  Communication latency has become one of the determining factors for the
performance of parallel clusters. To design low-latency network topologies for
high-performance computing clusters, we optimize the diameters, mean path
lengths, and bisection widths of circulant topologies. We obtain a series of
optimal circulant topologies of size $2^5$ through $2^{10}$ and compare them
with torus and hypercube of the same sizes and degrees. We further benchmark on
a broad variety of applications including effective bandwidth, FFTE, Graph 500
and NAS parallel benchmarks to compare the optimal circulant topologies and
Cartesian products of optimal circulant topologies and fully connected
topologies with corresponding torus and hypercube. Simulation results
demonstrate superior potentials of the optimal circulant topologies for
communication-intensive applications. We also find the strengths of the
Cartesian products in exploiting global communication with data traffic
patterns of specific applications or internal algorithms.
