Embedding Schemes for Interconnection Networks.

Graph embeddings play an important role in interconnection network and VLSI design. Designing efficient embedding strategies for simulating one network by another and determining the number of layers required to build a VLSI chip are just two of the many areas in which graph embeddings are used. In the area of network simulation we develop efficient, small dilation embeddings of a butterfly network into a different size and/or type of butterfly network. The genus of a graph gives an indication of how many layers are required to build a circuit. We have determined the exact genus for the permutation network called the star graph, and have given a lower bound for the genus of the permutation network called the pancake graph. The star graph has been proposed as an alternative to the binary hypercube and, therefore, we compare the genus of the star graph with that of the binary hypercube. Another type of embedding that is helpful in determining the number of layers is a book embedding. We develop upper and lower bounds on the pagenumber of a book embedding of the k-ary hypercube along with an upper bound on the cumulative pagewidth

Interconnection networks for parallel and distributed computing

Parallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))

Aspects of practical implementations of PRAM algorithms

The PRAM is a shared memory model of parallel computation which abstracts away from inessential engineering details. It provides a very simple architecture independent model and provides a good programming environment. Theoreticians of the computer science community have proved that it is possible to emulate the theoretical PRAM model using current technology. Solutions have been found for effectively interconnecting processing elements, for routing data on these networks and for distributing the data among memory modules without hotspots. This thesis reviews this emulation and the possibilities it provides for large scale general purpose parallel computation. The emulation employs a bridging model which acts as an interface between the actual hardware and the PRAM model. We review the evidence that such a scheme crn achieve scalable parallel performance and portable parallel software and that PRAM algorithms can be optimally implemented on such practical models. In the course of this review we presented the following new results: 1. Concerning parallel approximation algorithms, we describe an NC algorithm for finding an approximation to a minimum weight perfect matching in a complete weighted graph. The algorithm is conceptually very simple and it is also the first NC-approximation algorithm for the task with a sub-linear performance ratio. 2. Concerning graph embedding, we describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the de Bruijn and shuffle-exchange networks and the 2-dimcnsional mesh. In the embeddings the maximum distance from a leaf to the root of the tree is asymptotically optimally short. The embeddings facilitate efficient implementation of many PRAM algorithms on networks employing these graphs as interconnection networks. 3. Concerning bulk synchronous algorithmics, we describe scalable transportable algorithms for the following three commonly required types of computation; balanced tree computations. Fast Fourier Transforms and matrix multiplications

A Scalable and Adaptive Network on Chip for Many-Core Architectures

In this work, a scalable network on chip (NoC) for future many-core architectures is proposed and investigated. It supports different QoS mechanisms to ensure predictable communication. Self-optimization is introduced to adapt the energy footprint and the performance of the network to the communication requirements. A fault tolerance concept allows to deal with permanent errors. Moreover, a template-based automated evaluation and design methodology and a synthesis flow for NoCs is introduced

Proceedings of the 5th International Workshop on Reconfigurable Communication-centric Systems on Chip 2010 - ReCoSoC\u2710 - May 17-19, 2010 Karlsruhe, Germany. (KIT Scientific Reports ; 7551)

ReCoSoC is intended to be a periodic annual meeting to expose and discuss gathered expertise as well as state of the art research around SoC related topics through plenary invited papers and posters. The workshop aims to provide a prospective view of tomorrow\u27s challenges in the multibillion transistor era, taking into account the emerging techniques and architectures exploring the synergy between flexible on-chip communication and system reconfigurability

An Efficient NoC-based Framework To Improve Dataflow Thread Management At Runtime

This doctoral thesis focuses on how the application threads that are based on dataflow execution model can be managed at Network-on-Chip (NoC) level. The roots of the dataflow execution model date back to the early 1970’s. Applications adhering to such program execution model follow a simple producer-consumer communication scheme for synchronising parallel thread related activities. In dataflow execution environment, a thread can run if and only if all its required inputs are available. Applications running on a large and complex computing environment can significantly benefit from the adoption of dataflow model. In the first part of the thesis, the work is focused on the thread distribution mechanism. It has been shown that how a scalable hash-based thread distribution mechanism can be implemented at the router level with low overheads. To enhance the support further, a tool to monitor the dataflow threads’ status and a simple, functional model is also incorporated into the design. Next, a software defined NoC has been proposed to manage the distribution of dataflow threads by exploiting its reconfigurability. The second part of this work is focused more on NoC microarchitecture level. Traditional 2D-mesh topology is combined with a standard ring, to understand how such hybrid network topology can outperform the traditional topology (such as 2D-mesh). Finally, a mixed-integer linear programming based analytical model has been proposed to verify if the application threads mapped on to the free cores is optimal or not. The proposed mathematical model can be used as a yardstick to verify the solution quality of the newly developed mapping policy. It is not trivial to provide a complete low-level framework for dataflow thread execution for better resource and power management. However, this work could be considered as a primary framework to which improvements could be carried out

