Embedding Hamiltonian Cycles Into Folded Hypercubes with Faulty Links
It has been known that an n-dimensional hypercube (n-cube for short) can always embed a Hamiltonian cycle when the n-cube has no more than n-2 faulty links. In this paper, we study the link-fault tolerant embedding of a Hamiltonian cycle into the folded hypercube, which is a variant of the hypercube, obtained by adding a link to every pair of nodes with complementary addresses. We will show that a folded n-cube can tolerate up to n-1 faulty links when embedding a Hamiltonian cycle. We present an algorithm, FT_HAMIL, that finds a Hamiltonian cycle while avoiding any set of faulty links F provided that F≤n-1. An operation, called bit-flip, on links of hyper-cube is introduced. Simple yet elegant, bit-flip will be employed by FT_HAMIL as a basic operation to generate a new Hamiltonian cycle from an old one (that contains faulty links). It is worth pointing out that the algorithm is optimal in the sense that for a folded n-cube, n-1 is the maximum number for F that can be tolerated, F being an arbitrary set of faulty links.
MSU Digital Commons Citation
Wang, Dajin, "Embedding Hamiltonian Cycles Into Folded Hypercubes with Faulty Links" (2001). Department of Computer Science Faculty Scholarship and Creative Works. 250.