Kmeans++ is just a seed, this is the inner loop.

Also analogous to flash attention, a linear speedup in big O sense based on the typical algorithmoc complexity computing model can be a polynomial speedup in measured wall clock time due to memory hierarchy differences.

Still small compared to exponential differences, but for an NP-Hard problem, a linear 100x speedup is the difference between practically computable vs. not. There are a ton of things I'd wait 2 hours for that I wouldn't wait a week for.