A fast parallel algorithm for routing in permutation networks

An algorithm is given for routing in permutation networks-that is, for computing the switch settings that implement a given permutation. The algorithm takes serial time
O
(
n
(log
N
)
²
) (for one processor with random access to a memory of
O
(
n
) words) or parallel time
O
((log
n
)
³
) (for
n
synchronous processors with conflict-free random access to a common memory of
O
(
n
) words). These time bounds may be reduced by a further logarithmic factor when all of the switch sizes are integral powers of two.