  We consider the problem of fairly allocating a sequence of indivisible items
that arrive online in an arbitrary order to a group of n agents with additive
normalized valuation functions. We consider both the allocation of goods and
chores and propose algorithms for approximating maximin share (MMS)
allocations. When agents have identical valuation functions the problem
coincides with the semi-online machine covering problem (when items are goods)
and load balancing problem (when items are chores), for both of which optimal
competitive ratios have been achieved. In this paper, we consider the case when
agents have general additive valuation functions. For the allocation of goods,
we show that no competitive algorithm exists even when there are only three
agents and propose an optimal 0.5-competitive algorithm for the case of two
agents. For the allocation of chores, we propose a (2-1/n)-competitive
algorithm for n>=3 agents and a square root of 2 (approximately
1.414)-competitive algorithm for two agents. Additionally, we show that no
algorithm can do better than 15/11 (approximately 1.364)-competitive for two
agents.
