Conquering Edge Faults in a Butterfly with Automorphisms

Mapping an algorithm to an architecture with faults is an important problem in parallel processing. This paper deals with wrapped butterfly architectures with edge faults. We investigate the effect of automorphisms of a wrapped butterfly on its edges. Given a fault set, one can then choose an appropriate automorphism to map the algorithm to use only fault-free edges. By using an algebraic model of the butterfly, we obtain simple expressions for all its automorphisms. Use of powerful algebraic techniques then quickly yield the edge transformations due of these automorphisms. This strategy of avoiding edge faults using automorphisms is quite novel because previously automorphisms have been employed only to avoid the node faults. We illustrate our methods by mapping Hamilton cycle on the butterfly under various edge fault scenarios.