Longest common extensions in sublinear space

Philip Bille; Inge Li Gørtz; Mathias Bæk Tejs Knudsen; Moshe Lewenstein; Hjalte Wedel Vildhøj

doi:10.1007/978-3-319-19929-0_6

Longest common extensions in sublinear space

Philip Bille, Inge Li Gørtz, Mathias Bæk Tejs Knudsen, Moshe Lewenstein, Hjalte Wedel Vildhøj

Department of Computer Science

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

24 Scopus citations

Abstract

The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i, j) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions i and j in T. This classic problem has a well-known solution that uses (n) space and O(1) query time. In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the problem can be solved in O(image found) space and O(τ) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.

Original language	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	65-76
Number of pages	12
ISBN (Print)	9783319199283
DOIs	https://doi.org/10.1007/978-3-319-19929-0_6
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
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

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

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Funding

H. W. Vildhøj— This research was supported by a Grant from the GIF, the German-Israeli Foundation for Scientific Research and Development, and by a BSF grant 2010437. I. L. Gørtz— Research partly supported by Mikkel Thorup’s Advanced Grant from the Danish Council for Independent Research under the Sapere Aude research career programme and the FNU project AlgoDisc - Discrete Mathematics, Algorithms, and Data Structures. P. Bille— Supported by the Danish Research Council and the Danish Research Council under the Sapere Aude Program (DFF 4005-00267).

Funders	Funder number
Danish Research Council	DFF 4005-00267
Det Frie Forskningsråd
German-Israeli Foundation for Scientific Research and Development
United States-Israel Binational Science Foundation
Natur og Univers, Det Frie Forskningsråd
German-Israeli Foundation for Scientific Research and Development
United States-Israel Binational Science Foundation	2010437
Fujian Normal University

Access to Document

10.1007/978-3-319-19929-0_6

Cite this

Bille, P., Gørtz, I. L., Knudsen, M. B. T., Lewenstein, M., & Vildhøj, H. W. (2015). Longest common extensions in sublinear space. In U. Vaccaro, E. Porat, & F. Cicalese (Eds.), Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings (pp. 65-76). (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_6

Bille, Philip ; Gørtz, Inge Li ; Knudsen, Mathias Bæk Tejs et al. / Longest common extensions in sublinear space. Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. editor / Ugo Vaccaro ; Ely Porat ; Ferdinando Cicalese. Springer Verlag, 2015. pp. 65-76 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{4061cf7a068a4de08c73d0ccc0a538f5,

title = "Longest common extensions in sublinear space",

abstract = "The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i, j) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions i and j in T. This classic problem has a well-known solution that uses (n) space and O(1) query time. In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the problem can be solved in O(image found) space and O(τ) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.",

author = "Philip Bille and G{\o}rtz, {Inge Li} and Knudsen, {Mathias B{\ae}k Tejs} and Moshe Lewenstein and Vildh{\o}j, {Hjalte Wedel}",

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",

year = "2015",

doi = "10.1007/978-3-319-19929-0_6",

language = "אנגלית",

isbn = "9783319199283",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "65--76",

editor = "Ugo Vaccaro and Ely Porat and Ferdinando Cicalese",

booktitle = "Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings",

address = "גרמניה",

}

Bille, P, Gørtz, IL, Knudsen, MBT, Lewenstein, M & Vildhøj, HW 2015, Longest common extensions in sublinear space. 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. 65-76, 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_6

Longest common extensions in sublinear space. / Bille, Philip; Gørtz, Inge Li; Knudsen, Mathias Bæk Tejs et al.
Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. ed. / Ugo Vaccaro; Ely Porat; Ferdinando Cicalese. Springer Verlag, 2015. p. 65-76 (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

TY - GEN

T1 - Longest common extensions in sublinear space

AU - Bille, Philip

AU - Gørtz, Inge Li

AU - Knudsen, Mathias Bæk Tejs

AU - Lewenstein, Moshe

AU - Vildhøj, Hjalte Wedel

PY - 2015

Y1 - 2015

N2 - The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i, j) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions i and j in T. This classic problem has a well-known solution that uses (n) space and O(1) query time. In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the problem can be solved in O(image found) space and O(τ) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.

AB - The longest common extension problem (LCE problem) is to construct a data structure for an input string T of length n that supports LCE(i, j) queries. Such a query returns the length of the longest common prefix of the suffixes starting at positions i and j in T. This classic problem has a well-known solution that uses (n) space and O(1) query time. In this paper we show that for any trade-off parameter 1 ≤ τ ≤ n, the problem can be solved in O(image found) space and O(τ) query time. This significantly improves the previously best known time-space trade-offs, and almost matches the best known time-space product lower bound.

UR - http://www.scopus.com/inward/record.url?scp=84948951020&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-19929-0_6

DO - 10.1007/978-3-319-19929-0_6

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84948951020

SN - 9783319199283

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

SP - 65

EP - 76

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

A2 - Vaccaro, Ugo

A2 - Porat, Ely

A2 - Cicalese, Ferdinando

PB - Springer Verlag

T2 - 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015

Y2 - 29 June 2015 through 1 July 2015

ER -

Bille P, Gørtz IL, Knudsen MBT, Lewenstein M, Vildhøj HW. Longest common extensions in sublinear space. In Vaccaro U, Porat E, Cicalese F, editors, Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Springer Verlag. 2015. p. 65-76. (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_6

Longest common extensions in sublinear space

Abstract

Publication series

Conference

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this