Two dimensional range minimum queries and Fibonacci lattices

Gerth Stølting Brodal; Pooya Davoodi; Moshe Lewenstein; Rajeev Raman; Srinivasa Rao Satti

doi:10.1016/j.tcs.2016.02.016

Two dimensional range minimum queries and Fibonacci lattices

Gerth Stølting Brodal
, Pooya Davoodi
, Moshe Lewenstein
, Rajeev Raman
, Srinivasa Rao Satti

Aarhus University
Polytechnic University
University of Leicester
Seoul National University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Given a matrix of size N, two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique-the discrepancy properties of Fibonacci lattices-we give an indexing data structure for 2D-RMQs that uses O(N/c) bits additional space with O(clog c(log log c)²) query time, for any parameter c, 4≤c≤N. Also, when the entries of the input matrix are from {0, 1}, we show that the query time can be improved to O(clog c) with the same space usage.

Original language	English
Pages (from-to)	33-43
Number of pages	11
Journal	Theoretical Computer Science
Volume	638
DOIs	https://doi.org/10.1016/j.tcs.2016.02.016
State	Published - 25 Jul 2016

Bibliographical note

Publisher Copyright:
© 2016.

Keywords

Fibonacci lattices
Pattern matching
Range minimum queries

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10.1016/j.tcs.2016.02.016

Cite this

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AU - Davoodi, Pooya

AU - Lewenstein, Moshe

AU - Raman, Rajeev

AU - Satti, Srinivasa Rao

PY - 2016/7/25

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Two dimensional range minimum queries and Fibonacci lattices

Abstract

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Keywords

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