  We propose that clusters interconnected with network topologies having
minimal mean path length will increase their overall performance for a variety
of applications. We approach our heuristic by constructing clusters of up to 36
nodes having Dragonfly, torus, ring, Chvatal, Wagner, Bidiakis and several
other topologies with minimal mean path lengths and by simulating the
performance of 256-node clusters with the same network topologies. The optimal
(or sub-optimal) low-latency network topologies are found by minimizing the
mean path length of regular graphs. The selected topologies are benchmarked
using ping-pong messaging, the MPI collective communications, and the standard
parallel applications including effective bandwidth, FFTE, Graph 500 and NAS
parallel benchmarks. We established strong correlations between the clusters'
performances and the network topologies, especially the mean path lengths, for
a wide range of applications. In communication-intensive benchmarks, clusters
with optimal network topologies out-perform those with mainstream topologies by
several folds. It is striking that a mere adjustment of the network topology
suffices to reclaim performance from the same computing hardware.
