## 摘要

PMC model is the test-based diagnosis which a vertex performs the diagnosis by testing the neighbor vertices via the edges between them. If we only care about the status of a particular vertex, instead of doing global diagnosis, Hsu and Tan introduced the concept of local diagnosis and proposed two structures to diagnose a vertex. The local diagnosability of a vertex is upper bounded by its degree in the system. If the local diagnosability of a vertex is equal to its degree then we say it is locally optimal diagnosable. Usually, there is a gap between the local diagnosability and the lower bound guaranteed by the two structures mentioned above. Herein, we propose a new testing structure and corresponding diagnosis algorithm to diagnose a vertex under PMC model to better evaluate the local diagnosability. And this diagnosis algorithm takes linear time. Based on this new structure, we give a sufficient condition for a vertex to be locally optimal diagnosable. As its applications, we consider the sufficient and necessary condition for a vertex of hypercubes (resp. folded hypercubes) with faulty edges to be locally optimal diagnosable.

原文 | English |
---|---|

頁（從 - 到） | 81-90 |

頁數 | 10 |

期刊 | Theoretical Computer Science |

卷 | 934 |

DOIs | |

出版狀態 | Published - 23 10月 2022 |