I think your algorithm is ideal for odd N, but I see an issue for even N. If you look at your 6 contestant matrix, in even numbered rounds, two contestants have byes. To take the 6 nations Rugby Union tournament as an example, it is played over five rounds, not 6, and all teams play on the same week-ends. Every Monday, all teams have played the same number of matches. This isn't to say that your algorithm doesn't work - it does - but this behaviour is an oddity that may not be acceptable.
Regards,
John Davies
