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Asymptotically Optimal Encodings of Range Data Structures for Selection and Top-k Queries

Authors:

Roberto Grossi,

Gonzalo Navarro,

S. Rao SattiAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 13, Issue 2

Article No.: 28, Pages 1 - 31

https://doi.org/10.1145/3012939

Published: 06 March 2017 Publication History

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 nlg k - O(n+k lg k) bits of space; then, we design encodings using O(nlg k) bits, that is, asymptotically optimal up to constant factors, while preserving optimal query time.

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Cited By

Bernardini GChen HFici GLoukides GPissis S(2021)Reverse-Safe Text IndexingACM Journal of Experimental Algorithmics10.1145/346169826(1-26)Online publication date: 9-Jul-2021
https://dl.acm.org/doi/10.1145/3461698
Jo SLingala RSatti S(2021)Encoding Two-Dimensional Range Top-k QueriesAlgorithmica10.1007/s00453-021-00856-183:11(3379-3402)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s00453-021-00856-1
Tsur D(2019)The effective entropy of next/previous larger/smaller value queriesInformation Processing Letters10.1016/j.ipl.2019.01.011145(39-43)Online publication date: May-2019
https://doi.org/10.1016/j.ipl.2019.01.011
Show More Cited By

Index Terms

Asymptotically Optimal Encodings of Range Data Structures for Selection and Top-k Queries
1. Information systems
  1. Data management systems
    1. Data structures
      1. Data layout
        Data compression
  2. Information retrieval
    1. Search engine architectures and scalability
      1. Search engine indexing
      2. Search index compression

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 13, Issue 2

Special Issue on SODA'15 and Regular Papers

April 2017

316 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3040971

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2017 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 March 2017

Accepted: 01 October 2016

Revised: 01 May 2016

Received: 01 August 2015

Published in TALG Volume 13, Issue 2

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Millennium Nucleus Information and Coordination in Networks
Ministry of Education, Science and Technology
Basic Science Research Program through the National Research Foundation of Korea (NRF)
MIUR PRIN 2012C4E3KT national research project

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Cited By

Bernardini GChen HFici GLoukides GPissis S(2021)Reverse-Safe Text IndexingACM Journal of Experimental Algorithmics10.1145/346169826(1-26)Online publication date: 9-Jul-2021
https://dl.acm.org/doi/10.1145/3461698
Jo SLingala RSatti S(2021)Encoding Two-Dimensional Range Top-k QueriesAlgorithmica10.1007/s00453-021-00856-183:11(3379-3402)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s00453-021-00856-1
Tsur D(2019)The effective entropy of next/previous larger/smaller value queriesInformation Processing Letters10.1016/j.ipl.2019.01.011145(39-43)Online publication date: May-2019
https://doi.org/10.1016/j.ipl.2019.01.011
Gagie THe MNavarro G(2018)Path queries on functionsTheoretical Computer Science10.1016/j.tcs.2018.10.021Online publication date: Oct-2018
https://doi.org/10.1016/j.tcs.2018.10.021

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