Embedding of binomial trees in hypercubes with link faults

Abstract

We study the embedding of binomial trees with variable roots in n-dimensional hypercubes (n-cubes) with faulty links. A simple embedding algorithm is first proposed that can embed an n-level binomial tree in an n-cube with up to n-1 faulty links in log(n-1) steps. We then extend the result to show that spanning binomial trees exist in a connected n-cube with up to [3(n-1)/2]-1 faulty links. Our results reveal the fault tolerance property of hypercubes and they can be used to predict the performance of broadcasting and reduction operations, where the binomial tree structure is commonly used.