Hamiltonian path and cycle in hypercubes with faulty links

Abstract

We show that in an n-dimensional hypercube (Q/sub n/), up to n - 1 (resp. n $2) links can fail before destroying all available Hamiltonian paths (resp. cycles). We present an efficient algorithm which identifies a characterization of a Hamiltonian path (resp. cycle) in Q/sub n/, with as many as n - 1 (resp. n - 2) faulty links, in O(n/sup 2/) time. Generating a fault-free Hamiltonian cycle from this characterization can be easily done in linear time. An important application of this work is in optimal fault-tolerant simulation of multiprocessors or multicomputer systems based on linear array ring by hypercubes. While the existing fault-tolerant ring embeddings based on link-disjoint Hamiltonian cycles can only tolerate /spl lfloor/n/2/spl rfloor/ - 1 faulty links, our algorithm specifies a fault-free Hamiltonian cycle of Q/sub n/ with twice as many faulty links.