Before revision:  On the other hand, using N processors (one per port), their per-port computational complexity can be as low as O( \log ^2N) (more precisely O(\log N) iterations that each has O(\log N) computational complexity) for an N\times N switch .
After revision:  On the other hand, their computational complexity can be as low as O( \log ^2N) (more precisely O(\log N) iterations that each has O(\log N) computational complexity) for an N\times N switch .