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In large-scale supercomputers, the interconnection network plays a key role in system performance. Network topology highly defines the performance and cost of the interconnection network. Direct topologies are sometimes used due to its reduced hardware cost, but the number of network dimensions is limited by the physical 3-D space, which leads to an increase of the communication latency and a reduction of network throughput for large machines. Indirect topologies can provide better performance for large machines, but at higher hardware cost. In this paper, we propose a new family of hybrid topologies, the k-ary n-direct s-indirect, that combines the best features from both direct and indirect topologies to efficiently connect an extremely high number of processing nodes. The proposed network is an n-dimensional topology where the k nodes of each dimension are connected through a small indirect topology of s stages. This combination results in a family of topologies that provides high performance, with latency and throughput figures of merit close to indirect topologies, but at a lower hardware cost. In particular, it doubles the throughput obtained per cost unit compared with indirect topologies in most of the cases. Moreover, their fault-tolerance degree is similar to the one achieved by direct topologies built with switches with the same number of ports.

Exascale computing systems are being built with thousands of nodes. The high number of components of these systems significantly increases the probability of failure. A key component for them is the interconnection network. If failures occur in the interconnection network, they may isolate a large fraction of the machine. For this reason, an efficient fault-tolerant mechanism is needed to keep the system interconnected, even in the presence of faults. A recently proposed topology for these large systems is the hybrid k-ary n-direct s-indirect (KNS) family that provides optimal performance and connectivity at a reduced hardware cost. This paper presents a fault-tolerant routing methodology for the KNS topology that degrades performance gracefully in presence of faults and tolerates a large number of faults without disabling any healthy computing node. In order to tolerate network failures, the methodology uses a simple mechanism. For any source-destination pair, if necessary, packets are forwarded to the destination node through a set of intermediate nodes (without being ejected from the network) with the aim of circumventing faults. The evaluation results shows that the proposed methodology tolerates a large number of faults. For instance, it is able to tolerate more than 99.5% of fault combinations when there are ten faults in a 3-D network with 1,000 nodes using only one intermediate node and more than 99.98% if two intermediate nodes are used. Furthermore, the methodology offers a gracious performance degradation. As an example, performance degrades only by 1% for a 2-D network with 1,024 nodes and 1% faulty links.

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