  We consider the problem of cache-aided multi-user private information
retrieval (MuPIR). In this problem, $N$ independent files are replicated across
$S \geq 2$ non-colluding servers. There are $K$ users, each equipped with cache
memory which can store $M$ files. Each user wants to retrieve a file from the
servers, but the users don't want any of the servers to get any information
about their demand. The user caches are filled with some arbitrary function of
the files before the users decide their demands, known as the placement phase.
After deciding their demands, users cooperatively send queries to the servers
to retrieve their desired files privately. Upon receiving the queries, servers
broadcast coded transmissions which are a function of the queries they received
and the files, known as the delivery phase. Conveying queries to the servers
incurs an upload cost for the users, and downloading the answers broadcasted by
the servers incurs a download cost. To implement cache-aided MuPIR schemes,
each file has to be split into $F$ packets. In this paper, we propose MuPIR
schemes that utilize placement delivery arrays (PDAs) to characterize placement
and delivery. Proposed MuPIR schemes significantly reduce subpacketization
levels while slightly increasing the download cost. The proposed scheme also
substantially reduces the upload cost for the users. For PDAs based on {\it
Ali-Niesen} scheme for centralized coded caching, we show that our scheme is
order optimal in terms of download cost. We recover the optimal single-user PIR
scheme presented by {\it Tian et al.} as a special case. Our scheme also
achieves optimal rate for single-user cache-aided PIR setup reported by R.
Tondon.
