Congestion-free Optimal Routings of Hypercube Automorphisms
Mark Ramras · SIAM Journal on Discrete Mathematics · 1997
We present an off-line method for routing a hypercube automorphism $\pi$ in the minimum number of steps. The routing has the added virtue of being congestion-free. Our method is purely algebraic, and the routing is obtained easily from the standard representation of $\pi$ as the product of a complementation and a bit permutation.