For the commonest model of rearrangeable networks with $n$ inputs and $n$ outputs, it is shown that such a network must contain at least $6n \log _6 n + O( n )$ switches. Similar lower bounds for other models are also presented.
© 1980 Society for Industrial and Applied Mathematics
Pippenger, Nicholas. “A New Lower Bound for the Number of Switches in Rearrangeable Networks.” SIAM Journal on Algebraic and Discrete Methods 1, no. 2 (June 1980): 164-167.