  We consider a MapReduce-type task running in a distributed computing model
which consists of ${K}$ edge computing nodes distributed across the edge of the
network and a Master node that assists the edge nodes to compute output
functions. The Master node and the edge nodes, both equipped with some storage
memories and computing capabilities, are connected through a multicast network.
We define the communication time spent during the transmission for the
sequential implementation (all nodes send symbols sequentially) and parallel
implementation (the Master node can send symbols during the edge nodes'
transmission), respectively. We propose a mixed coded distributed computing
scheme that divides the system into two subsystems where the coded distributed
computing (CDC) strategy proposed by Songze Li \emph{et al.} is applied into
the first subsystem and a novel master-aided CDC strategy is applied into the
second subsystem. We prove that this scheme is optimal, i.e., achieves the
minimum communication time for both the sequential and parallel implementation,
and establish an {\emph{optimal}} information-theoretic tradeoff between the
overall communication time, computation load, and the Master node's storage
capacity. It demonstrates that incorporating a Master node with storage and
computing capabilities can further reduce the communication time. For the
sequential implementation, we deduce the approximately optimal file allocation
between the two subsystems, which shows that the Master node should map as many
files as possible in order to achieve smaller communication time. For the
parallel implementation, if the Master node's storage and computing
capabilities are sufficiently large (not necessary to store and map all files),
then the proposed scheme requires at most 1/2 of the minimum communication time
of system without the help of the Master node.
