Uniform quasi-uniformity of P-greedy centres across kernel scales

Determine whether the quasi-uniformity result for the P-greedy algorithm extends uniformly to a range of kernel shape parameters.

Background

The paper interprets the classical multiscale method on quasi-uniform point sets as a P-greedy multiscale algorithm because the P-greedy algorithm is known to produce asymptotically quasi-uniform centres for a fixed shape parameter. The cited result, however, does not establish uniformity when the kernel shape parameter varies over a range. Establishing such a uniform extension would clarify the precise relationship between classical multiscale constructions and P-greedy multiscale algorithms under changing kernel scales.