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

Diagnosis is an important technique for fault detection and location in interconnection network. The half hypercube, constructed from the hypercube, has been proven to possess several advantageous properties for interconnection networks, such as symmetry, smaller diameter, fewer edges and lower overhead. 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 the half hypercube is Hamiltonian with no more than (inverted right perpendicularn/2inverted left perpendicular - 1) faulty edges. Finally, we design a parallel adaptive diagnosis scheme under the PMC model, a system-level diagnosis model proposed by P, M, and C, which can identify almost all faulty vertices in five rounds. Simulation results demonstrate that the proposed algorithm is more effective, reducing running time by approximately 50% when compared to the Hamiltonian cycle embedding algorithm for the hypercube with the same dimension.