On The Fault-tolerant Diameter And Routing Of Directed Double-loop Networks

Double-loop network is the important topology of interconnection networks and communications systems. Compared with ring networks, due to its good properties such as smaller diameter, expandability, regularity and optimal fault-tolerance, the double-loop networks have been widely used in local area networks and parallel processing architectures. Double-loop networks have been widely studied as architecture for local area networks and parallel distribution system.Fault-tolerance refers to the reliability of data transmission. So that, it is important concepts to measure the network performance. High fault tolerance of interconnection network have been one of the important objectives to pursue. So far, on the research of double-loop networks fault-tolerant diameter and fault-tolerant routing, there is little research findings.This paper is based on the mathematical theory. We studied on the fault-tolerant diameter and routing of directed double-loop networks.We used C # to design the simulation platform and studied the inherent laws about fault-tolerant diameter and tight optimal. The major findings are as follows:(1)This paper is based on the superposition principle of L-shaped tile. We introduced the conception of equal nodes and the inherent laws about the distribution of equal nodes for fault-tolerant nodes in the Z2.(2)A optimal fault-tolerant routing algorithm of directed double-loop networks was introduced.The time complexity of the algorithm is O(d).'d'is the diameter of the networks.(3)In this paper, we provided a method for computing the tolerant-diameter of double-loop networks. We can get the fault-diameter by four geometric parameters a,b,p,q.(4)we proved that for any directed double-loop networks G(N;r,s), the lower and upper bounds of tolerant-diameter are (?)and N+1.(5)Then, we use simulation results to demonstrate the relationship between tolerant-diameter and tight optimal directed double-loop networks. It is proved that the tolerant-diameter of tight optimal double-loop networks is not necessarily to obtain the minimum, while the double-loop network must be tight optimal double-loop network if its tolerant-diameter obtains the minimum value.