Efficient diagnosis of multiprocessor systems under probabilistic models

The problem of fault diagnosis in multiprocessor systems is considered under a probabilistic fault model. The focus is on minimizing the number of tests that must be conducted in order to correctly diagnose the state of every processor in the system with high probability. A diagnosis algorithm that can correctly diagnose the state of every processor with probability approaching one in a class of systems performing slightly greater than a linear number of tests is presented. A nearly matching lower bound on the number of tests required to achieve correct diagnosis in arbitrary systems is also proven. Lower and upper bounds on the number of tests required for regular systems are also presented. A class of regular systems which includes hypercubes is shown to be correctly diagnosable with high probability. In all cases, the number of tests required under this probabilistic model is shown to be significantly less than under a bounded-size fault set model. Because the number of tests that must be conducted is a measure of the diagnosis overhead, these results represent a dramatic improvement in the performance of system-level diagnosis techniques

Finding Isolated Cliques by Queries -- An Approach to Fault Diagnosis with Many Faults

A well-studied problem in fault diagnosis is to identify the set of all good processors in a given set ${p_1,p_2,ldots,p_n}$ of processors via asking some processors $p_i$ to test whether processor $p_j$ is good or faulty. Mathematically, the set $C$ of the indices of good processors forms an isolated clique in the graph with the edges E = {(i,j): if you ask $p_i$ to test $p_j$ then $p_i$ states that ``$p_j$ is good\u27\u27}; where $C$ is an isolated clique iff it holds for every $i in C$ and $j neq i$ that $(i,j) in E$ iff $j in C$. In the present work, the classical setting of fault diagnosis is modified by no longer requiring that $C$ contains at least $frac{n+1}{2}$ of the $n$ nodes of the graph. Instead, one is given a lower bound $a$ on the size of $C$ and the number $n$ of nodes and one has to find a list of up to $n/a$ candidates containing all isolated cliques of size $a$ or more where the number of queries whether a given edge is in $E$ is as small as possible. It is shown that the number of queries necessary differs at most by $n$ for the case of directed and undirected graphs. Furthermore, for directed graphs the lower bound $n^2/(2a-2)-3n$ and the upper bound $2n^2/a$ are established. For some constant values of $a$, better bounds are given. In the case of parallel queries, the number of rounds is at least $n/(a-1)-6$ and at most $O(log(a)n/a)$

Estratégias eficientes para identificação de falhas utilizando o diagnóstico baseado em comparações

Orientador: Prof. Dr. Elias Procópio Duarte Jr.Tese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Curso de Pós-Graduaçao em Informática. Defesa: Curitiba, 12/04/2013Bibliografia: fls. 126-148Resumo: O diagnóstico baseado em comparações e uma forma realista para detectar falhas em hardware, software, redes e sistemas distribuídos. O diagnostico se baseia na comparaçao de resultados de tarefas produzidos por pares de unidades para determinar quais sao as unidades falhas e sem-falha do sistema. Qualquer diferenca no resultado da comparacao indica que uma ou ambas as unidades estao falhas. O diagnostico completo do sistema e baseado no resultado de todas as comparações. Este trabalho apresenta um novo algoritmo de diagnostico para identificar falhas em sistemas de topologia arbitraria com base no modelo MM*. A complexidade do algoritmo proposto e O(t2AN) no pior caso para sistemas de N unidades, onde t denota o numero maximo permitido de unidades falhas e A e o grau da unidade de maior grau no sistema. Esta complexidade e significativamente menor que a dos outros algoritmos previamente publicados. Alem da especificacao do algoritmo e das provas de correcão, resultados obtidos atraves da execucao exaustiva de experimentos sao apresentados, mostrando o desempenho me dio do algoritmo para diferentes sistemas. Al em do novo algoritmo para sistemas de topologia arbitraria, este trabalho tambem apresenta duas outras solucoes para deteccão e combate a poluicao de conteudo, ou alteracoes nao autorizadas, em transmissões de mídia contínua ao vivo em redes P2P - a primeira e uma solucão centralizada e que realiza o diagnostico da poluicao na rede, e a segunda e uma solucao completamente distribuída e descentralizada que tem o objetivo de combater a propagacao da poluicao na rede. Ambas as solucoes utilizam o diagnostico baseado em comparacoes para detectar alterações no conteudo dos dados transmitidos. As soluções foram implementadas no Fireflies, um protocolo escalavel para redes overlay, e diversos experimentos atraves de simulacao foram conduzidos. Os resultados mostram que ambas as estrategias sao solucães viaveis para identificar e combater a poluiçcãao de conteudo em transmissãoes ao vivo e que adicionam baixa sobrecarga ao trafego da rede. Em particular a estrategia de combate a poluicao foi capaz de reduzir consideravelmente a poluicão de conteudo em diversas configurações, em varios casos chegando a elimina-la no decorrer das transmissoães.Abstract: Comparison-based diagnosis is a practical approach to detect faults in hardware, software, and network-based systems. Diagnosis is based on the comparison of task outputs returned by pairs of system units in order to determine whether those units are faulty or fault-free. If the comparison results in a mismatch then one ore both units are faulty. System diagnosis is based on the complete set of all comparison results. This work introduces a novel diagnosis algorithm to identify faults in t-diagnosable systems of arbitrary topology under the MM* model. The complexity of the proposed algorithm is O(t2AN) in the worst case for systems with N units, where t denotes the maximum number of faulty units allowed and A corresponds to the maximum degree of a unit in the system. This complexity is significantly lower than those of previously published algorithms. Besides the algorithm specification and correctness proofs, exhaustive simulations results are presented, showing the typical performance of the algorithm for different systems. Moreover, this work also presents two different strategies to detect and fight content pollution in P2P live streaming transmissions - the first strategy is centralized and performs the diagnosis of content pollution in the network, and the second strategy is a completely distributed solution to combat the propagation of the pollution. Both strategies employ comparison-based diagnosis in order to detect any modification in the data transmitted. The solutions were also implemented in Fireflies, a scalable and fault-tolerant overlay network protocol, and a large number of simulation experiments were conduced. Results show that both strategies are feasible solutions to identify and fight content pollution in live streaming sessions and that they add low overhead in terms of network bandwidth usage. In particular, the solution proposed to combat content pollution was able to significantly reduce the pollution over the system in diverse network configurations - in many cases the solution nearly eliminated the pollution during the transmission