Butterfly Automorphisms and Edge Faults

This paper obtains all the automorphisms of a wrapped Butterfly network of degree n using an algebraic model. It also investigates the translation of butterfly edges by automorphisms. It proposes a new strategy for algorithm mappings on an architecture with faulty edges. This strategy essentially consists of finding an automorphism that would map the faulty edges to the free edges in the graph. Having a set of n2
ⁿ⁺¹
well defined simple automorphisms which translate graph edges deterministically, makes this a very powerful technique for dealing with edge faults. We illustrate the technique by mapping Hamilton cycle on the butterfly under various edge fault scenarios.