Optimal circulant graphs as low-latency network topologies

TL;DR

This paper designs and evaluates optimal circulant network topologies for high-performance computing clusters, demonstrating their superior communication efficiency over traditional topologies through extensive benchmarks.

Contribution

It introduces a method to optimize circulant topologies for low latency and compares their performance with torus and hypercube topologies across various benchmarks.

Findings

Optimal circulant topologies have smaller diameters and mean path lengths.

They outperform torus and hypercube in communication-intensive benchmarks.

Cartesian products of circulant topologies effectively exploit global communication patterns.

Abstract

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.