下EFX分配的存在性：(i) 家务数量不超过代理数量的两倍，(ii) 除一名代理外所有代理的成本函数具有相同序关系，以及(iii) 代理数量为三且每位代理具有个性化双值成本函数。此外，我们针对每种情况提供了寻找EFX分配的多项式时间算法。