An Algorithm to Embed Hamiltonian Cycles in Crossed Cubes

In this paper, we study the problem of embedding a family of regularly-structured Hamiltonian cycles in a crosses cube. Since the crossed cube shows performance improvement over a regular hypercube in many aspects, we are interested in knowing whether it has the comparable capability in terms of structure embedding - specifically in this paper, the embedding of Hamiltonian cycles. It needs to be pointed out that we are only considering a family of Hamiltonian cycles that can be systematically constructed, characterized by the permutation of link dimensions (link permutation for short). The total number h(n) of Hamiltonian cycles in a regular n-dimensional hypercube happens to be huge, and many of them cannot be constructed in a systematic way. The exact h(n) has not been established for large n. The main work of this paper is that for those Hamiltonian facilitating permutations, we propose an algorithm that works out a well-structured Hamiltonian cycle