  User mobility has a large effect on optimal content placement in D2D caching
networks. Since a typical user can communicate neighboring users who stay in
the D2D communication area of the typical user, the optimal content placement
should be changed according to the user mobility. Under consideration of
randomness of incoming and outgoing users, we formulate an optimization problem
to minimize the average data load of a BS. It is proved that minimization of
the average data load of a BS can be transformed to maximization of a monotonic
submodular function with a matroid constraint, for which a greedy algorithm can
find near-optimal solutions. Moreover, when motions of neighboring users are
rapid, the optimal content placement is derived in closed-form, aided by
reasonable approximation and relaxation. In the high mobility regime, the
optimal content placement is shown to cache partial amounts of the most popular
contents.
