Towards Optimal Range Medians

We consider the following problem: given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O(n) space and needs O(n log k + k log n) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a lower bound for k = O(n). Since, in contrast to previous approaches, the algorithm decomposes the range of element values rather than the array, it has natural generalizations to higher-dimensional problems ? it reduces a range median query to a logarithmic number of range counting queries.

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Beat Gfeller, Peter Sanders
• Keywords: ICALP 2009, Median Queries, Range Counting Queries, Range Median Query, Theoretical Computer Science