  We propose the CLEX supercomputer topology and routing scheme. We prove that
CLEX can utilize a constant fraction of the total bandwidth for point-to-point
communication, at delays proportional to the sum of the number of intermediate
hops and the maximum physical distance between any two nodes. Moreover, %
applying an asymmetric bandwidth assignment to the links, all-to-all
communication can be realized $(1+o(1))$-optimally both with regard to
bandwidth and delays. This is achieved at node degrees of $n^{\varepsilon}$,
for an arbitrary small constant $\varepsilon\in (0,1]$. In contrast, these
results are impossible in any network featuring constant or polylogarithmic
node degrees. Through simulation, we assess the benefits of an implementation
of the proposed communication strategy. Our results indicate that, for a
million processors, CLEX can increase bandwidth utilization and reduce average
routing path length by at least factors $10$ respectively $5$ in comparison to
a torus network. Furthermore, the CLEX communication scheme features several
other properties, such as deadlock-freedom, inherent fault-tolerance, and
canonical partition into smaller subsystems.
