Embedding of rings and meshes onto faulty hypercubes using free dimensions

Fault tolerance in hypercubes is achieved by exploiting inherent redundancy and executing tasks on faulty hypercubes. The authors consider tasks that require linear chain, ring, mesh, and torus structure, which are quite useful in parallel and pipeline computations. They assume the number of faults is on the order of the number of dimensions of the hypercube. The techniques are based on a key concept called free dimension, which can be used to partition a cube into subcubes such that each subcube contains, at most, one faulty node. Subgraphs are embedded in each subcube and then merged to form the entire graph