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A Study for Conditional Diagnosability of Pancake Graphs

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Computing and Combinatorics (COCOON 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

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Abstract

Due to the increasing size of a multi-processor system, processor fault diagnosis has played an important role in measuring the reliability of the system. The diagnosability of many well-known multiprocessor systems has been widely investigated. The conditional diagnosability is a new measure of diagnosability by restricting an additional condition that any faulty set cannot contain all the neighbors of any node in a system. In this paper, we evaluate the conditional diagnosability for pancake graphs under the PMC model. We first derive several properties of pancake graphs, and then based on these properties, the conditional diagnosability of an n-dimensional pancake graph is shown to be 2 for \(n=3\) and \(8n-21\) for \(n\ge 4\).

Supported by the Ministry of Science and Technology in Taiwan.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan, 70101, Taiwan

    Nai-Wen Chang, Hsuan-Jung Wu & Sun-Yuan Hsieh

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  1. Nai-Wen Chang
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  2. Hsuan-Jung Wu
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  3. Sun-Yuan Hsieh
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Editor information

Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Chang, NW., Wu, HJ., Hsieh, SY. (2021). A Study for Conditional Diagnosability of Pancake Graphs. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_25

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

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