Range minimum query indexes in higher dimensions

Pooya Davoodi; John Iacono; Gad M. Landau; Moshe Lewenstein

doi:10.1007/978-3-319-19929-0_13

Range minimum query indexes in higher dimensions

Pooya Davoodi, John Iacono, Gad M. Landau, Moshe Lewenstein

University of Haifa, Bar-Ilan University

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

Abstract

Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA’10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.

Original language	American English
Title of host publication	Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings
Editors	Ugo Vaccaro, Ely Porat, Ferdinando Cicalese
Publisher	Springer Verlag
Pages	149-159
Number of pages	11
ISBN (Print)	9783319199283
DOIs	https://doi.org/10.1007/978-3-319-19929-0_13
State	Published - 2015
Event	26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy Duration: 29 Jun 2015 → 1 Jul 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9133

Conference

Conference	26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015
Country/Territory	Italy
City	Ischia Island
Period	29/06/15 → 1/07/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-19929-0_13

Cite this

Davoodi, P., Iacono, J., Landau, G. M., & Lewenstein, M. (2015). Range minimum query indexes in higher dimensions. In U. Vaccaro, E. Porat, & F. Cicalese (Eds.), Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings (pp. 149-159). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_13

Davoodi, Pooya ; Iacono, John ; Landau, Gad M. et al. / Range minimum query indexes in higher dimensions. Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. editor / Ugo Vaccaro ; Ely Porat ; Ferdinando Cicalese. Springer Verlag, 2015. pp. 149-159 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Range minimum query indexes in higher dimensions",

abstract = "Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA{\textquoteright}10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.",

author = "Pooya Davoodi and John Iacono and Landau, \{Gad M.\} and Moshe Lewenstein",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 ; Conference date: 29-06-2015 Through 01-07-2015",

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language = "American English",

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Davoodi, P, Iacono, J, Landau, GM & Lewenstein, M 2015, Range minimum query indexes in higher dimensions. in U Vaccaro, E Porat & F Cicalese (eds), Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9133, Springer Verlag, pp. 149-159, 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015, Ischia Island, Italy, 29/06/15. https://doi.org/10.1007/978-3-319-19929-0_13

Range minimum query indexes in higher dimensions. / Davoodi, Pooya; Iacono, John; Landau, Gad M. et al.
Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. ed. / Ugo Vaccaro; Ely Porat; Ferdinando Cicalese. Springer Verlag, 2015. p. 149-159 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133).

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

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AU - Landau, Gad M.

AU - Lewenstein, Moshe

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PY - 2015

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N2 - Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA’10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.

AB - Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA’10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.

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M3 - Conference contribution

SN - 9783319199283

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings

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ER -

Davoodi P, Iacono J, Landau GM, Lewenstein M. Range minimum query indexes in higher dimensions. In Vaccaro U, Porat E, Cicalese F, editors, Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Springer Verlag. 2015. p. 149-159. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-19929-0_13

Range minimum query indexes in higher dimensions

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