Online Sorted Range Reporting

Gerth Stølting Brodal, Rolf Fagerberg, Mark Greve, Alejandro López-Ortiz

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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.
Original languageEnglish
Title of host publicationAlgorithms and Computation, 20th International ymposium, ISAAC
Volume5878
PublisherSpringer
Publication date2009
Pages173-182
DOIs
Publication statusPublished - 2009
EventAlgorithms and Computation -
Duration: 24. Aug 2010 → …
Conference number: 20

Conference

ConferenceAlgorithms and Computation
Number20
Period24/08/2010 → …
SeriesLecture Notes in Computer Science
Volume5878

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Data structures
Random access storage
Search engines

Cite this

Brodal, G. S., Fagerberg, R., Greve, M., & López-Ortiz, A. (2009). Online Sorted Range Reporting. In Algorithms and Computation, 20th International ymposium, ISAAC (Vol. 5878, pp. 173-182). Springer. Lecture Notes in Computer Science, Vol.. 5878 https://doi.org/10.1007/978-3-642-10631-6_19
Brodal, Gerth Stølting ; Fagerberg, Rolf ; Greve, Mark ; López-Ortiz, Alejandro. / Online Sorted Range Reporting. Algorithms and Computation, 20th International ymposium, ISAAC. Vol. 5878 Springer, 2009. pp. 173-182 (Lecture Notes in Computer Science, Vol. 5878).
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Brodal, GS, Fagerberg, R, Greve, M & López-Ortiz, A 2009, Online Sorted Range Reporting. in Algorithms and Computation, 20th International ymposium, ISAAC. vol. 5878, Springer, Lecture Notes in Computer Science, vol. 5878, pp. 173-182, Algorithms and Computation, 24/08/2010. https://doi.org/10.1007/978-3-642-10631-6_19

Online Sorted Range Reporting. / Brodal, Gerth Stølting; Fagerberg, Rolf; Greve, Mark; López-Ortiz, Alejandro.

Algorithms and Computation, 20th International ymposium, ISAAC. Vol. 5878 Springer, 2009. p. 173-182 (Lecture Notes in Computer Science, Vol. 5878).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Brodal GS, Fagerberg R, Greve M, López-Ortiz A. Online Sorted Range Reporting. In Algorithms and Computation, 20th International ymposium, ISAAC. Vol. 5878. Springer. 2009. p. 173-182. (Lecture Notes in Computer Science, Vol. 5878). https://doi.org/10.1007/978-3-642-10631-6_19