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Three-round adaptive diagnosis schemes under the PMC model have been demonstrated to be effective in undirected n-cubes. However, existing local diagnosis approaches under the MM model cannot be directly applied to directed graphs due to the constraints imposed by directed edges. In this work, we consider a vertex u in a digraph D, and propose a directed local diagnosis structure \(\mathcal {T}(u,m)\) along with a corresponding three-round adaptive algorithm \(\texttt {ThrDiag}(\mathcal {T}(u, m), m)\) under the MM model. The proposed method ensures accurate identification of the faulty or fault-free status of u, provided that the total number of faulty vertices in the network does not exceed m.

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Three-Round Adaptive Local Diagnosis for Digraph Under MM Model

  • 会议论文

  • 发表日期：

    2026年

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  • Xiawei Zhang,
  • Yihong Wang,
  • Eddie Cheng,
  • László Lipták,
  • Cheng-Kuan Lin

摘要

Three-round adaptive diagnosis schemes under the PMC model have been demonstrated to be effective in undirected n-cubes. However, existing local diagnosis approaches under the MM model cannot be directly applied to directed graphs due to the constraints imposed by directed edges. In this work, we consider a vertex u in a digraph D, and propose a directed local diagnosis structure \(\mathcal {T}(u,m)\) along with a corresponding three-round adaptive algorithm \(\texttt {ThrDiag}(\mathcal {T}(u, m), m)\) under the MM model. The proposed method ensures accurate identification of the faulty or fault-free status of u, provided that the total number of faulty vertices in the network does not exceed m.