In this paper three communication algorithms are proposed for two types of
generalized hypercube multiprocessor. The algorithms are intended to Solve
three intensive communication problems: complete broadcast, single-node sca
tter and total exchange. The algorithms achieve both the time and transmiss
ion complexity bounds for the three problems on the balanced generalized hy
percube (BGHC). The BGHC is a w(d)-node network with w nodes along each of
the d dimensions. These communication algorithms are performed based on a b
alanced spanning tree, called a compatible tree, which can be used to solve
any of the tree problems. Several theoretical results related to the compa
tible tree and then the sufficient and necessary condition for concurrent t
ransmissions are presented. The concurrent condition ensures the maximum us
e of network bandwidth so that the optimal bounds are achieved. It is shown
that the proposed scheduling algorithms achieve the optimal bounds for any
w and d.