Reliable unicasting in faulty hypercubes using safety levels

We propose a unicasting algorithm for faulty hypercubes (including disconnected hypercubes) using the safety level concept. A faulty hypercube is a hypercube with faulty nodes and unicasting is a one-to-one communication between two nodes in the hypercube. Each node is associated with a safety level which is an approximated measure of the number and distribution of faulty nodes in the neighborhood. The safety level of each node in an n-dimensional hypercube (or n-cube) can be easily calculated through n-1 rounds of information exchange among neighboring nodes. Optimal unicasting between two nodes is guaranteed if the safety level of the source node is no less than the Hamming distance between the source and the destination. The proposed unicasting algorithm can also be used in disconnected hypercubes, where nodes in a hypercube are disjointed into two or more parts. The feasibility of an optimal or suboptimal unicasting can be easily determined at the source node by comparing its safety level, its neighbors´ safety levels, and the Hamming distance between the source and the destination. The proposed scheme is the first attempt to address the unicasting problem in disconnected hypercubes. The safety level concept is also extended to be used in hypercubes with both faulty nodes and links and in generalized hypercubes