On the shuffle-exchange permutation network

The shuffle-exchange permutation network (SEP_n) is a fixed degree Cayley graph which has been proposed as a basis for massively parallel systems. We propose a routing algorithm with an upper bound of (5/8)n²+O(n), where n is the length of the permutation. (This improves on a (9/8)n² routing algorithm described earlier (Latifi and Srimani, 1996)). Thus, the diameter of SEP _n is at most (5/8) n²+O(n). We also show that the diameter is at least n²/2-O(n). We demonstrate that SEP_n has a Hamilton cycle, for n⩾3, and describe embeddings of variable-degree Cayley networks, such as bubble-sort networks, star networks and pancake networks into SEP_n. Our embeddings for these networks are substantial improvement of earlier results stated in Latifi and Srimani (1996)