Space-Efficient Routing Tables for Almost All Networks and the Incompressibility Method

We use the incompressibility method based on Kolmogorov complexity to determine the total number of bits of routing information for almost all network topologies. In most models for routing, for almost all labeled graphs $\Theta (n^2)$ bits are necessary and sufficient for shortest path routing. By `almost all graphs' we mean the Kolmogorov random graphs which constitute a fraction of $1-1/n^c$ of all graphs on $n$ nodes, where $c > 0$ is an arbitrary fixed constant. There is a model for which the average case lower bound rises to $\Omega(n^2 \log n)$ and another model where the average case upper bound drops to $O(n \log^2 n)$. This clearly exposes the sensitivity of such bounds to the model under consideration. If paths have to be short, but need not be shortest (if the stretch factor may be larger than 1), then much less space is needed on average, even in the more demanding models. Full-information routing requires $\Theta (n^3)$ bits on average. For worst-case static networks we prove a $\Omega(n^2 \log n)$ lower bound for shortest path routing and all stretch factors $<2$ in some networks where free relabeling is not allowed.Comment: 19 pages, Latex, 1 table, 1 figure; SIAM J. Comput., To appea

Cost Effective Routing Implementations for On-chip Networks

Arquitecturas de múltiples núcleos como multiprocesadores (CMP) y soluciones multiprocesador para sistemas dentro del chip (MPSoCs) actuales se basan en la eficacia de las redes dentro del chip (NoC) para la comunicación entre los diversos núcleos. Un diseño eficiente de red dentro del chip debe ser escalable y al mismo tiempo obtener valores ajustados de área, latencia y consumo de energía. Para diseños de red dentro del chip de propósito general se suele usar topologías de malla 2D ya que se ajustan a la distribución del chip. Sin embargo, la aparición de nuevos retos debe ser abordada por los diseñadores. Una mayor probabilidad de defectos de fabricación, la necesidad de un uso optimizado de los recursos para aumentar el paralelismo a nivel de aplicación o la necesidad de técnicas eficaces de ahorro de energía, puede ocasionar patrones de irregularidad en las topologías. Además, el soporte para comunicación colectiva es una característica buscada para abordar con eficacia las necesidades de comunicación de los protocolos de coherencia de caché. En estas condiciones, un encaminamiento eficiente de los mensajes se convierte en un reto a superar. El objetivo de esta tesis es establecer las bases de una nueva arquitectura para encaminamiento distribuido basado en lógica que es capaz de adaptarse a cualquier topología irregular derivada de una estructura de malla 2D, proporcionando así una cobertura total para cualquier caso resultado de soportar los retos mencionados anteriormente. Para conseguirlo, en primer lugar, se parte desde una base, para luego analizar una evolución de varios mecanismos, y finalmente llegar a una implementación, que abarca varios módulos para alcanzar el objetivo mencionado anteriormente. De hecho, esta última implementación tiene por nombre eLBDR (effective Logic-Based Distributed Routing). Este trabajo cubre desde el primer mecanismo, LBDR, hasta el resto de mecanismos que han surgido progresivamente.Rodrigo Mocholí, S. (2010). Cost Effective Routing Implementations for On-chip Networks [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8962Palanci

NC-G-SIM: A Parameterized Generic Simulator for 2D-Mesh, 3D-Mesh

As chip density keeps doubling during each course of generation, the use of NoC has become an integral part of modern microprocessors and a very prevalent architectural feature of all types of SoCs. To meet the ever expanding communication challenges, diverse and novel NoC solutions are being developed which rely on accurate modeling and simulations to evaluate the impact and analyze their performances. Consequently, this aggravates the need to rely on simulation tools to probe and optimize these NoC architectures. In this work, we present NC-G-SIM (Network on Chip-Generic-SIMulator), a highly flexible, modular, cycle-accurate, configurable simulator for NoCs. To make NC-G-SIM suitable for advanced NoC exploration, it is made highly generic that supports extensive range of cores in any kind of topology whether 2D, 3D or irregular. Simulation results have been evaluated in terms of latencies, throughput and the amount of energy consumed during the simulation period at different levels

