On reliable unicast and broadcast in bijective connection networks with the restricted node/edge faults

In this paper, we give an O(NlogN) algorithm to establish a spanning tree rooted at any node of height at most n + ⌈log₂|F|⌉ + 3 in X_n - F, where F is a restricted node set with |F| ≤ 2n - 3 and N = 2ⁿ denotes the node number of X_n. We also give and analyze the simulation results to apply the reliable unicast and broadcast algorithms in the literature and this paper to some existing bijective connection networks such as CQ_n, TQ_n, 0-MQ_n, and 1-MQ_n and general bijective connection networks X_n. The simulation results make us conjecture that there would be some special bijective connection networks whose diameters are smaller than the smallest diameter ⌈n+1/2⌉ of CQ_n, TQ_n, 0-MQ_n, and 1-MQ_n.