  Stability of persistence diagrams under slight perturbations is a key
characteristic behind the validity and growing popularity of topological data
analysis in exploring real-world data. Central to this stability is the use of
Bottleneck distance which entails matching points between diagrams. Use of this
metric in practical studies has, however, been few and sparingly because of the
computational obstruction, especially in dimension zero where the computational
cost explodes with the growth of data size. We present LUM\'AWIG, a novel
efficient algorithm to compute dimension zero bottleneck distance between two
persistent diagrams which runs significantly faster and provides significantly
sharper approximates with respect to the output of the original algorithm than
any other available algorithm. We bypass the overwhelming matching problem in
previous implementations of the bottleneck distance, and prove that the zero
dimensional bottleneck distance can be recovered from a very small number of
matching cases. We show that LUM\'AWIG generally enjoys linear complexity as
shown by empirical tests. We also present an application that leverages
dimension zero persistence diagrams and the bottleneck distance to produce
features for classification tasks.
