Multidimensional Period Recovery

Amihood Amir; Ayelet Butman; Eitan Kondratovsky; Avivit Levy; Dina Sokol

doi:10.1007/978-3-030-59212-7_9

Multidimensional Period Recovery

Amihood Amir, Ayelet Butman, Eitan Kondratovsky, Avivit Levy, Dina Sokol

Department of Computer Science

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

1 Scopus citations

Abstract

Multidimensional data are widely used in real-life applications. Intel’s new brand of SSDs, called 3D XPoint, is an example of three-dimensional data. Motivated by a structural analysis of multidimensional data, we introduce the multidimensional period recovery problem, defined as follows. The input is a d-dimensional text array, with dimensions, that contains corruptions, while the original text without the corruptions is periodic. The goal is then to report the period of the original text. We show that, if the number of corruptions is at most, where and are the period’s dimensions, then the amount of possible period candidates is, where. The independency of this bound of the number of dimensions is a surprising key contribution of this paper. We present an algorithm, for any constant dimension d, (linear time up to logarithmic factor) to report these candidates. The tightness of the bound on the number of errors enabling a small size candidate set is demonstrated by showing that if the number of errors is equal to, a family of texts with period candidates can be constructed for any dimension.

Original language	English
Title of host publication	String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings
Editors	Christina Boucher, Sharma V. Thankachan
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	115-130
Number of pages	16
ISBN (Print)	9783030592110
DOIs	https://doi.org/10.1007/978-3-030-59212-7_9
State	Published - 2020
Event	27th International Symposium on String Processing and Information Retrieval, SPIRE 2020 - Orlando, United States Duration: 13 Oct 2020 → 15 Oct 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12303 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Symposium on String Processing and Information Retrieval, SPIRE 2020
Country/Territory	United States
City	Orlando
Period	13/10/20 → 15/10/20

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Funding

A. Amir—Partly supported by ISF grant 1475/18 and BSF grant 2018141. D. Sokol—Partly supported by BSF grant 2018141.

Funders	Funder number
United States-Israel Binational Science Foundation	2018141
Israel Science Foundation	1475/18

Access to Document

10.1007/978-3-030-59212-7_9

Cite this

Amir, A., Butman, A., Kondratovsky, E., Levy, A., & Sokol, D. (2020). Multidimensional Period Recovery. In C. Boucher, & S. V. Thankachan (Eds.), String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings (pp. 115-130). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12303 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-59212-7_9

Amir, Amihood ; Butman, Ayelet ; Kondratovsky, Eitan et al. / Multidimensional Period Recovery. String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings. editor / Christina Boucher ; Sharma V. Thankachan. Springer Science and Business Media Deutschland GmbH, 2020. pp. 115-130 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Amir, A, Butman, A, Kondratovsky, E, Levy, A & Sokol, D 2020, Multidimensional Period Recovery. in C Boucher & SV Thankachan (eds), String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12303 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 115-130, 27th International Symposium on String Processing and Information Retrieval, SPIRE 2020, Orlando, United States, 13/10/20. https://doi.org/10.1007/978-3-030-59212-7_9

Multidimensional Period Recovery. / Amir, Amihood; Butman, Ayelet; Kondratovsky, Eitan et al.
String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings. ed. / Christina Boucher; Sharma V. Thankachan. Springer Science and Business Media Deutschland GmbH, 2020. p. 115-130 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12303 LNCS).

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

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Amir A, Butman A, Kondratovsky E, Levy A, Sokol D. Multidimensional Period Recovery. In Boucher C, Thankachan SV, editors, String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings. Springer Science and Business Media Deutschland GmbH. 2020. p. 115-130. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-59212-7_9

Multidimensional Period Recovery

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