No description available.

The hypercube Qn is the graph whose vertices are the ordered n-tuples of zeros and ones, where two vertices are adjacent iff they differ in exactly one coordinate. A partial edge coloring f of a graph G is a mapping from a subset of edges of G to a set of colors; it is called proper if no pair of adjacent edges share the same color. A (possibly partial and unproper) coloring f is avoidable if there exists a proper coloring g such that no edge has the same color under f and g. An unavoidable coloring h is called minimal if it would be avoidable by letting any colored edge turn noncolored. We construct a computer program to find all minimal unavoidable edge colorings of Q3 using up to 3 colors, and draw some conclusions for general Qn.

Voltage graph theory can be used to describe embeddings of product graphs if one factor is a Cayley graph. We use voltage graphs to explore embeddings of various products where one factor is a hypercube, describing some minimal and symmetrical embeddings. We then define a graph product, the weak symmetric difference, and illustrate a voltage graph construction useful for obtaining an embedding of the weak symmetric difference of an arbitrary graph with a hypercube.

Cette thèse s'articule autour de la notion de plongement de graphe. Un plongement de graphe consiste à envoyer les sommets d'un graphe dans une autre structure par une application qui conserve certaines propriétés à déterminer. Nous pouvons distinguer deux grandes familles de plongements. D'une part les plongements purement combinatoires qui envoient les éléments d'un graphe G dans un autre graphe H. La propriété la plus naturelle à conserver est la notion d'adjacence entre les sommets. Nous nous intéressons à la conservation d'une propriété supplémentaire : la distance entre les sommets. Nous caractérisons plusieurs familles de graphes se plongeant de cette façon dans les hypercubes ou les graphes de Hamming. Les plongements topologiques visent à représenter un graphe G sur une surface quelconque. Les sommets sont envoyés vers des points d'une surface et les arêtes vers des courbes continues entre ces points. Comment représenter un graphe afin de minimiser le nombre de croisements d'arêtes ? Nous nous posons ces questions à travers l'étude de la planarité et des nombres de croisements de certains graphes.

This thesis, presents a multiprocessor topology, the hierarchical network of hyper-cubes, which has a low diameter, low degree of connectivity and yet exhibits hypercube like versatile characteristics. The hierarchical network of hyper-cubes consists of k-cubes interconnected in two or more hierarchical levels. The network has a hierarchical, expansive, recursive structure with a constant pre-defined building block. The basic building block of the hierarchical network of hyper-cubes comprises of a k-cube of processor elements and a network controller. The hierarchical network of hyper-cubes retains the positive features of the k-cube at different levels of hierarchy and has been found to perform better than the binary hypercube in executing a variety of application problems. The ASCEND/DESCEND class of algorithms can be executed in O(log2 N) parallel steps (N is the number of data elements) on a hierarchical network of hypercubes with N processor elements. A description of the topology of the hierarchical network of hypercubes is presented and its architectural potential in terms of fault-tolerant message routing, executing a class of highly parallel algorithms, and in simulating artificial neural networks is analyzed. Further, the proposed topology is found to be very efficient in executing multinode broadcast and total exchange algorithms. We subsequently, propose an improvisation of the network to counter faults, and explore implementation of artificial neural networks to demonstrate efficient implementation of application problems on the network. The fault-tolerant capabilities of the hierarchical network of hypercubes with two network controllers per k-cube of processor elements are comparable to those of the hypercube and the folded hypercube. We also discuss various issues related to the suitability of multiprocessor architectures for simulating neural networks. Performance analysis of ring, hypercube, mesh and hierarchical network of hypercubes for simulating artificial neural networks is presented. Our studies reveal that the performance of the hierarchical network of hypercubes is better than those of ring, mesh, hypernet and hypercube topologies in implementing artificial neural networks. Design and implementation aspects of hierarchical network of hypercubes based on two schemes, viz., dual-ported RAM communication, and transputers are also presented. Results of simulation studies for robotic applications using neural network paradigms on the transputer-based hierarchical network of hypercubes reveal that the proposed network can produce fast response times of the order of hundred microseconds.

