Before revision:  however, they only provideapproximate inference. This paper presents dynamic-programming algorithms and proofs for exact inference in hierarchical clustering at small but useful scales.
After revision:  however, they only provideapproximate Typically approximate algorithms are used for inference due to the combinatorial number of possible hierarchical clusterings. In contrast to existing methods, we present novel dynamic-programming algorithms and proofs for exact inference in hierarchical clustering at small but useful scales.