We study several fairness notions in allocating indivisible chores (i.e., items with non-positive values): envy-freeness and its relaxations. For allocations under each fairness criterion, we establish their approximation guarantee for other fairness criteria. Under the setting of additive cost functions, our results show strong connections between these fairness criteria and, at the same time, reveal intrinsic differences between goods allocation and chores allocation. Furthermore, we investigate the efficiency loss under these fairness constraints and establish their prices of fairness.

翻译：我们研究在分配不可分割的家务(即非积极价值的物品):无忌妒及其放松方面的若干公平概念;对于在每一项公平标准下的拨款,我们为其他公平标准建立近似保证;在确定累加成本功能时,我们的结果显示这些公平标准之间有着密切的联系,同时揭示了货物分配和家务分配之间的内在差异;此外,我们调查在这种公平限制下的效率损失并确定其公平价格。