Reviews: An algorithm for L1 nearest neighbor search via monotonic embedding

While the fundamental technical contribution is interesting and should be published, the contextualization is very far from ideal. Here are some points that the authors should address: - besides the l_1 methods based on Cauchy distribution, there is also LSH methods directly for the l_1 space: just impose a randomly shifted grid (see, e.g., the description in the CACM article by Andoni & Indyk). In particular, if we want to solve a c-approximation under l_1, this would translate into requiring a \sqrt{c} approximation for l_2 after the embedding. I.e., the resulting problem in l_2 is harder! Luckily, in l_2, LSH achieves runtime n {1/c 2} (cf, l_1 achieves runtime n {1/c}); however the corresponding l_2 algorithns are much harder (compare the algorithms from the reference [10] versus [5]).