On the correctness of inside-out routing algorithm

Recently, a new routing algorithm called inside-out routing algorithm was proposed for routing an arbitrary permutation in the omega-based 2log₂ N stage networks. This paper discusses the problems of the inside-out routing algorithm and shows that the suggested condition for proper routing in the omega-omega network is insufficient. An extended necessary and sufficient condition for proper routing in the omega-omega network is also suggested. However, it is unknown if any permutation can be successfully routed by a heuristic algorithm which follows the condition. Thus, the rearrangeability of the omega-omega network still remains an open problem