Online Sorted Range Reporting

10 years 4 days ago
Online Sorted Range Reporting
Abstract. We study the following one-dimensional range reporting problem: On an array A of n elements, support queries that given two indices i ≤ j and an integer k report the k smallest elements in the subarray A[i..j] in sorted order. We present a data structure in the RAM model supporting such queries in optimal O(k) time. The structure uses O(n) words of space and can be constructed in O(n log n) time. The data structure can be extended to solve the online version of the problem, where the elements in A[i..j] are reported one-by-one in sorted order, in O(1) worst-case time per element. The problem is motivated by (and is a generalization of) a problem with applications in search engines: On a tree where leaves have associated rank values, report the highest ranked leaves in a given subtree. Finally, the problem studied generalizes the classic range minimum query (RMQ) problem on arrays.
Gerth Stølting Brodal, Rolf Fagerberg, Mark
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Authors Gerth Stølting Brodal, Rolf Fagerberg, Mark Greve, Alejandro López-Ortiz
Comments (0)