  In this paper, we study the classic problem of fairly allocating indivisible
items with the extra feature that the items lie on a line. Our goal is to find
a fair allocation that is contiguous, meaning that the bundle of each agent
forms a contiguous block on the line. While allocations satisfying the
classical fairness notions of proportionality, envy-freeness, and equitability
are not guaranteed to exist even without the contiguity requirement, we show
the existence of contiguous allocations satisfying approximate versions of
these notions that do not degrade as the number of agents or items increases.
We also study the efficiency loss of contiguous allocations due to fairness
constraints.
