Routing algorithms on the bus-based hypercube network

In this paper, we study the properties of the bus-based hypercube, denoted as U(n,b), which is a kind of multiple-bus networks (MBN). U(n,b) consists of 2ⁿ processors and 2^b buses, where 0 ≤ b ≤ n - 1, and each processor is connected to either ┌(b+2)/2┐ or ┌(b+1)/2┐ buses. We show that the diameter of U(n,b) is ┌(b-1)/2┐ if b ≥ 2. We also present an algorithm to select the best neighbor processor via which we can obtain one shortest routing path. In U(n,b), we show that if there exist some faults, the fault diameter DF(n,b,f) ≤ b+1, where f is the sum of bus faults and processor faults and 0 ≤ f ≤ ┌(b+3)/2┐. Furthermore, we also show that the bus fault diameter DB(n,b,f) ≤ b/-2┘ - 3, where 0 ≤ f ≤ ┌(b-1)/2┐ and f is the number of bus faults. These results improve significantly the previous result that DB(n,b,f) ≤ b - 2f + 1, where f is the number of bus faults.