Symmetric Interconnection Networks from Cubic Crystal Lattices

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of these networks. By using integral matrices to deal with Cayley graphs over Abelian groups, we have been able to propose and analyze a family of high-dimensional grid-based interconnection networks. As they are built over $n$-dimensional grids that induce a regular tiling of the space, these topologies have been denoted \textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling symmetric 3D networks. Other higher dimensional networks can be composed over these graphs, as illustrated in this research. Easy network partitioning can also take advantage of this network composition operation. Minimal routing algorithms are also provided for these new topologies. Finally, some practical issues such as implementability and preliminary performance evaluations have been addressed

Analysing Mechanisms for Virtual Channel Management in Low-Diameter networks

To interconnect their growing number of servers, current supercomputers and data centers are starting to adopt low-diameter networks, such as HyperX, Dragonfly and Dragonfly+. These emergent topologies require balancing the load over their links and finding suitable non-minimal routing mechanisms for them becomes particularly challenging. The Valiant load balancing scheme is a very popular choice for non-minimal routing. Evolved adaptive routing mechanisms implemented in real systems are based on this Valiant scheme. All these low-diameter networks are deadlock-prone when non-minimal routing is employed. Routing deadlocks occur when packets cannot progress due to cyclic dependencies. Therefore, developing efficient deadlock-free packet routing mechanisms is critical for the progress of these emergent networks. The routing function includes the routing algorithm for path selection and the buffers management policy that dictates how packets allocate the buffers of the switches on their paths. For the same routing algorithm, a different buffer management mechanism can lead to a very different performance. Moreover, certain mechanisms considered efficient for avoiding deadlocks, may still suffer from hard to pinpoint instabilities that make erratic the network response. This paper focuses on exploring the impact of these buffers management policies on the performance of current interconnection networks, showing a 90\% of performance drop if an incorrect buffers management policy is used. Moreover, this study not only characterizes some of these undesirable scenarios but also proposes practicable solutions

Energy-Efficient Interconnection Networks for High-Performance Computing

In recent years, energy has become one of the most important factors for de- signing and operating large scale computing systems. This is particularly true in high-performance computing, where systems often consist of thousands of nodes. Especially after the end of Dennard’s scaling, the demand for energy- proportionality in components, where energy is depending linearly on utilization, increases continuously. As the main contributor to the overall power consumption, processors have received the main attention so far. The increasing energy proportionality of processors, however, shifts the focus to other components such as interconnection networks. Their share of the overall power consumption is expected to increase to 20% or more while other components further increase their efficiency in the near future. Hence, it is crucial to improve energy proportionality in interconnection networks likewise to reduce overall power and energy consumption. To facilitate these attempts, this work provides comprehensive studies about energy saving in interconnection networks at different levels. First, interconnection networks differ fundamentally from other components in their underlying technology. To gain a deeper understanding of these differences and to identify targets for energy savings, this work provides a detailed power analysis of current network hardware. Furthermore, various applications at different scales are analyzed regarding their communication patterns and locality properties. The findings show that communication makes up only a small fraction of the execution time and networks are actually idling most of the time. Another observation is that point-to-point communication often only occurs within various small subsets of all participants, which indicates that a coordinated mapping could further decrease network traffic. Based on these studies, three different energy-saving policies are designed, which all differ in their implementation and focus. Then, these policies are evaluated in an event-based, power-aware network simulator. While two policies that operate completely local at link level, enable significant energy savings of more than 90% in most analyses, the hybrid one does not provide further benefits despite significant additional design effort. Additionally, these studies include network design parameters, such as transition time between different link configurations, as well as the three most common topologies in supercomputing systems. The final part of this work addresses the interactions of congestion management and energy-saving policies. Although both network management strategies aim for different goals and use opposite approaches, they complement each other and can increase energy efficiency in all studies as well as improve the performance overhead as opposed to plain energy saving

Polarized routing for large interconnection networks

Supercomputers and datacenters comprise hundreds of thousands of servers. Different network topologies have been proposed to attain such a high scalability, from flattened Butterfly and Dragonfly to the most disruptive Jellyfish, which is based on a random graph. The routing problem on such networks remains a challenge that can be tackled either as a topology-aware solution or with an agnostic approach. The case of random networks is a very special one since no a priori topological clues can be exploited. In this article, we introduce the polarized routing algorithm, an adaptive nonminimal hop-by-hop mechanism that can be used in most of topologies, including Jellyfish. Polarized routing follows two design criteria: a source-destination symmetry in the routes and avoiding backtracking. Experimental evaluation proves that polarized routing not only outperforms other routings in random graphs but also attains the best performance provided by ad hoc solutions for specific outstanding low-diameter interconnection networks.This work has been supported by the Spanish Ministry of Science and Innovation under contracts PID2019-105660RB-C22 and FJCI-2017-31643. Simulations were performed in the Altamira supercomputer, a node of the Spanish Super-computing Network

On random wiring in practicable folded clos networks for modern datacenters

Big scale, high performance and fault-tolerance, low-cost and graceful expandability are pursued features in current datacenter networks (DCN). Although there have been many proposals for DCNs, most modern installations are equipped with classical folded Clos networks. Recently, regular random topologies, as the Jellyfish, have been proposed for DCNs. However, their completely unstructured nature entails serious design problems. In this paper we propose Random Folded Clos (RFC) and Hydra networks in which the interconnection between certain switches levels is made randomly. Both RFCs and Hydras preserve important properties of Clos networks that provide a straightforward deadlock-free multi-path routing. The proposed networks leverage randomness to be gracefully expandable, thereby allowing for fine grain upgrading. RFCs and Hydras are compared in the paper, in topological and cost terms, against fat-trees, orthogonal fat-trees and random regular networks. Also, experiments are carried out to simulate their performance under synthetic traffic patterns emulating common loads present in warehouse scale computers. These theoretical and empirical studies reveal the interest of these topologies, concluding that Hydra constitutes a practicable alternative to current datacenter networks since it appropriately balance all the main design requirements. Moreover, Hydras perform better than the fat-trees, their natural competitor, being able to connect the same or more computing nodes with significant lower cost and latency while exhibiting comparable throughput. © 1990-2012 IEEE

The impact of global communication latency at extreme scales on Krylov methods

Krylov Subspace Methods (KSMs) are popular numerical tools for solving large linear systems of equations. We consider their role in solving sparse systems on future massively parallel distributed memory machines, by estimating future performance of their constituent operations. To this end we construct a model that is simple, but which takes topology and network acceleration into account as they are important considerations. We show that, as the number of nodes of a parallel machine increases to very large numbers, the increasing latency cost of reductions may well become a problematic bottleneck for traditional formulations of these methods. Finally, we discuss how pipelined KSMs can be used to tackle the potential problem, and appropriate pipeline depths