A fault-tolerant reconfiguration scheme in the faulty star graph

We propose a scheme to identify the maximal fault-free substar-ring. This is the first result to derive a reconfiguration scheme with high processor utilization in the faulty n-star graph. The maximal fault-free substar-ring is connected by a ring of fault-free virtual substars with dilation 3 and maximal length of the ring is n(n-l)(n-2). Our proposed scheme can tolerate n-3 faults such that the processor utilisation is (n²-2n+3)/(n²-n). This is a near optimal result since the maximal fault-free substar-ring is constructed by using all of the possible fault-free (n-2)-substars. Moreover, our algorithm can still work when number of faults exceeds n-3. The simulation results also show that the processor utilization is more than 50% if the number of faults is less than (n²-n-1)/(2) in the n-star graph