A supplementary for the paper Falconn++: ALocality-sensitive Filtering Approach for Approximate Nearest Neighbor Search

We define µ = µ1 µ2 > 0 and set the threshold t = µ1 = (1 r2/2) 2lnD. Since µ/σ2 is monotonic with respect to c, further points has a higher probability of being discarded. Therefore, the second property holds for any far away point y, i.e. y q cr. The first property holds for any close point x, i.e. x q r, since their projection value onto r1 follows a Gaussian distribution with mean µ µ1. Figure 1 shows the recall-speed comparison between Falconn++ and recent theoretical LSF frameworks [2, 3]. All 3 data sets use L = 100, α = {0.1,0.5},