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We study the following one-dimensional range reporting problem: On an arrayA of n elements, support queries that given two indices i ≤ j and an integerk 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 language | English |
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Book series | Lecture Notes in Computer Science |
Volume | 5878 |
Pages (from-to) | 173-182 |
Number of pages | 10 |
ISSN | 0302-9743 |
DOIs | |
Publication status | Published - 2009 |
Event | International Symposium on Algorithms and Computation, ISAAC - Honolulu, United States Duration: 18 Nov 2009 → 16 Dec 2009 Conference number: 20 |
Conference | International Symposium on Algorithms and Computation, ISAAC |
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Number | 20 |
Country | United States |
City | Honolulu |
Period | 18/11/2009 → 16/12/2009 |
Title of the vol.: Algorithms and Computation. Proceedings. / Yingfei Dong, Ding-Zhu Du and Oscar Ibarra (eds.)
ISBN: 978-3-642-10630-9
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ID: 18068093