On The Shuffle-Exchange Permutation Network

The shuffle-exchange permutation network (SEPn) 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)n 2 + O(n), where n is the length of the permutation. (This improves on a (9/8)n 2 routing algorithm described earlier [5].) Thus, the diameter of SEPn is at most (5/8) n 2 + O(n). We also show that the diameter is at least n 2 / 2 - O(n). We demonstrate that SEPn has a Hamilton cycle, for n   3, left open in [5], and describe embeddings of variable-degree Cayley networks, such as bubble-sort networks [1], star networks [2] and pancake networks [4] into SEPn. Our embeddings for these networks are substantial improvements of earlier results stated in [5].

• Type: Conference
• Year: 1997
• Where: ISPAN
• Authors: Douglas W. Bass, Ivan Hal Sudborough
• Keywords: Degree Cayley Graph, Distributed And Parallel Computing, ISPAN 1997, Routing Algorithm, Shuffle-exchange Permutation Network