Two dimensional range minimum queries and Fibonacci lattices

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

doi:10.1007/978-3-642-33090-2_20

Two dimensional range minimum queries and Fibonacci lattices

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

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 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(clogc(loglogc) 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(clogc) with the same space usage.

Original language	English
Title of host publication	Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings
Pages	217-228
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-33090-2_20
State	Published - 2012
Event	20th Annual European Symposium on Algorithms, ESA 2012 - Ljubljana, Slovenia Duration: 10 Sep 2012 → 12 Sep 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7501 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th Annual European Symposium on Algorithms, ESA 2012
Country/Territory	Slovenia
City	Ljubljana
Period	10/09/12 → 12/09/12

Access to Document

10.1007/978-3-642-33090-2_20

Cite this

Brodal, G. S., Davoodi, P., Lewenstein, M., Raman, R., & Srinivasa Rao, S. (2012). Two dimensional range minimum queries and Fibonacci lattices. In Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings (pp. 217-228). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7501 LNCS). https://doi.org/10.1007/978-3-642-33090-2_20

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Brodal, GS, Davoodi, P, Lewenstein, M, Raman, R & Srinivasa Rao, S 2012, Two dimensional range minimum queries and Fibonacci lattices. in Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7501 LNCS, pp. 217-228, 20th Annual European Symposium on Algorithms, ESA 2012, Ljubljana, Slovenia, 10/09/12. https://doi.org/10.1007/978-3-642-33090-2_20

Two dimensional range minimum queries and Fibonacci lattices. / Brodal, Gerth Stølting; Davoodi, Pooya; Lewenstein, Moshe et al.
Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings. 2012. p. 217-228 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7501 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Brodal GS, Davoodi P, Lewenstein M, Raman R, Srinivasa Rao S. Two dimensional range minimum queries and Fibonacci lattices. In Algorithms, ESA 2012 - 20th Annual European Symposium, Proceedings. 2012. p. 217-228. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-33090-2_20

Two dimensional range minimum queries and Fibonacci lattices

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