Reviews: Near Neighbor: Who is the Fairest of Them All?

The writing up to page 4 is very wordy and I believe could be more succinctly written. First of all, I am not entirely sure why the problem of sampling from sub collection of sets need to be repeated twice in the paper. In addition, the paper should clearly state that the new sampling strategy can be embedded in the existing LSH method to achieve unbiased query results. Nevertheless, the algorithm does seem interesting - the key bottleneck of estimating the degree of a particular point (basically the number of distinct buckets that contain it) is identified and there are interesting solutions based on existing work in this paper. Section 3 - line 161 states the union of G but G is a set of sets.