Fault diagnosability of regular graphs

An interconnection network\u27s diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the $h$-good-neighbor conditional diagnosability, which requires that every fault-free node has at least $h$ fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The {\it $h$-good-neighbor diagnosability} under the PMC (resp. MM*) model of a graph $G$, denoted by $t_h^{PMC}(G)$ (resp. $t_h^{MM^*}(G)$), is the maximum value of $t$ such that $G$ is $h$-good-neighbor $t$-diagnosable under the PMC (resp. MM*) model. In this paper, we study the $2$-good-neighbor diagnosability of some general $k$-regular $k$-connected graphs $G$ under the PMC model and the MM* model. The main result $t_2^{PMC}(G)=t_2^{MM^*}(G)=g(k-1)-1$ with some acceptable conditions is obtained, where $g$ is the girth of $G$. Furthermore, the following new results under the two models are obtained: $t_2^{PMC}(HS_n)=t_2^{MM^*}(HS_n)=4n-5$ for the hierarchical star network $HS_n$, $t_2^{PMC}(S_n^2)=t_2^{MM^*}(S_n^2)=6n-13$ for the split-star networks $S_n^2$ and $t_2^{PMC}(\Gamma_{n}(\Delta))=t_2^{MM^*}(\Gamma_{n}(\Delta))=6n-16$ for the Cayley graph generated by the $2$-tree $\Gamma_{n}(\Delta)$

The Nature Diagnosability of Bubble-sort Star Graphs under the PMC Model and MM Model

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No fault set can contain all the neighbors of any fault-free vertex in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a famous topology structure of interconnection networks, the -dimensionalnbsp bubble-sort star graph nbsphas many good properties. In this paper, we prove that the nature diagnosability of nbspis nbspunder the PMC model for , the nature diagnosability of nbspis nbspunder the MM model for

Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability

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

Diagnosability of Star Graphs Under the Comparison Diagnosis Model

In this paper, the diagnosability of n-dimensional star graph Sn under the comparison diagnosis model has been studied. It is proved that Sn is (n−1)-diagnosable under the comparison diagnosis model when n⩾4

Diagnosability of Star Graphs Under the Comparison Diagnosis Model

In this paper, the diagnosability of n -dimensional star graph Sn under the comparison diagnosis model has been studied. It is proved that Sn is (n−1)-diagnosable under the comparison diagnosis model when n⩾4