Before revision:  Our method supports a wide range of hierarchical clustering models and only requires a cluster compatibility function. Rather than scaling with the number of hierarchical clusterings of N elements (( 2N-3)!! ), 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.
After revision:  Our algorithms scale in time and space proportional to the powerset of N elements which is super-exponentially more efficient than explicitly considering each of the ( 2N-3)!! ), 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.