Cartesian tree matching and indexing

Sung Gwan Park; Amihood Amir; Gad M. Landau; Kunsoo Park

doi:10.4230/LIPIcs.CPM.2019.16

Cartesian tree matching and indexing

Sung Gwan Park, Amihood Amir, Gad M. Landau, Kunsoo Park

Department of Computer Science

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

Abstract

We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a pattern of length m, and multiple pattern matching for a text of length n and k patterns of total length m. We present an O(n + m) time algorithm for single pattern matching, and an O((n + m) log k) deterministic time or O(n + m) randomized time algorithm for multiple pattern matching. We also define an index data structure called Cartesian suffix tree, and present an O(n) randomized time algorithm to build the Cartesian suffix tree. Our efficient algorithms for Cartesian tree matching use a representation of the Cartesian tree, called the parent-distance representation.

Original language	English
Title of host publication	30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019
Editors	Nadia Pisanti, Solon P. Pissis
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	16:1-16:14
ISBN (Electronic)	9783959771030
DOIs	https://doi.org/10.4230/LIPIcs.CPM.2019.16
State	Published - 1 Jun 2019
Event	30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 - Pisa, Italy Duration: 18 Jun 2019 → 20 Jun 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	128
ISSN (Print)	1868-8969

Conference

Conference	30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019
Country/Territory	Italy
City	Pisa
Period	18/06/19 → 20/06/19

Bibliographical note

Funding Information:
Acknowledgements S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Funding Information:
S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).

Publisher Copyright:
© Sung Gwan Park, Amihood Amir, Gad M. Landau, and Kunsoo Park.

Keywords

Cartesian tree matching
Indexing
Parent-distance representation
Pattern matching

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.CPM.2019.16

Cite this

Park, S. G., Amir, A., Landau, G. M., & Park, K. (2019). Cartesian tree matching and indexing. In N. Pisanti, & S. P. Pissis (Eds.), 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 (pp. 16:1-16:14). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 128). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2019.16

@inproceedings{4bc69274d29a4db2a8e7e36575c540fb,

title = "Cartesian tree matching and indexing",

abstract = "We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a pattern of length m, and multiple pattern matching for a text of length n and k patterns of total length m. We present an O(n + m) time algorithm for single pattern matching, and an O((n + m) log k) deterministic time or O(n + m) randomized time algorithm for multiple pattern matching. We also define an index data structure called Cartesian suffix tree, and present an O(n) randomized time algorithm to build the Cartesian suffix tree. Our efficient algorithms for Cartesian tree matching use a representation of the Cartesian tree, called the parent-distance representation.",

keywords = "Cartesian tree matching, Indexing, Parent-distance representation, Pattern matching",

author = "Park, {Sung Gwan} and Amihood Amir and Landau, {Gad M.} and Kunsoo Park",

note = "Funding Information: Acknowledgements S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Funding Information: S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Publisher Copyright: {\textcopyright} Sung Gwan Park, Amihood Amir, Gad M. Landau, and Kunsoo Park.; 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 ; Conference date: 18-06-2019 Through 20-06-2019",

year = "2019",

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Park, SG, Amir, A, Landau, GM & Park, K 2019, Cartesian tree matching and indexing. in N Pisanti & SP Pissis (eds), 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019. Leibniz International Proceedings in Informatics, LIPIcs, vol. 128, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 16:1-16:14, 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019, Pisa, Italy, 18/06/19. https://doi.org/10.4230/LIPIcs.CPM.2019.16

Cartesian tree matching and indexing. / Park, Sung Gwan; Amir, Amihood; Landau, Gad M. et al.
30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019. ed. / Nadia Pisanti; Solon P. Pissis. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. p. 16:1-16:14 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 128).

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

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T1 - Cartesian tree matching and indexing

AU - Park, Sung Gwan

AU - Amir, Amihood

AU - Landau, Gad M.

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N1 - Funding Information: Acknowledgements S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Funding Information: S.G. Park and K. Park were supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No. 2018-0-00551, Framework of Practical Algorithms for NP-hard Graph Problems). A. Amir and G.M. Landau were partially supported by the Israel Science Foundation grant 571/14, and Grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF). Publisher Copyright: © Sung Gwan Park, Amihood Amir, Gad M. Landau, and Kunsoo Park.

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N2 - We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a pattern of length m, and multiple pattern matching for a text of length n and k patterns of total length m. We present an O(n + m) time algorithm for single pattern matching, and an O((n + m) log k) deterministic time or O(n + m) randomized time algorithm for multiple pattern matching. We also define an index data structure called Cartesian suffix tree, and present an O(n) randomized time algorithm to build the Cartesian suffix tree. Our efficient algorithms for Cartesian tree matching use a representation of the Cartesian tree, called the parent-distance representation.

AB - We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a pattern of length m, and multiple pattern matching for a text of length n and k patterns of total length m. We present an O(n + m) time algorithm for single pattern matching, and an O((n + m) log k) deterministic time or O(n + m) randomized time algorithm for multiple pattern matching. We also define an index data structure called Cartesian suffix tree, and present an O(n) randomized time algorithm to build the Cartesian suffix tree. Our efficient algorithms for Cartesian tree matching use a representation of the Cartesian tree, called the parent-distance representation.

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M3 - Conference contribution

AN - SCOPUS:85068059266

T3 - Leibniz International Proceedings in Informatics, LIPIcs

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BT - 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019

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Cartesian tree matching and indexing

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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