Routing algorithms for the shuffle-exchange permutation network

For a natural number n , let S n denote the symmetric group on n letters. Let SEP n be the Cayley graph Cay ( S n , { σ , σ - 1 , τ } ) , where τ = ( 12 ) and σ = ( 1 , … , n ) . In this note, we present an easy static routing algorithm for SEP n which gives us an exact formula for the path between every pair of nodes in SEP n and it does not need any calculations. Also, we show that an upper bound of this algorithm is ⌊ ( 3 n + 1 ) 2 / 9 ⌋ . Furthermore, we use our results to present a dynamic routing algorithm for SEP n which needs at most n calculations for routing and also it does not need large amount of memory for routing tables.