Tolerating faults in hypercubes using subcube partitioning

Abstract

We examine the issue of running algorithms on a hypercube which has both node and edge faults, and we assume a worst case distribution of the faults. We prove that for any constant c, an n-dimensional hypercube (n-cube) with n^c faulty components contains a fault-free subgraph that can implement a large class of hypercube algorithms with only a constant factor slowdown. In addition, our approach yields practical implementations for small numbers of faults. For example, we show that any regular algorithm can be implemented on an n-cube that has at most n-1 faults with slowdowns of at most 2 for computation and at most 4 for communication. To the best of our knowledge this is the first result showing that an n-cube can tolerate more than O(n) arbitrarily placed faults with a constant factor slowdown.