  We investigate the problem of private read update write (PRUW) in relation to
federated submodel learning (FSL) with storage constrained databases. In PRUW,
a user privately reads a submodel from a system of $N$ databases containing $M$
submodels, updates it locally, and writes the update back to the databases
without revealing the submodel index or the value of the update. The databases
considered in this problem are only allowed to store a given amount of
information specified by an arbitrary storage constraint. We provide a storage
mechanism that determines the contents of each database prior to the
application of the PRUW scheme, such that the total communication cost is
minimized. We show that the proposed storage scheme achieves a lower total cost
compared to what is achieved by using \emph{coded storage} or \emph{divided
storage} to meet the given storage constraint.