Adaptive turn-prohibition routing algorithm for the networks of workstations

Deadlock occurrence is a critical problem for any computer network. Various solutions have been proposed over last two decades to solve problem of deadlocks in networks using different routing schemes, like up/down routing algorithm used in Myrinet switches. However, most of existing approaches for deadlock-free routing either try to eliminate any possibility of deadlock occurrence, which can result in putting extra restrictions on the routing in the networks or put no restrictions on routing, which leads to other approach namely deadlock recovery. In this thesis emphasis is on developing hybrid approach for routing in wormhole networks, wherein some prohibition is imposed on routing along with some kind of deadlock recovery. This adaptive approach allows changing the amount of routing restrictions depending on network traffic, thus providing a flexible method to achieve better network performance compared to the existing techniques. The main idea of the proposed method consists in the sequential selections of some turns, which are prohibited to be selected during routing. After each additional turn is added, the probability of deadlock occurrence decreases gradually. Cost formula is proposed to estimate cost of implementing both strategies in a network which is basis of proposed adaptive model

Non-minimal adaptive routing for efficient interconnection networks

RESUMEN: La red de interconexión es un concepto clave de los sistemas de computación paralelos. El primer aspecto que define una red de interconexión es su topología. Habitualmente, las redes escalables y eficientes en términos de coste y consumo energético tienen bajo diámetro y se basan en topologías que encaran el límite de Moore y en las que no hay diversidad de caminos mínimos. Una vez definida la topología, quedando implícitamente definidos los límites de rendimiento de la red, es necesario diseñar un algoritmo de enrutamiento que se acerque lo máximo posible a esos límites y debido a la ausencia de caminos mínimos, este además debe explotar los caminos no mínimos cuando el tráfico es adverso. Estos algoritmos de enrutamiento habitualmente seleccionan entre rutas mínimas y no mínimas en base a las condiciones de la red. Las rutas no mínimas habitualmente se basan en el algoritmo de balanceo de carga propuesto por Valiant, esto implica que doblan la longitud de las rutas mínimas y por lo tanto, la latencia soportada por los paquetes se incrementa. En cuanto a la tecnología, desde su introducción en entornos HPC a principios de los años 2000, Ethernet ha sido usado en un porcentaje representativo de los sistemas. Esta tesis introduce una implementación realista y competitiva de una red escalable y sin pérdidas basada en dispositivos de red Ethernet commodity, considerando topologías de bajo diámetro y bajo consumo energético y logrando un ahorro energético de hasta un 54%. Además, propone un enrutamiento sobre la citada arquitectura, en adelante QCN-Switch, el cual selecciona entre rutas mínimas y no mínimas basado en notificaciones de congestión explícitas. Una vez implementada la decisión de enrutar siguiendo rutas no mínimas, se introduce un enrutamiento adaptativo en fuente capaz de adaptar el número de saltos en las rutas no mínimas. Este enrutamiento, en adelante ACOR, es agnóstico de la topología y mejora la latencia en hasta un 28%. Finalmente, se introduce un enrutamiento dependiente de la topología, en adelante LIAN, que optimiza el número de saltos de las rutas no mínimas basado en las condiciones de la red. Los resultados de su evaluación muestran que obtiene una latencia cuasi óptima y mejora el rendimiento de algoritmos de enrutamiento actuales reduciendo la latencia en hasta un 30% y obteniendo un rendimiento estable y equitativo.ABSTRACT: Interconnection network is a key concept of any parallel computing system. The first aspect to define an interconnection network is its topology. Typically, power and cost-efficient scalable networks with low diameter rely on topologies that approach the Moore bound in which there is no minimal path diversity. Once the topology is defined, the performance bounds of the network are determined consequently, so a suitable routing algorithm should be designed to accomplish as much as possible of those limits and, due to the lack of minimal path diversity, it must exploit non-minimal paths when the traffic pattern is adversarial. These routing algorithms usually select between minimal and non-minimal paths based on the network conditions, where the non-minimal paths are built according to Valiant load-balancing algorithm. This implies that these paths double the length of minimal ones and then the latency supported by packets increases. Regarding the technology, from its introduction in HPC systems in the early 2000s, Ethernet has been used in a significant fraction of the systems. This dissertation introduces a realistic and competitive implementation of a scalable lossless Ethernet network for HPC environments considering low-diameter and low-power topologies. This allows for up to 54% power savings. Furthermore, it proposes a routing upon the cited architecture, hereon QCN-Switch, which selects between minimal and non-minimal paths per packet based on explicit congestion notifications instead of credits. Once the miss-routing decision is implemented, it introduces two mechanisms regarding the selection of the intermediate switch to develop a source adaptive routing algorithm capable of adapting the number of hops in the non-minimal paths. This routing, hereon ACOR, is topology-agnostic and improves average latency in all cases up to 28%. Finally, a topology-dependent routing, hereon LIAN, is introduced to optimize the number of hops in the non-minimal paths based on the network live conditions. Evaluations show that LIAN obtains almost-optimal latency and outperforms state-of-the-art adaptive routing algorithms, reducing latency by up to 30.0% and providing stable throughput and fairness.This work has been supported by the Spanish Ministry of Education, Culture and Sports under grant FPU14/02253, the Spanish Ministry of Economy, Industry and Competitiveness under contracts TIN2010-21291-C02-02, TIN2013-46957-C2-2-P, and TIN2013-46957-C2-2-P (AEI/FEDER, UE), the Spanish Research Agency under contract PID2019-105660RBC22/AEI/10.13039/501100011033, the European Union under agreements FP7-ICT-2011- 7-288777 (Mont-Blanc 1) and FP7-ICT-2013-10-610402 (Mont-Blanc 2), the University of Cantabria under project PAR.30.P072.64004, and by the European HiPEAC Network of Excellence through an internship grant supported by the European Union’s Horizon 2020 research and innovation program under grant agreement No. H2020-ICT-2015-687689

