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Title: Asymptotically Optimal Encodings of Range Data Structures for Selection and Top-k Queries
Authors: Grossi, Roberto
Iacono, John
Navarro, Gonzalo
Raman, Rajeev
Satti, S. Rao
First Published: Mar-2017
Publisher: Association for Computing Machinery (ACM)
Citation: ACM Transactions on Algorithms (TALG), 2017, 13(2)
Abstract: Given an array A[1, n] of elements with a total order, we consider the problem of building a data structure that solves two queries: (a) selection queries receive a range [i, j] and an integer k and return the position of the kth largest element in A[i, j]; (b) top-k queries receive [i, j] and k and return the positions of the k largest elements in A[i, j]. These problems can be solved in optimal time, O(1 + lg k/ lg lg n) and O(k), respectively, using linear-space data structures. We provide the first study of the encoding data structures for the above problems, where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A, and their positions, rather their actual values, and thus we do not need to keep A at query time. In those cases, encodings save storage space: we first show that any encoding answering such queries requires n lg k − O(n + k lg k) bits of space; then, we design encodings using O(n lg k) bits, that is, asymptotically optimal up to constant factors, while preserving optimal query time.
DOI Link: 10.1145/3012939
ISSN: 1549-6325
eISSN: 1549-6333
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, Association for Computing Machinery (ACM). Deposited with reference to the publisher’s open access archiving policy.
Appears in Collections:Published Articles, Dept. of Computer Science

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