1.) l Line 8,56,70,93,: Usage of the word equivalent. I would suggest a more cautious usage of this word. Especially, if the equivalence is not verified. 2.) A differentiation between the ultrametric d and the ultrametric u would make their different usages clearer. 3.) Line 186 ff. : A usage of the subdominant ultrametric for the cluster-size regularization, would make the algorithms part more consistent with the following considerations in this paper. 4) The paper is not sufficiently clear in some aspects (see below for a list of questions) Overall, I have the impressions the the weaknesses could be fixed until the final paper submission.
3.) Line 186 ff. : A usage of the subdominant ultrametric for the cluster-size regularization, would make the algorithms part more consistent with the following considerations in this paper.