Efficient algorithms to embed Hamiltonian Paths and Cycles in faulty crossed cubes

The crossed cube is an important variation of the hypercube. It possesses many desirable properties for interconnection networks. Hamiltonicity is a critical property in interconnection networks. In this paper, we study fault-tolerant embedding algorithms of Hamiltonian paths and cycles in crossed cubes. We provide two algorithms Hamiltonian path and Hamiltonian cycle. For any integer n ges 3, letting CQ_n(V, E) denote the n-dimensional crossed cubes and F sub V (CQ_n)cupE(CQ_n) denote a faulty set in CQ_n, (1) if |F| les n - 3, Hamiltonian path can construct a Hamiltonian path between any two distinct nodes in CQ_n - F in O(N log N) time; and (2) if |F| les n - 2, Hamiltonian cycle can construct a Hamiltonian cycle in CQ_n-F in O(N log N) time, where N is the node number of CQ_n - F.