  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.