Architectural Exploration and Design Methodologies of Photonic Interconnection Networks

Photonic technology is becoming an increasingly attractive solution to the problems facing today's electronic chip-scale interconnection networks. Recent progress in silicon photonics research has enabled the demonstration of all the necessary optical building blocks for creating extremely high-bandwidth density and energy-efficient links for on- and off-chip communications. From the feasibility and architecture perspective however, photonics represents a dramatic paradigm shift from traditional electronic network designs due to fundamental differences in how electronics and photonics function and behave. As a result of these differences, new modeling and analysis methods must be employed in order to properly realize a functional photonic chip-scale interconnect design. In this work, we present a methodology for characterizing and modeling fundamental photonic building blocks which can subsequently be combined to form full photonic network architectures. We also describe a set of tools which can be utilized to assess the physical-layer and system-level performance properties of a photonic network. The models and tools are integrated in a novel open-source design and simulation environment called PhoenixSim. Next, we leverage PhoenixSim for the study of chip-scale photonic networks. We examine several photonic networks through the synergistic study of both physical-layer metrics and system-level metrics. This holistic analysis method enables us to provide deeper insight into architecture scalability since it considers insertion loss, crosstalk, and power dissipation. In addition to these novel physical-layer metrics, traditional system-level metrics of bandwidth and latency are also obtained. Lastly, we propose a novel routing architecture known as wavelength-selective spatial routing. This routing architecture is analogous to electronic virtual channels since it enables the transmission of multiple logical optical channels through a single physical plane (i.e. the waveguides). The available wavelength channels are partitioned into separate groups, and each group is routed independently in the network. Each partition is spectrally multiplexed, as opposed to temporally multiplexed in the electronic case. The wavelength-selective spatial routing technique benefits network designers by provider lower contention and increased path diversity