We study a generalization of the classical median finding problem to batched query case: given an array of unsorted n items and k (not necessarily disjoint) intervals in the array, the goal is to determine the median in each of the intervals in the array. We give an algorithm that uses O(n log n + k log k log n) comparisons and show a lower bound of Ω(n log k) comparisons for this problem. This is optimal for k = O(n/ log n).
The authors of REF give a solution of the RMP which requires O(n log k+ k log n log k) time and O(n log k) space.
Range Medians
ArXiv
ArXiv
Computer Science