Hoffman–Singleton graph

Abstract: The flourishing large-scale and high-throughput web applications have emphasized the importance of high-density servers for their distinct advantages, such as high computing density, low power and low space requirements. To achieve above advantages, an efficient intra-server interconnection network is necessary. Most state-of-the-art high-density servers adopt the fully-connected intra-server network to achieve high network performance. Unfortunately, this solution is very expensive due to the high degree of nodes. To address this problem, we exploit the theory optimized moore graph to interconnect the chips within a server. Considering the size of applications, the 50-size moore graph, namely the Hoffman-Singleton graph, is extensively discussed in this paper. The simulation results show that it could attain comparative performance as the fully-connected network with much lower cost. In practice, however, chips could be integrated onto multiple boards. Thus, the graph should be divided into self-connected sub-graphs with the same size. Unfortunately, state-of-the-art solutions do not consider the production problem and generate heterogeneous sub graphs. To address this problem, we propose two equivalent-partition solutions for Hoffman-Singleton graph depending on the density of boards. Finally, we propose and evaluate a deadlock-free routing algorithm for each partition scheme.