  We study the problem of fairly allocating a divisible resource, also known as
cake cutting, with an additional requirement that the shares that different
agents receive should be sufficiently separated from one another. This
captures, for example, constraints arising from social distancing guidelines.
While it is sometimes impossible to allocate a proportional share to every
agent under the separation requirement, we show that the well-known criterion
of maximin share fairness can always be attained. We then provide algorithmic
analysis of maximin share fairness in this setting -- for instance, the maximin
share of an agent cannot be computed exactly by any finite algorithm, but can
be approximated with an arbitrarily small error. In addition, we consider the
division of a pie (i.e., a circular cake) and show that an ordinal relaxation
of maximin share fairness can be achieved. We also prove that an envy-free or
equitable allocation that allocates the maximum amount of resource exists under
separation.
