On Solving the Decycling Problem in a Torus Network

Abstract

Modern supercomputers are massively parallel systems: they embody thousands of computing nodes and sometimes several millions. The torus topology has proven very popular for the interconnect of these high-performance systems. Notably, this network topology is employed by the supercomputer ranked number one in the world as of November 2020, the supercomputer Fugaku. Given the high number of compute nodes in such systems, efficient parallel processing is critical to maximise the computing performance. It is well known that cycles harm the parallel processing capacity of systems: for instance, deadlocks and starvations are two notorious issues of parallel computing that are directly linked to the presence of cycles. Hence, network decycling is an important issue, and it has been extensively discussed in the literature. We describe in this paper a decycling algorithm for the 3-dimensional $k$ -ary torus topology and compare it with established results, both theoretically and experimentally. (This paper is a revised version of Antoine Bossard (2020)).