We consider the problem of approximate maximin share (MMS) allocation of indivisible items among three agents with additive valuation functions. For goods, we show that an $\frac{11}{12}$ - MMS allocation always exists, improving over the previously known bound of $\frac{8}{9}$ . Moreover, in our allocation, we can prespecify an agent that is to receive her full proportional share (PS); we also present examples showing that for such allocations the ratio of $\frac{11}{12}$ is best possible. For chores, we show that a $\frac{19}{18}$-MMS allocation always exists. Also in this case, we can prespecify an agent that is to receive no more than her PS, and we present examples showing that for such allocations the ratio of $\frac{19}{18}$ is best possible.

翻译：我们考虑的是三个具有添加性估价功能的代理商之间分配不可分割物品的大致最大份额(MMS)问题。对于货物,我们表明始终存在美元(frac{11}12}-MMS分配额,这比以前已知的$(frac}8}9}美元约束额有所改善。此外,在我们的分配中,我们可以预先确定一个代理商将获得其全部比例份额(PS);我们还举出一些例子,表明对于这种分配,最有可能的是美元(frac{11}12}美元的比例。对于杂务,我们表明始终存在美元(frac{19}18}-MMS分配额。同样,我们可以预先确定一个不会得到超过PS的代理商,我们举例表明,对于这种分配,最有可能得到$(frac}19{18}。