Before revision:  Rather than scaling with the number of hierarchical clusterings of n elements (\omega(n n!/ 2^{n-1 , our approach runs in time and space proportional to the significantly smaller powerset of n . Despite still being large, these algorithms enable exact inference in small-data applications and are also interesting from a theoretical perspective.
After revision:  Rather than scaling with the number of hierarchical clusterings of n elements (\omega(n n!/ 2^{n-1 , our approach runs in time and space proportional to the significantly smaller powerset of n . Despite still being large, there are many important applications at the practically-computable range of N < 20.