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 logn) 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.
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© 2009 Springer-Verlag Berlin Heidelberg
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Brodal, G.S., Fagerberg, R., Greve, M., López-Ortiz, A. (2009). Online Sorted Range Reporting. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_19
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DOI: https://doi.org/10.1007/978-3-642-10631-6_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
Online ISBN: 978-3-642-10631-6
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