  The device-to-device communication-aided fog radio access network, referred
to as \textit{D2D-aided F-RAN}, takes advantage of caching at enhanced remote
radio heads (eRRHs) and D2D proximity for improved system performance. For
D2D-aided F-RAN, we develop a framework that exploits the cached contents at
eRRHs, their transmission rates/powers, and previously received contents by
different users to deliver the requesting contents to users with a minimum
completion time. Given the intractability of the completion time minimization
problem, we formulate it at each transmission by approximating the completion
time and decoupling it into two subproblems. In the first subproblem, we
minimize the possible completion time in eRRH downlink transmissions, while in
the second subproblem, we maximize the number of users to be scheduled on D2D
links. We design two theoretical graphs, namely \textit{interference-aware
instantly decodable network coding (IA-IDNC)} and \textit{D2D conflict} graphs
to reformulate two subproblems as maximum weight clique and maximum independent
set problems, respectively. Using these graphs, we heuristically develop joint
and coordinated scheduling approaches. Through extensive simulation results, we
demonstrate the effectiveness of the proposed schemes against existing baseline
schemes. Simulation results show that the proposed two approaches achieve a
considerable performance gain in terms of the completion time minimization.
