In this paper, we consider the problem of how to fairly dividing $m$ indivisible chores among $n$ agents. The fairness measure we considered here is the maximin share. The previous best known result is that there always exists a $\frac{4}{3}$ approximation maximin share allocation. With a novel algorithm, we can always find a $\frac{11}{9}$ approximation maximin share allocation for any instances. We also discuss how to improve the efficiency of the algorithm and its connection to the job scheduling problem.

翻译：在本文中,我们思考了如何将百万美元的不可分割的家务劳动公平分成于一美元代理商的问题。我们在这里考虑的公平性衡量标准是最大份额。 先前最已知的结果是始终存在$\frac{4 ⁇ 3}$近似份额最大分配。 使用一种新奇的算法, 我们总是可以找到$\frac{11 ⁇ 9}$近似份额最大分配方式。 我们还讨论如何提高算法的效率及其与工作时间安排问题的联系。