Cristobal Camarero

On-the-Fly Adaptive Routing in High-Radix Hierarchical Networks

Dragonfly networks have been recently proposed for the interconnection network of forthcoming exascale supercomputers. Relying on large-radix routers, they build a topology with low diameter and high throughput, divided into multiple groups of routers. While minimal routing is appropriate for uniform traffic patterns, adversarial traffic patterns can saturate inter-group links and degrade the obtained performance. Such traffic patterns occur in typical communication patterns used by many HPC applications, such as neighbor data exchanges in multi-dimensional space decompositions. Non-minimal traffic routing is employed to handle such cases. Adaptive policies have been designed to select between minimal and nonminimal routing to handle variable traffic patterns. However, previous papers have not taken into account the effect of saturation of intra-group (local) links. This paper studies how local link saturation can be common in these networks, and shows that it can largely reduce the performance. The solution to this problem is to use nonminimal paths that avoid those saturated local links. However, this extends the maximum path length, and since all previous routing proposals prevent deadlock by relying on an ascending order of virtual channels, it would imply unaffordable cost and complexity in the network routers. In this paper we introduce a novel routing/flow-control scheme that decouples the routing and the deadlock avoidance mechanisms. Our model does not impose any dependencies between virtual channels, allowing for on-the-fly (in-transit) adaptive routing of packets. To prevent deadlock we employ a deadlock-free escape sub network based on injection restriction. Simulations show that our model obtains lower latency, higher throughput, and faster adaptation to transient traffic, because it dynamically exploits a higher path diversity to avoid saturated links. Notably, our proposal consumes traffic bursts 43% faster than previous ones.

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

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.

L-Networks: A Topological Model for Regular 2D Interconnection Networks

A complete family of Cayley graphs of degree four, denoted as L-networks, is considered in this paper. L-networks are 2D mesh-based topologies with wrap-around connections. L-networks constitute a graph-based model which englobe many previously proposed 2D interconnection networks. Some of them have been extensively used in the industry as the underlying topology for parallel and distributed computers of different scales. Tori, twisted and doubly twisted tori, toroidal diagonal meshes, chordal rings, and circulant graphs are, among others, members of the L-network family. Therefore, many results obtained in previous studies on these networks can be deduced from the general framework presented in this work. In addition, the network model presented in this work allows for new results on the domain of low-degree interconnection networks. Particularly, closed expressions for the graph distance properties have been derived and an optimal routing algorithm of constant complexity is provided. Since symmetry has a big impact on network performance, we have also identified which L-networks are symmetric by studying their group of automorphisms. Finally, a very simple model that predicts the performance of L-networks is also presented. Such model has been contrasted with empirical evaluation.

Cluster architecture based on low cost reconfigurable hardware

The SMILE project accelerates scientific and industrial applications by means of a cluster of low-cost FPGA boards. With this approach the intensive calculation tasks are accelerated using the FPGA logic, while the communication patterns of the applications remains unchanged by using a Message Passing Library over Linux. This paper explains the cluster architecture: the SMILE nodes and the developed high-speed communication network for the FPGA RocketIO interfaces. A SystemC model developed to simulate the cluster is also detailed. In order to show the potential of the SMILE proposal a Content-Based Information Retrieval parallel application has been developed and compared with a HP cluster architecture in terms of response time andpower consumption.

A first approach to king topologies for on-chip networks

In this paper we propose two new topologies for on-chip networks that we have denoted as king mesh and king torus. These are a higher degree evolution of the classical mesh and torus topologies. In a king network packets can traverse the networks using orthogonal and diagonal movements like the king on a chess board. First we present a topological study addressing distance properties, bisection bandwidth and path diversity as well as a folding scheme. Second we analyze different routing mechanisms. Ranging from minimal distance routings to missrouting techniques which exploit the topological richness of these networks. Finally we make an exhaustive performance evaluation comparing the new king topologies with their classical counterparts. The experimental results show a performance improvement, that allow us to present these new topologies as better alternative to classical topologies.

Quasi-Perfect Lee Codes of Radius 2 and Arbitrarily Large Dimension

A construction of two-quasi-perfect Lee codes is given over the space ℤnp for p prime, p ≡ ±5 (mod 12), and n = 2[p/4]. It is known that there are infinitely many such primes. Golomb and Welch conjectured that perfect codes for the Lee metric do not exist for dimension n ≥ 3 and radius r ≥ 2. This conjecture was proved to be true for large radii as well as for low dimensions. The codes found are very close to be perfect, which exhibits the hardness of the conjecture. A series of computations show that related graphs are Ramanujan, which could provide further connections between coding and graph theories.

Financial applications on multi-CPU and multi-GPU architectures

The use of high-performance computing systems to help to make the right investment decisions in financial markets is an open research field where multiple efforts have being carried out during the past few years. Specifically, the Heath–Jarrow–Morton (HJM) model has a number of features that make it well suited for implementation on massively parallel architectures. This paper presents a multi-CPU and multi-GPU implementation of the HJM model that improves both the performance and energy efficiency. The experimental results reveal that the proposed architectures achieve excellent performance improvements, as well as optimize the energy efficiency and the cost/performance ratio.

Graph-based metrics over QAM constellations

In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defined over quotients of the Gaussian integers are introduced in this paper. Distance properties of the constellations are detailed by means of the vertex-to-vertex distribution of this family of graphs. Moreover, perfect codes for this metric are considered. Finally, notable subgraphs of diagonal Gaussian graphs are studied which leads to relate the proposed metric to other well-known graph-based metrics such as the Lee distance.

Throughput Unfairness in Dragonfly Networks under Realistic Traffic Patterns

Dragonfly networks have a two-level hierarchical arrangement of the network routers, and allow for a competitive cost-performance solution in large systems. Non-minimal adaptive routing is employed to fully exploit the path diversity and increase the performance under adversarial traffic patterns. Throughput unfairness prevents a balanced use of the resources across the network nodes and degrades severely the performance of any application running on an affected node. Previous works have demonstrated the presence of throughput unfairness in Dragonflies under certain adversarial traffic patterns, and proposed different alternatives to effectively combat such effect. In this paper we introduce a new traffic pattern denoted adversarial consecutive (ADVc), which portrays a real use case, and evaluate its impact on network performance and throughput fairness. This traffic pattern is the most adversarial in terms of network fairness. Our evaluations, both with or without transit-over-injection priority, show that global misrouting policies do not properly alleviate this problem. Therefore, explicit fairness mechanisms are required for these networks.

Perfect graph codes over two dimensional lattices

In this paper we consider perfect codes over two dimensional QAM-type constellations of any cardinal. Such constellations are going to be modeled by L-graphs, which are the two-dimensional family of multidimensional circulants, defined in [3]. We show that Gaussian graphs, Lee graphs and the Kronecker product of two cycles are included in this family. Therefore, our method to obtain perfect codes over these lattice subsets is a generalization of the techniques for searching perfect two-dimensional Lee codes and perfect codes over the Kronecker products of two cycles. In addition, we introduce some previously unreported perfect codes.