Most of the changes here are small and pretty uncontroversial. I have some issues with the complexity calculations though. I've spent a good while going through the calculations, and have got increasingly confused. Some basic points:
Why 2N individuals rather than N? I find this gratuitously confusing...
I've updated the first paragraph. I think there wasn't much point in the precision of the calculation here (and I think there was an error---more below), so I abstracted up a bit to try and pull out the high-level points. We're doing from O(N^2) to O(N + N log N) is the key thing, right?
I'm afraid I don't follow the argument in the next paragraph... The 2Ns aren't helping, but it's just moving too quickly for me. I really would like to be able to understand this!
I'll comment on the changes below for more details.
Most of the changes here are small and pretty uncontroversial. I have some issues with the complexity calculations though. I've spent a good while going through the calculations, and have got increasingly confused. Some basic points:
I'll comment on the changes below for more details.