Encodings for range selection and top-k queries

We study the problem of encoding the positions the top-k elements of an array A[1..n] for a given parameter 1 ≤ k ≤ n. Specifically, for any i and j, we wish create a data structure that reports the positions of the largest k elements in A[i..j] in decreasing order, without accessing A at query time. This is a natural extension of the well-known encoding range-maxima query problem, where only the position of the maximum in A[i..j] is sought, and finds applications in document retrieval and ranking. We give (sometimes tight) upper and lower bounds for this problem and some variants thereof.