Hamiltonian cycle embedding with fault-tolerant edges and adaptive diagnosis in half hypercube

Interconnection network directly affects the efficiency of parallel and distributed systems. Hypercube is one of the most important interconnection networks in parallel computing systems. As a significant variant of hypercube, half hypercube has the same number of vertices as hypercube while its degree is only half that of hypercube, which indicates that it has lower network overhead than hypercube. In this paper, we study the fault-tolerant embedding of Hamiltonian cycles and design an adaptive diagnosis algorithm for the half hypercube. Firstly, we prove that the half hypercube is Hamiltonian and propose an algorithm to construct a Hamiltonian cycle in the network. Furthermore, we prove that half hypercube is Hamiltonian with no more than (⌈n/2⌉−1) faulty edges. Finally, we present a parallel adaptive diagnosis scheme under PMC model, which can identify almost all faulty vertices in five rounds.