La quantification des incertitudes est essentielle à la bonne maîtrise de la production des réservoirs pétroliers. Ce problème est complexe car l'impact des paramètres incertains sur la production est souvent non-régulier. Du fait du coût important d'une simulation numérique d'écoulement, les méthodes traditionnelles d'analyse de risque sont basées sur un modèle approché du modèle d'écoulement. Ce modèle, construit à partir de plans d'expériences supposant un comportement polynomial de la réponse, ignore les non-régularités. L'objectif de cette thèse est la mise en place d'un formalisme de modélisation de réponses non-régulières. Nous proposons de construire des plans évolutifs afin d'intégrer graduellement les non-régularités. Cette approche est inspirée conjointement de méthodes géostatistiques et de plans d'expériences. En partant d'une surface de réponse initiale, la méthodologie consiste à déterminer itérativement de nouvelles simulations afin d'enrichir le dispositif expérimental et ainsi améliorer l'approximation de la réponse. Différents critères d'ajout de simulations sont proposés. Nous préconisons l'intégration de l'information apportée par les extrema et les points de dérivée partielle nulle de l'approximation. De plus, l'ajout d'information fictive par points pilotes permet une optimisation de la prédictivité de l'approximation ainsi que la détermination de nouveaux points candidats à la simulation. Cette méthodologie originale d'ajustement de surfaces complexes a montré son efficacité, en terme de modélisation comme en terme de réduction du nombre de simulations, notamment pour une quantification d'incertitudes pour deux cas de réservoir pétrolier.

An open queueing network model (QNM) is proposed for wormhole-routed hypercubes with finite buffers and deterministic routing subject to a compound Poisson arrival process (CPP) with geometrically distributed batches or, equivalently, a generalised exponential (GE) interarrival time distribution. The GE/G/1/K queue and appropriate GE-type flow formulae are adopted, as cost-effective building blocks, in a queue-by-queue decomposition of the entire network. Consequently, analytic expressions for the channel holding time, buffering delay, contention blocking and mean message latency are determined. The validity of the analytic approximations is demonstrated against results obtained through simulation experiments. Moreover, it is shown that the wormholerouted hypercubes suffer progressive performance degradation with increasing traffic variability (burstiness).

This thesis presents a simple method for the concurrent manipulation of linearly ordered data structures on hypercubes. The method is based on the existence of a pruned binomial search tree rooted at any arbitrary node of the binary hypercube. The tree spans any arbitrary sequence of n consecutive nodes containing the root, using a fan-out of at most [log₂ 𝑛] and a depth of [log₂ 𝑛] +1. Search trees spanning non-overlapping processor lists are formed using only local information, and can be used concurrently without contention problems. Thus, they can be used for performing broadcast and merge operations simultaneously on sets with non-uniform sizes. Extensions to generalized and faulty hypercubes and applications to image processing algorithms and for m-way search are discussed.

An open queueing network model (QNM) is proposed for wormhole-routed hypercubes with finite buffers and deterministic routing subject to a compound Poisson arrival process (CPP) with geometrically distributed batches or, equivalently, a generalised exponential (GE) interarrival time distribution. The GE/G/1/K queue and appropriate GE-type flow formulae are adopted, as cost-effective building blocks, in a queue-by-queue decomposition of the entire network. Consequently, analytic expressions for the channel holding time, buffering delay, contention blocking and mean message latency are determined. The validity of the analytic approximations is demonstrated against results obtained through simulation experiments. Moreover, it is shown that the wormholerouted hypercubes suffer progressive performance degradation with increasing traffic variability (burstiness).

