The authors give a set of provable algorithms for dynamic facility location and k-clustering under the additional assumption that the solution should remain relatively static from one iteration to the next. There is much to like about the paper, the theory is clean, and the experiments validate the theory and show that the constant factors are better than those predicted. At the same time, the paper lacks polish. As the reviewers pointed out, the empirical experiments were poorly written (fixed in the rebuttal), and the theory itself can be clarified (some of the algorithm blocks are missing and the text is hard to parse. I would encourage the authors to make a very careful revision of this work.