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According to that chart, seems that FALCONN is faster & better than all the competition. Great!
FALCONN performs better than other methods like k-d tree, Kgraph,PANNS, (http://www.cl.cam.ac.uk/~lw525/). Recently proposed methods like spatial sorting (data partitioning method), http://www.sciencedirect.com/science/article/pii/S009784931630019X. shoul also be compared with FALCONN. More research is needed w.r.t data partitioning methods.