The academic literature on register allocation is scary.
First is presented a linear time optimal algorithm for graph coloring then it is claimed better can be done by a O(N^2) algorithm that uses a heuristic.
I do believe the dragon book got caught with the emperor's new register allocator and the literature hasn't really recovered yet.
I didn't believe the optimal algorithm is linear time, so I checked the source:
"Most of the performance" is not optimal. Were you referring to a different source?