Cross-cube在PMC诊断模型下的可诊断性

Diagnosability of Cross-cube under PMC diagnostic model

可诊断性度是衡量一个互连网络可靠性的重要指标。Cross-cube是超立方体的一种重要变型,与超立方体相比有许多好的性质。PMC模型是并行计算系统中的一种经典的诊断模型,在该模型下有两个著名的诊断策略:精确策略和悲观策略。证明了n维Cross-cube在精确策略下的可诊断性度是n+1(n≥4),在悲观策略下的可诊断性度是2n-2(n≥4)。证明了Cross-cube在精确策略下的可诊断性度大于超立方体的可诊断性度,在悲观策略下的可诊断性度与超立方体的可诊断性度相同。

The degree of diagnosability is an important standard to measure the reliability of the interconnection network. The Cross-cube is a variant of the hypercube,whose natures are superior to the hypercube.The PMC model is a classical diagnostic model,which has two famous diagnosis strategies：precise strategy and pessimistic strategy.It is proved that the degree of diagnosability of n-dimensional Cross-cube is n ＋ 1（n≥ 4） under the precise strategy and 2n-2（n ≥ 4） under the pessimistic strategy.Thus, it proves that the degree of diagnosability of the Cross-cube is greater than that of the hypercube under the precise diagnosis strategy,and the same as that of hypercube under the pessimistic strategy.