SymSig: A low latency interconnection topology for HPC clusters

Brahme, Dhananjay; Bhardwaj, Onkar; Chaudhary, Vipin

doi:10.1109/hipc.2013.6799144

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…This relaxed problem consists in finding for every diameter k an infinite family of graphs with about k vertices. Such graphs exist for k = 1 (complete graphs), k = 2 [Brown 1966;Brahme et al 2013], k = 3, and k = 5 [Delorme 1985]. They are conjectured to exist for any diameter, but even the best general bounds are exponential in k. The work in Brahme et al [2013] seems to be the first to propose one of these families as interconnection networks but fails to address many practical problems.…”

Section: Related Workmentioning

confidence: 91%

Topological Characterization of Hamming and Dragonfly Networks and Its Implications on Routing

Camarero

Vallejo

Beivide

2014

ACM Trans. Archit. Code Optim.

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Current High-Performance Computing (HPC) and data center networks rely on large-radix routers. Hamming graphs (Cartesian products of complete graphs) and dragonflies (two-level direct networks with nodes organized in groups) are some direct topologies proposed for such networks. The original definition of the dragonfly topology is very loose, with several degrees of freedom, such as the inter-and intragroup topology, the specific global connectivity, and the number of parallel links between groups (or trunking level). This work provides a comprehensive analysis of the topological properties of the dragonfly network, providing balancing conditions for network dimensioning, as well as introducing and classifying several alternatives for the global connectivity and trunking level. From a topological study of the network, it is noted that a Hamming graph can be seen as a canonical dragonfly topology with a high level of trunking. Based on this observation and by carefully selecting the global connectivity, the Dimension Order Routing (DOR) mechanism safely used in Hamming graphs is adapted to dragonfly networks with trunking. The resulting routing algorithms approximate the performance of minimal, nonminimal, and adaptive routings typically used in dragonflies but without requiring virtual channels to avoid packet deadlock, thus allowing for lower cost router implementations. This is obtained by properly selecting the link to route between groups based on a graph coloring of network routers. Evaluations show that the proposed mechanisms are competitive with traditional solutions when using the same number of virtual channels and enable for simpler implementations with lower cost. Finally, multilevel dragonflies are discussed, considering how the proposed mechanisms could be adapted to them. ACM Reference Format:Cristóbal Camarero, Enrique Vallejo, and Ramón Beivide. 2014. Topological characterization of Hamming and dragonfly networks and its implications on routing. ACM Trans.

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Section: Related Workmentioning

confidence: 91%

Topological Characterization of Hamming and Dragonfly Networks and Its Implications on Routing

Camarero

Vallejo

Beivide

2014

ACM Trans. Archit. Code Optim.

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“…Independently and simultaneously, Brown in [7] and Erdős et al in [15] defined this graph, which is introduced next. Interestingly, Brahme et al have recently unknowingly reinvented these graphs with a different construction and in [5] they already proposed them for HPC clusters. However, in this paper the next definition will be considered as the network topology model.…”

Section: Modified Incidence Graph Of Finite Projective Planesmentioning

confidence: 99%

“…As stated in previous sections, our aim is to find topologies being optimal according to Equations (2) and (5). That is, for a givenk and R, the goal is to find well-balanced topologies with maximum number of terminals T .…”

Section: Topologies Near the Moore Boundmentioning

confidence: 99%

“…In fact, Valerio et al already use them to define Orthogonal Fat Trees (OFT) [39], which are highly scalable cost optimal indirect networks. Brahme et al [5] propose other topologies for direct networks for HPC clusters. Al it is shown in this paper, they can also be defined using projective planes, although the authors use perfect difference sets for their definition.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Projective Networks: Topologies for Large Parallel Computer Systems

Camarero

Martínez

Vallejo

et al. 2017

IEEE Trans. Parallel Distrib. Syst.

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The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance topologies with the aim of minimizing these costs. However, they fail to consider potential unbalance in the network utilization, which in some cases results in suboptimal designs. Based on an appropriate cost model, this paper advocates the use of networks based on incidence graphs of projective planes, broadly denoted as Projective Networks. Projective Networks rely on highly symmetric generalized Moore graphs and encompass several proposed direct (PN and demi-PN) and indirect (OFT) topologies under a common mathematical framework. Compared to other proposals with average distance between 2 and 3 hops, these networks provide very high scalability while preserving a balanced network utilization, resulting in low network costs. Overall, Projective Networks constitute a competitive alternative for exascale-level interconnection network design.

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Ant Mill: an adversarial traffic pattern for low-diameter direct networks

Camarero,

Martínez,

Beivide

2024

J Supercomput

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Since today’s HPC and data center systems can comprise hundreds of thousands of servers and beyond, it is crucial to equip them with a network that provides high performance. New topologies proposed to achieve such performance need to be evaluated under different traffic conditions, aiming to closely replicate real-world scenarios. While most optimizations should be guided by common traffic patterns, it is essential to ensure that no pathological traffic pattern can compromise the entire system. Determining synthetic adversarial traffic patterns for a network typically relies on a thorough understanding of its topology and routing. In this paper, we address the problem of identifying a generic adversarial traffic pattern for low-diameter direct interconnection networks. We first focus on Random Regular Graphs (RRGs), which represent a typical case for these networks. Moreover, RRGs have been proposed as topologies for interconnection networks due to their superior scalability and expandability, among other advantages. We introduce Ant Mill, an adversarial traffic pattern for RRGs when using routes of minimal length. Secondly, we demonstrate that the Ant Mill traffic pattern is also adversarial in other low-diameter direct interconnection networks such as Slimfly, Dragonfly, and Projective networks. Ant Mill is thoroughly motivated and evaluated, enabling future studies of low-diameter direct interconnection networks to leverage its findings.

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SymSig: A low latency interconnection topology for HPC clusters

Cited by 7 publications

References 9 publications

Topological Characterization of Hamming and Dragonfly Networks and Its Implications on Routing

Topological Characterization of Hamming and Dragonfly Networks and Its Implications on Routing

Projective Networks: Topologies for Large Parallel Computer Systems

Ant Mill: an adversarial traffic pattern for low-diameter direct networks

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