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

A Local Diagnosis Algorithm for Hypercube-like Networks under the BGM Diagnosis Model

System diagnosis is process of identifying faulty nodes in a system. An efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis model is a modification of the PMC diagnosis model, which is a test-based diagnosis. In this paper, we present a specific structure and propose an algorithm for diagnosing a node in a system under the BGM model. We also give a polynomial-time algorithm that a node in a hypercube-like network can be diagnosed correctly in three test rounds under the BGM diagnosis model

Second Annual Workshop on Space Operations Automation and Robotics (SOAR 1988)

Papers presented at the Second Annual Workshop on Space Operation Automation and Robotics (SOAR '88), hosted by Wright State University at Dayton, Ohio, on July 20, 21, 22, and 23, 1988, are documented herein. During the 4 days, approximately 100 technical papers were presented by experts from NASA, the USAF, universities, and technical companies. Panel discussions on Human Factors, Artificial Intelligence, Robotics, and Space Systems were held but are not documented herein. Technical topics addressed included knowledge-based systems, human factors, and robotics