Weaknesses: - Presentation: I think the space that the paper spends on the BP background is more than necessary since the BP algorithm is just the standard one. The paper would be more compelling if the BP background is compressed and a more complete explanation of their algorithm is presented, for example some visual illustration that comes with the explanation of their implementation in Section 3.3. Moreover, since there are not many notations used in the paper, it is better not to use the same notation for different meanings to avoid confusion. For example, k is used for the number of top elements throughout the paper and also index of variable at Line 285; at Line 301 the parameter H is used without definition, and later on at Line 302 it denotes the tree height while at Line 334 a parameter in the Splash algorithm. Could the authors provide some conceptual or empirical comparison of them with the proposed one? Distributed Parallel Inference on Large Factor Graphs.

Reviewers agreed, in reviews and discussion, that this paper presents a nice, simple idea very clearly. The author feedback included new experiments and a new baseline, with positive results. I enjoyed reading the paper too.