1. A computer-implemented method for identifying users colluding with a user represented by vector x in a first plurality of vectors, wherein each of the vectors represents a corresponding user, wherein each feature of each vector represents the corresponding user's click-behavior with regard to a content item, the method comprising: for each of a second plurality of vectors y, wherein each vector y is a vector in the first plurality of vectors, and each vector y includes at least one feature indexed in an index: computing, using one or more computers, a similarity estimate between the vector x and the vector y using features of vector x and only the indexed features of vector y; if and only if the similarity estimate satisfies a similarity threshold, computing a similarity score for the pair of vectors (x, y), wherein the similarity score for the pair of vectors (x, y) is a measure of similarity between the vector x and the vector y; if the similarity score satisfies the similarity threshold, including the pair of vectors (x, y) in a set of similar pairs of vectors; and identifying users corresponding to vectors in the set of similar pairs of vectors as users colluding with the user represented by vector x.