# Neighbor chains

The nearest-neighbor chain algorithm, a method for speeding up hierarchical clustering algorithms by merging pairs of clusters out-of-order while guaranteeing that the results will be the same as if the clusters were merged greedily, using a stack in a way that resembles Graham's scan for convex hulls.

W. T. Williams, an English-Australian botanist who helped systematize the theory of hierarchical clustering algorithms by showing that many commonly used distance functions were all really reflections of the same formula.

And, just for fun, a cross-number puzzle made up by Williams in his student days.

Thanks to UCSD grad student Matus Telgarsky for telling me about the nearest-neighbor chain algorithm; given my own past work in clustering, I should have known about it, but I didn't.