Three-Round Adaptive Diagnosis in Twisted Cubes

Abstract

In this paper, we propose a scheme to solve the problem of adaptive fault diagnosis in n-dimensional twisted cubes in at most three test rounds, provided that the number of faulty vertices is at most n for n ≥ 9. First, each vertex tests one specific neighbour and is tested by another specific neighbour to provide a basic syndrome in two rounds in our scheme. Then, we assign other necessary tests to diagnose the vertices that cannot be identified according to the previous syndrome in one more round. The scheme is optimal for at most three rounds since the adaptive diagnosis needs at least three rounds to complete.KeywordsInterconnection networkstwisted cubeshypercubesadaptive diagnosisHamiltoniandistributed systemsmultiprocessors