Dynamic dictionary matching in the online model

Shay Golan; Tomasz Kociumaka; Tsvi Kopelowitz; Ely Porat

doi:10.1007/978-3-030-24766-9_30

Dynamic dictionary matching in the online model

Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, Ely Porat

Department of Computer Science

Bar-Ilan University

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

1 Scopus citations

Abstract

In the classic dictionary matching problem, the input is a dictionary of patterns D= { P₁, P₂, …, P_k} and a text T, and the goal is to report all the occurrences in T of every pattern from D. In the dynamic version of the dictionary matching problem, patterns may be either added or removed from D. In the online version of the dictionary matching problem, the characters of T arrive online, one at a time, and the goal is to establish, immediately after every new character arrival, which of the patterns in D are a suffix of the current text. In this paper, we consider the dynamic version of the online dictionary matching problem. For the case where all the patterns have the same length m, we design an algorithm that adds or removes a pattern in (formula presented) time and processes a text character in (formula presented) time, where(formula presented). For the general case where patterns may have different lengths, the cost of adding or removing a pattern P is (formula presented) while the cost per text character is (formula presented), where d= | D| is the number of patterns in D and occ is the size of the output. These bounds improve on the state of the art for dynamic dictionary matching, while also providing online features. All our algorithms are Las-Vegas randomized and the time costs are in the worst-case with high probability. A by-product of our work is a solution for the fringed colored ancestor problem, resolving an open question of Breslauer and Italiano [J. Discrete Algorithms, 2013].

Original language	English
Title of host publication	Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings
Editors	Zachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack
Publisher	Springer Verlag
Pages	409-422
Number of pages	14
ISBN (Print)	9783030247652
DOIs	https://doi.org/10.1007/978-3-030-24766-9_30
State	Published - 2019
Event	16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada Duration: 5 Aug 2019 → 7 Aug 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11646 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Symposium on Algorithms and Data Structures, WADS 2019
Country/Territory	Canada
City	Edmonton
Period	5/08/19 → 7/08/19

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Funding

This research is supported by ISF grants no. 824/17 and 1278/16 and by an ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064). The authors thank Tatiana Starikovskaya for early discussions on the online dynamic dictionary problem.

Funders	Funder number
Horizon 2020 Framework Programme	683064
European Commission
Israel Science Foundation	824/17, 1278/16

Access to Document

10.1007/978-3-030-24766-9_30

Cite this

Golan, S., Kociumaka, T., Kopelowitz, T., & Porat, E. (2019). Dynamic dictionary matching in the online model. In Z. Friggstad, M. R. Salavatipour, & J.-R. Sack (Eds.), Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings (pp. 409-422). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11646 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-24766-9_30

Golan, Shay ; Kociumaka, Tomasz ; Kopelowitz, Tsvi et al. / Dynamic dictionary matching in the online model. Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings. editor / Zachary Friggstad ; Mohammad R. Salavatipour ; Jörg-Rüdiger Sack. Springer Verlag, 2019. pp. 409-422 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Dynamic dictionary matching in the online model",

abstract = "In the classic dictionary matching problem, the input is a dictionary of patterns D= { P1, P2, …, Pk} and a text T, and the goal is to report all the occurrences in T of every pattern from D. In the dynamic version of the dictionary matching problem, patterns may be either added or removed from D. In the online version of the dictionary matching problem, the characters of T arrive online, one at a time, and the goal is to establish, immediately after every new character arrival, which of the patterns in D are a suffix of the current text. In this paper, we consider the dynamic version of the online dictionary matching problem. For the case where all the patterns have the same length m, we design an algorithm that adds or removes a pattern in (formula presented) time and processes a text character in (formula presented) time, where(formula presented). For the general case where patterns may have different lengths, the cost of adding or removing a pattern P is (formula presented) while the cost per text character is (formula presented), where d= | D| is the number of patterns in D and occ is the size of the output. These bounds improve on the state of the art for dynamic dictionary matching, while also providing online features. All our algorithms are Las-Vegas randomized and the time costs are in the worst-case with high probability. A by-product of our work is a solution for the fringed colored ancestor problem, resolving an open question of Breslauer and Italiano [J. Discrete Algorithms, 2013].",

author = "Shay Golan and Tomasz Kociumaka and Tsvi Kopelowitz and Ely Porat",

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Golan, S, Kociumaka, T, Kopelowitz, T & Porat, E 2019, Dynamic dictionary matching in the online model. in Z Friggstad, MR Salavatipour & J-R Sack (eds), Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11646 LNCS, Springer Verlag, pp. 409-422, 16th International Symposium on Algorithms and Data Structures, WADS 2019, Edmonton, Canada, 5/08/19. https://doi.org/10.1007/978-3-030-24766-9_30

Dynamic dictionary matching in the online model. / Golan, Shay; Kociumaka, Tomasz; Kopelowitz, Tsvi et al.
Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings. ed. / Zachary Friggstad; Mohammad R. Salavatipour; Jörg-Rüdiger Sack. Springer Verlag, 2019. p. 409-422 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11646 LNCS).

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

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Golan S, Kociumaka T, Kopelowitz T , Porat E. Dynamic dictionary matching in the online model. In Friggstad Z, Salavatipour MR, Sack JR, editors, Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings. Springer Verlag. 2019. p. 409-422. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-24766-9_30

Dynamic dictionary matching in the online model

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