  Recently, a higher dimensional Eisenstein-Jacobi networks, has been proposed
in [22], which is shown that they have better average distance with more number
of nodes than a single dimensional EJ networks. Some communication algorithms
such as one-to-all and all-to-all communications are well known and used in
interconnection networks. In one-to-all communication, a source node sends a
message to every other node in the network. Whereas, in all-to-all
communication, every node is considered as a source node and sends its message
to every other node in the network. In this paper, an improved one-to-all
communication algorithm in higher dimensional EJ networks is presented. The
paper shows that the proposed algorithm achieves a lower average number of
steps to receiving the broadcasted message. In addition, since the links are
assumed to be half-duplex, the all-to-all broadcasting algorithm is divided
into three phases. The simulation results are discussed and showed that the
improved one-to-all algorithm achieves better traffic performance than the
well-known one-to-all algorithm and has 2.7% less total number of senders
