Optimal, and Reliable Communication in Hypercubes Using Extended Safety Vectors
Jie Wu, F. Gao, Z. Li, Y. Min · IEEE Transactions on Reliability · 2005
We propose a new coding method of limited global fault information in an n-cube. First, each node collects precise fault information within distance-d, and then fault information about nodes that are more than distance-d away is coded in a special way. Specifically, in our approach, each node in a cube-based multicomputer of dimension n is associated with an extended safety vector of n bits. In the extended safety vector model, each node knows fault information within distance-2; fault information outside distance-2 is coded in a special way based on the coded information of its neighbors. The extended safety vector of each node can be easily calculated through n-1 rounds of information exchanges among neighboring nodes. Therefore, each extended safety vector is an approximated measure of the number & distribution of faults in the neighborhood. Optimal unicasting between two nodes is guaranteed if the kth bit of the safety vector of the source node is one, where k is the Hamming distance between the source & destination nodes. In addition, the extended safety vector can be used as a navigation tool to direct a message to its destination through a minimal path. A simulation study has been conducted based on different selections of d, and results have shown a significant improvement under the proposed model over the safety vector model in handling link faults, even for a small value of d as in the extended safety vector model where d=2.