Deterministic Algorithm for the t-Threshold Set Problem

Given k sorted arrays, the t-Threshold problem, which is motivated by indexed search engines, consists of finding the elements which are present in at least t of the arrays. We present a new deterministic algorithm for it and prove that, asymptotically in the sizes of the arrays, it is optimal in the alternation model used to study adaptive algorithms. We define the Opt-Threshold problem as finding the smallest non empty t-threshold set, which is equivalent to find the largest t such that the t-threshold set is non empty, and propose a naive algorithm to solve it.