The non-inclusive g-good-neighbor diagnosability of interconnection networks

超立方体 数学 组合数学 一般化 明星(博弈论) 分类 k-最近邻算法 离散数学 计算机科学 算术 数学分析 人工智能
作者
Jun Yuan,Ying Li,Aixia Liu,Huijuan Qiao
出处
期刊:Theoretical Computer Science [Elsevier BV]
卷期号:922: 179-192 被引量:3
标识
DOI:10.1016/j.tcs.2022.04.023
摘要

Motivated by the definitions of g-good-neighbor diagnosability and non-inclusive diagnosability, we propose a new diagnosability—the non-inclusive g-good-neighbor diagnosability tNg(G) of a multiprocessor system G, which requires every pair of g-good-neighbor faulty sets is non-inclusive. The Rg-conditional diagnosability tRg(G) of a system G is a generalization of conditional diagnosability, which requires at least g fault-free neighbors for each node. In this paper, we explore the relationships between the non-inclusive g-good-neighbor diagnosability and the Rg-conditional diagnosability of G under the PMC and MM* models. We first show tNg(G)≤tRg(G) for g≥1, and also give some conditions for equality. Next, we discuss the non-inclusive g-good-neighbor diagnosability of hypercubes, (n,k)-star graphs and (n,k)-bubble-sort graphs. We show that the non-inclusive g-good-neighbor diagnosability of n-dimensional hypercubes is less that its Rg-conditional diagnosability for 2≤g≤n−22, and determine the non-inclusive g-good-neighbor diagnosability of (n,k)-star graphs and (n,k)-bubble-sort graphs. Finally, we plot and compare the non-inclusive g-good-neighbor diagnosability and the g-good-neighbor diagnosability of (n,k)-star graphs and (n,k)-bubble-sort graphs under the PMC and MM* models, respectively. It can be seen that their non-inclusive g-good-neighbor diagnosability is significantly larger than their g-good-neighbor diagnosability.
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