Reliability-aware memory design using advanced reconfiguration mechanisms

Fast and Complex Data Memory systems has become a necessity in modern computational units in today's integrated circuits. These memory systems are integrated in form of large embedded memory for data manipulation and storage. This goal has been achieved by the aggressive scaling of transistor dimensions to few nanometer (nm) sizes, though; such a progress comes with a drawback, making it critical to obtain high yields of the chips. Process variability, due to manufacturing imperfections, along with temporal aging, mainly induced by higher electric fields and temperature, are two of the more significant threats that can no longer be ignored in nano-scale embedded memory circuits, and can have high impact on their robustness. Static Random Access Memory (SRAM) is one of the most used embedded memories; generally implemented with the smallest device dimensions and therefore its robustness can be highly important in nanometer domain design paradigm. Their reliable operation needs to be considered and achieved both in cell and also in architectural SRAM array design. Recently, and with the approach to near/below 10nm design generations, novel non-FET devices such as Memristors are attracting high attention as a possible candidate to replace the conventional memory technologies. In spite of their favorable characteristics such as being low power and highly scalable, they also suffer with reliability challenges, such as process variability and endurance degradation, which needs to be mitigated at device and architectural level. This thesis work tackles such problem of reliability concerns in memories by utilizing advanced reconfiguration techniques. In both SRAM arrays and Memristive crossbar memories novel reconfiguration strategies are considered and analyzed, which can extend the memory lifetime. These techniques include monitoring circuits to check the reliability status of the memory units, and architectural implementations in order to reconfigure the memory system to a more reliable configuration before a fail happens.Actualmente, el diseño de sistemas de memoria en circuitos integrados busca continuamente que sean más rápidos y complejos, lo cual se ha vuelto de gran necesidad para las unidades de computación modernas. Estos sistemas de memoria están integrados en forma de memoria embebida para una mejor manipulación de los datos y de su almacenamiento. Dicho objetivo ha sido conseguido gracias al agresivo escalado de las dimensiones del transistor, el cual está llegando a las dimensiones nanométricas. Ahora bien, tal progreso ha conllevado el inconveniente de una menor fiabilidad, dado que ha sido altamente difícil obtener elevados rendimientos de los chips. La variabilidad de proceso - debido a las imperfecciones de fabricación - junto con la degradación de los dispositivos - principalmente inducido por el elevado campo eléctrico y altas temperaturas - son dos de las más relevantes amenazas que no pueden ni deben ser ignoradas por más tiempo en los circuitos embebidos de memoria, echo que puede tener un elevado impacto en su robusteza final. Static Random Access Memory (SRAM) es una de las celdas de memoria más utilizadas en la actualidad. Generalmente, estas celdas son implementadas con las menores dimensiones de dispositivos, lo que conlleva que el estudio de su robusteza es de gran relevancia en el actual paradigma de diseño en el rango nanométrico. La fiabilidad de sus operaciones necesita ser considerada y conseguida tanto a nivel de celda de memoria como en el diseño de arquitecturas complejas basadas en celdas de memoria SRAM. Actualmente, con el diseño de sistemas basados en dispositivos de 10nm, dispositivos nuevos no-FET tales como los memristores están atrayendo una elevada atención como posibles candidatos para reemplazar las actuales tecnologías de memorias convencionales. A pesar de sus características favorables, tales como el bajo consumo como la alta escabilidad, ellos también padecen de relevantes retos de fiabilidad, como son la variabilidad de proceso y la degradación de la resistencia, la cual necesita ser mitigada tanto a nivel de dispositivo como a nivel arquitectural. Con todo esto, esta tesis doctoral afronta tales problemas de fiabilidad en memorias mediante la utilización de técnicas de reconfiguración avanzada. La consideración de nuevas estrategias de reconfiguración han resultado ser validas tanto para las memorias basadas en celdas SRAM como en `memristive crossbar¿, donde se ha observado una mejora significativa del tiempo de vida en ambos casos. Estas técnicas incluyen circuitos de monitorización para comprobar la fiabilidad de las unidades de memoria, y la implementación arquitectural con el objetivo de reconfigurar los sistemas de memoria hacia una configuración mucho más fiables antes de que el fallo suced