Recently proposed irregular networks can reduce the latency for both on-chip and off-chip systems with a large number of computing nodes and thus can improve the performance of parallel applications. However, these networks usually suffer from deadlocks in routing packets when using a naive minimal path routing algorithm. To solve this problem, we focus attention on a lately proposed theory that generalizes the turn model to maintain the network performance with deadlock-freedom. The theorems remain a challenge of applying themselves to arbitrary topologies including fully irregular networks. In this paper, we advance the theorems to completely general ones. Moreover, we provide a feasible implementation of a deadlock-free routing method based on our advanced theorem. Experimental results show that the routing method based on our proposed theorem can improve the network throughput by up to 138 % compared to a conventional deterministic minimal routing method. Moreover, when utilized as the escape path in Duato's protocol, it can improve the throughput by up to 26.3 % compared with the conventional up*/down* routing.

Inter-switch networks for HPC systems and data-centers can be improved by applying random shortcut topologies with a reduced number of hops. With minimal routing in such networks; however, deadlock-freedom is not guaranteed. Multiple Virtual Channels (VCs) are efficiently used to avoid this problem. However, previous works do not provide good trade-offs between the number of required VCs and the time and memory complexities of an algorithm. In this work, a novel and fast algorithm, named ACRO, is proposed to endorse the arbitrary routing functions with deadlock-freedom, as well as consuming a small number of VCs. A heuristic approach to reduce VCs is achieved with a hash table, which improves the scalability of the algorithm compared with our previous work. Moreover, experimental results show that ACRO can reduce the average number of VCs by up to 63% when compared with a conventional algorithm that has the same time complexity. Furthermore, ACRO reduces the time complexity by a factor of O(|N|⋅log|N|), when compared with another conventional algorithm that requires almost the same number of VCs.

A Modified Hierarchical 3D-Torus (MH3DT) network is a 3D-torus network consisting of multiple basic modules, in which each basic module itself is a 3D-torus network. Inter-node communication performance has been evaluated using dimension-order routing and 2 virtual channels (VCs) under uniform traffic patterns but not under non-uniform traffic patterns. In this paper, we evaluate the inter-node communication performance of MH3DT under five non-uniform traffic patterns and compare it with other networks. We found that under non-uniform traffic patterns, the MH3DT yields high throughput and low latency, providing better inter-node communication performance compared to H3DT, TESH, mesh, and torus networks. Also, we found that non-uniform traffic patterns have higher throughput than uniform traffic in the MH3DT network.

Interconnection networks play a crucial role in the performance of massively parallel computers. Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Tori connected Torus Network (TTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 2D-torus networks that are hierarchically interconnected for higher-level networks. This paper addresses the architectural details of the TTN and explores aspects such as node degree, network diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the TTN using four virtual channels and evaluate the network's dynamic communication performance using the proposed routing algorithm under uniform and various non-uniform traffic patterns. We evaluate the dynamic communication performance of TTN, TESH, MH3DT, mesh, and torus networks by computer simulation. It is shown that the TTN possesses several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate (neither too low, nor too high) bisection width, and high throughput and very low zero load latency, which provide better dynamic communication performance than that of other conventional and hierarchical networks.

Three-dimensional (3D) wafer stacked implementation (WSI) has been proposed as a promising technology for massively parallel computers. A hierarchical 3D-torus (H3DT) network, which is a 3D-torus network of multiple basic modules in which the basic modules are 3D-mesh networks, has been proposed for efficient 3D-WSI. However, the restricted use of physical links between basic modules in the higher level networks reduces the dynamic communication performance of this network. A torus network has better dynamic communication performance than a mesh network. Therefore, we have modified the H3DT network by replacing the 3D-mesh modules by 3D-tori, calling it a Modified H3DT (MH3DT) network. This paper addresses the architectural details of the MH3DT network and explores aspects such as degree, diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the MH3DT network using two virtual channels and evaluate the network's dynamic communication performance under the uniform traffic pattern, using the proposed routing algorithm. It is shown that the MH3DT network possesses several attractive features including small diameter, small cost, small average distance, better bisection width, and better dynamic communication performance.

Interconnection networks play a crucial role in the performance of massively parallel computers. Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Hierarchical Torus Network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher level networks. The static network performance of the HTN has already been studied and has been shown to be good. Dynamic communication performance has been evaluated under uniform traffic pattern but not under non-uniform traffic patterns. In this paper, we present a deadlock-free routing algorithm for the HTN using 3 virtual channels and evaluate the network's dynamic communication performance under three non-uniform traffic patterns, using the proposed routing algorithm. We evaluate the dynamic communication performance of HTN, H3D-mesh, H3D-torus, TESH, and mesh networks by computer simulation. We find that the dynamic communication performance of HTN is better than that of the H3D-mesh, H3D-torus, TESH, and mesh networks.