Nos últimos anos, máquinas maciçamente paralelas, compostas de centenas de processadores, vem sendo estudadas como uma alternativa para a construção de supercomputadores. Neste novo conceito de processamento de dados, grandes velocidades são alcançadas através da cooperação entre os diversos elementos processadores na resolução de um problema. Grande parte das máquinas maciçamente paralelas encontradas no mercado utilizam-se da topologia hipercúbica para a interconexão de seus múltiplos processadores, ou podem ser configuradas como tal. Uma alternativa interessante para o compartilhamento da capacidade de processamento destas máquinas é sua utilização como computador agregado a uma rede, servindo a diversos usuários [DUT 91]. Desta forma, a máquina hipercúbica se comporta como um banco de processadores, que permite que cada usuário aloque parte de seus processadores para seu uso pessoal. Isto resulta em um aumento no desempenho da rede ao nível de supercomputadores com um custo relativamente baixo e viabiliza a construção de máquinas hipercúbicas com altas dimensões, evitando que estas sejam sub-utilizadas. Neste tipo de contexto, cabe ao sistema operacional atender as requisições dos usuários do hipercubo compartilhado de forma eficiente, a fim de evitar uma rápida fragmentação do cubo e de não exceder o tempo máximo de espera de uma determinada aplicação. A partir dos algoritmos propostos é apresentada a definição de um servidor de processadores para o compartilhamento de uma máquina multiprocessadora hipercúbica em uma rede de estações de trabalho. Algumas funções deste servidor são implementadas por um protótipo denominado Sub-Cube RPC. Com o objetivo de analisar o comportamento da rede de estações em relação a inclusão de um novo recurso a ser compartilhado, foi desenvolvido, juntamente com o grupo de Avaliação de Desempenho ADMP, um simulador para o ambiente SUN/UNIX. Através desta ferramenta e dos tempos de resposta obtidos pelo protótipo do servidor desenvolvido é possível avaliar o custo que o tráfego gerado pelo servidor adiciona à rede, sendo possível a manipulação de parâmetros da rede e do servidor. Os resultados obtidos nas versões paralelas implementadas são comparados com o desempenho das versões seqüenciais. Para viabilizar esta comparação, todos os algoritmos seqüenciais encontrados na literatura também foram implementados na linguagem "C" no ambiente alvo UNIX e encontram-se em anexo. As versões paralelas foram implementadas utilizando-se recursos da própria rede de estações, através de diretivas socket, e também em Transputers na linguagem C paralela. O protótipo do servidor de processadores foi implementado como um servidor RPC para uma rede de estações UNIX também na linguagem "C". A ferramenta de simulação para o funcionamento do servidor foi implementada na linguagem "C" e seu sistema de entrada de dados e visualização utiliza a interface X-Windows. Com os resultados deste trabalho se pode ter uma boa idéia dos efeitos e das dificuldades encontradas na paralelização dos algoritmos de alocação e gerência de processadores para máquinas Hipercúbicas. As informações contidas no trabalho auxiliam na melhoria do tempo de resposta dos algoritmos seqüenciais atuais e no desenvolvimento de novos algoritmos com mais recursos e ainda assim viáveis em ambientes interativos, graças a utilização de paralelismo. O protótipo Sub-Cube RPC demonstra como os algoritmos estudados neste trabalho podem ser aplicados na construção de um servidor de processadores para máquinas multiprocessadas. O protótipo servirá como base para a implementação de um servidor semelhante no CPGCC/UFRGS, que colocará uma placa de Transputers à disposição da rede de estações do grupo de processamento paralelo. / In the last years massively parallel machines, build with hundreds of processors, are becoming an alternative for the construction of supercomputers. In this new concept of data processing, high performance is achieved by processor cooperation in the resolution of a problem. A great part of the commercial massively parallel machines utilizes the hypercubic topology to interconnect their multiple processors, or may be configured as hypercubes. A very interesting alternative for sharing the processing power of this machines is their utilization as aggregated computer in a network, serving various users [DUT 91]. In such environment, the hypercube behaves like a processor server, permitting the users to allocate part of its processors for local use. This result in a enhancement in the performance of workstation networks to the level of supercomputers and allow higher dimension hypercubes to be better utilized. In such environment the operating system is responsible for serving the users of a shared multiprocessor in a efficient way, not allowing a quick fragmentation of the hypercube and observing the maximal waiting time for the applications. The algorithms for processor allocation and management are responsible for obtention and control of one or more processors of the shared machine for the user's task execution. In this study, parallel versions of the most important algorithms for processor allocation and management in hypercubes found in the literature are proposed. The intention with this paralelization is to achieved a better response time of the more complex algorithms, making their use possible in a real time sharing environment. Because the allocation is considered the most important part of the processor server, the utilization of more complex algorithms allows a better utilization of the shared processors, resulting in a performance increase of the parallel machine. Based on the proposed algorithms, a processor server is defined for sharing a hypercubic multiprocessor in a workstation network. Some functions of this server are implemented in a prototype called Sub-Cube RPC. To analyze the behavior of the network, in relation to the inclusion of this new shared resource, a simulator for the SUN/UNIX environment has been developed together with the Performance Evaluation Group ADMP. With this tool and with the response times of the developed server prototype, it is possible to evaluate the cost of the additional network traffic generated by the server, with the possibility to change parameters of the server and network. The results obtained in the implemented parallel versions are compared with the performance of the sequential algorithms. To make this comparison possible all the sequential algorithms found in the literature are also implemented in the "C" language and can be found in annex. The parallel versions were implemented using network resources, through the socket directive, and also using Transputers in parallel "C". The processor server prototype was implemented as a RPC server for an UNIX network, also in the "C" language. The simulation tool was coded in "C" and the I/O interface use the X-Windows protocol. The results of this study may give a background about the effects and difficulties found in the pa ralelization of the allocation algorithms for the hypercubic machines. The information found in this study will help the operating system designer to obtain a better response time of the sequential algorithms found in the literature and in the development of new and more complex algorithms that will be still practicable in a real time environment due to parallelism utilization. The Sub-Cube RPC prototype demonstrates how the algorithms studied in this work can be applied in the construction of a processor server for multiprocessors. The prototype is the first step for the implementation of a similar server in the CPGCC/UFRGS that will share a Transputer board in a network of workstations from the parallel processing group.