Fault Tolerant Routing in Toroidal Networks 1

1 Summary: In this paper, we study the following node-to-node and node-to-set routing problems in r-dimensional torus T r n with r 2 and n 4 nodes in each dimension: given at most 2r 0 1 faulty nodes and non-faulty nodes s and t in T r n , nd a fault-free path s ! t; and given at most 2r 0 k faulty nodes and non-faulty nodes s and t 1 ;. .. ; t k in T r n , nd k fault-free node-disjoint paths s ! t i , 1 i k. We give an O(r 2) time algorithm which nds a fault-free path s ! t of length at most d(T r n) + 1 for the node-to-node routing, where d(T r n) is the diameter of T r n. For node-to-set routing, we show an O(r 3) time algorithm which nds k fault-free node-disjoint paths s ! t i , 1 i k, of length at most d(T r n) + 1. The upper bounds on the length of the found paths are optimal. From this, Rabin diameter of T r n is d(T r n) + 1.