Fault tolerance on star graphs

Fault tolerance capability is one of the advantages of multiprocessor systems. We prove that the fault tolerance of star graphs is 2n-5 with restriction to the forbidden faulty set. We propose an algorithm for examining the connectivity of star graphs when 2n-4 faults exist. The algorithm requires O(n³ logn) time. We also improve the fault-tolerant routing algorithm proposed by Bagherzadeh et al. (1993) by calculating the cycle structure of a permutation and the avoidance of routing messages to a node without another nonfaulty neighbor. This calculation needs only constant time. We propose an efficient fault-tolerant broadcasting algorithm. When no fault occurs, our broadcasting algorithm remains optimal. The penalty is O(n² ) if at most n-2 faults exist