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

Classes of Symmetric Cayley Graphs over Finite Abelian Groups of Degrees 4 and 6

The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.Comment: 12 pages. A previous version of some of the results in this paper where first announced at 2010 International Workshop on Optimal Interconnection Networks (IWONT 2010). It is accessible at http://upcommons.upc.edu/revistes/handle/2099/1037

Symmetric L-graphs

In this paper we characterize symmetric L-graphs, which are either Kronecker products of two cycles or Gaussian graphs. Vertex symmetric networks have the property that the communication load is uniformly distributed on all the vertices so that there is no point of congestion. A stronger notion of symmetry, edge symmetry, requires that every edge in the graph looks the same. Such property ensures that the communication load is uniformly distributed over all the communication links, so that there is no congestion at any link.Peer Reviewe

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

S-SMART++: A Low-Latency NoC Leveraging Speculative Bypass Requests

Many-core processors demand scalable, efficient and low latency NoCs. Bypass routers are an affordable solution to attain low latency in relatively simple topologies like the mesh. SMART improves on traditional bypass routers implementing multi-hop bypass which reduces the importance of the distance between pairs of nodes. Nevertheless, the conservative buffer reallocation policy of SMART requires a large number of Virtual Channels (VCs) to offer high performance, penalizing its implementation cost. Besides, SMART zero-load latency values highly depend on HPC Max HPCMax, the maximum number of hops that can be jumped per cycle. In this article, we present Speculative-SMART++ (S-SMART++), with two mechanisms that significantly improve multi-hop bypass. First, zero-load latency is reduced by speculatively setting consecutive multi-hops. Second, the inefficient buffer reallocation policy of SMART is reduced by combining multi-packet buffers, Non-Empty Buffer Bypass and per-packet allocation. These proposals are evaluated using functional simulation, with synthetic and real loads, and synthesis tools. S-SMART++ does not need VCs to obtain the performance of SMART with 8 VCs, reducing notably logic resources and dynamic power. Additionally, S-SMART++ reduces the base-latency of SMART by at least 29.2 percent, even when using the biggest HPC Max HPCMax possibleThis work was supported by the Spanish Ministry of Science, Innovation and Universities, FPI grant BES2017-079971, the Spanish Ministry of Science, Innovation and Universities under contracts TIN2016-76635-C2-2-R (AEI/FEDER, UE) and TIC PID2019-105660RB-C22, and the European HiPEAC Network of Excellence. The Mont-Blanc project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 671697

Lattice Graphs for High-Scale Interconnection Topologies

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 this kind of 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 mesh-based interconnection networks. As they are built over n-dimensional grids that induce a regular tiling of space, these topologies have been denoted lattice graphs. Higher dimensional networks can be composed over these graphs by means of a lift operation, which is also introduced in the paper. Easy network partitioning and minimal routing algorithm are also provided for these topologies based on this new network operation. Later we focus on cubic crystal lattices for modeling symmetric 3D networks and to show how lattice graphs can help in the design of twisted interconnection networks. In all cases, the networks obtained are better, in topological terms, than their standard tori counterparts. Finally, some practical issues such as implementability and preliminary performance evaluations have been addressed at the end of this work.This work has been supported by the Spanish FPU grant AP2010-4900, the Spanish Science and Technology Commission (CICYT) under contracts TIN2010-21291-C02-02 and TIN2013-46957-C2-2-P, the European Union FP7 under Agreements ICT-288777 (Mont-Blanc) and ERC-321253 (RoMoL), the European HiPEAC Network of Excellence and the JSA no. 2013-119 as part of the IBM/BSC Technology Center for Supercomputing agreement

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

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