SymSig: A low latency interconnection topology for HPC clusters

This paper presents the underlying theory and the performance of a cluster using a new 2-hop network topology. This topology is constructed using a symmetric equation and Singer Difference Sets and is called SymSig. The degree of connections at each node with SymSig is about half compared to previous methods using Singer Difference Sets. A comparison with a cluster of Clos topology shows significant advantages. The worst case congestion in SymSig topology for unicast permutation is 2, where as in Clos it is proportional to the radix of the building block switches used. The number of switches required is smaller by about 25%, the size of the cluster is larger by about 15% and the worst bandwidth is better by about 50% for SymSig. These advantages are retained for peta and exascale systems. Its performance on a set of collectives like exchange-all, shift-all, broadcast-all and all-to-all send/receive shows improvements ranging from 39% to 83%. Its performance on a molecular dynamics application GROMMACS shows improvement of upto 33%. This network is particularly suitable for applications that require global all to all communications. The low latency of this network makes it scaleable and an attractive alternative for building peta and exascale systems.