Corrigendum to “Efficient Similarity Search and Classification via Rank Aggregation” by

In this corrigendum, we correct an error in the paper [1]. The error was discovered by Alexandr Andoni, and the corrected theorem is due to the three authors of [1], along with Alexandr Andoni and Mihai Pǎtraşcu. Theorem 4 of [1] states: Let D be a collection of n points in R. Let r1, . . . rm be random unit vectors in R, where m = α −2 logn with α suitably chosen. Let q ∈ R be an arbitrary point, and define, for each i with 1 ≤ i ≤ m, the ranked list Li of the n points in D by sorting them in increasing order of their distances to the projection of q along ri. For each element x of D, let medrank(x) = median(L1(x), . . . , Lm(x)). Let z be a member of D such that medrank(z) is minimized. Then with probability at least 1−1/n, we have ‖z−q‖2 ≤ (1+ )‖x−q‖2 for all x ∈ D. As stated, the above theorem does not hold, but a version of it holds if one replaces the median over ranks by a median over suitably defined scores. Below, we give a counterexample to the original theorem, and then present our modification to the theorem, and the resulting algorithm.