Finding patterns and periods in Cartesian tree matching

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

doi:10.1016/j.tcs.2020.09.014

Finding patterns and periods in Cartesian tree matching

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

Department of Computer Science

Research output: Contribution to journal › Article › 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, multiple pattern matching, and indexing problems. We propose a linear time algorithm for single pattern matching, and randomized linear time algorithms for multiple pattern matching and indexing. We also define three types of periods, called full period, initial period, and general period. We propose O(n) time, O(nlog⁡log⁡n) time, and O(nlog⁡n) time algorithms for finding all the full periods, initial periods, and general periods of a string of length n, respectively. Our efficient algorithms use a representation of the Cartesian tree, called parent-distance representation.

Original language	English
Pages (from-to)	181-197
Number of pages	17
Journal	Theoretical Computer Science
Volume	845
DOIs	https://doi.org/10.1016/j.tcs.2020.09.014
State	Published - 12 Dec 2020

Bibliographical note

Funding Information:
S.G. Park, M. Bataa 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, M. Bataa 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:
© 2020 Elsevier B.V.

Keywords

Cartesian tree matching
Indexing
Parent-distance representation
Pattern matching
Periods

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1016/j.tcs.2020.09.014

Cite this

@article{ce5edfcd8f124dfaa507831debe52eb1,

title = "Finding patterns and periods in Cartesian tree matching",

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, multiple pattern matching, and indexing problems. We propose a linear time algorithm for single pattern matching, and randomized linear time algorithms for multiple pattern matching and indexing. We also define three types of periods, called full period, initial period, and general period. We propose O(n) time, O(nlog⁡log⁡n) time, and O(nlog⁡n) time algorithms for finding all the full periods, initial periods, and general periods of a string of length n, respectively. Our efficient algorithms use a representation of the Cartesian tree, called parent-distance representation.",

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

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

note = "Funding Information: S.G. Park, M. Bataa 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, M. Bataa 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} 2020 Elsevier B.V.",

year = "2020",

month = dec,

day = "12",

doi = "10.1016/j.tcs.2020.09.014",

language = "English",

volume = "845",

pages = "181--197",

journal = "Theoretical Computer Science",

issn = "0304-3975",

publisher = "Elsevier",

}

TY - JOUR

T1 - Finding patterns and periods in Cartesian tree matching

AU - Park, Sung Gwan

AU - Bataa, Magsarjav

AU - Amir, Amihood

AU - Landau, Gad M.

AU - Park, Kunsoo

N1 - Funding Information: S.G. Park, M. Bataa 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, M. Bataa 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: © 2020 Elsevier B.V.

PY - 2020/12/12

Y1 - 2020/12/12

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, multiple pattern matching, and indexing problems. We propose a linear time algorithm for single pattern matching, and randomized linear time algorithms for multiple pattern matching and indexing. We also define three types of periods, called full period, initial period, and general period. We propose O(n) time, O(nlog⁡log⁡n) time, and O(nlog⁡n) time algorithms for finding all the full periods, initial periods, and general periods of a string of length n, respectively. Our efficient algorithms use a representation of the Cartesian tree, called 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, multiple pattern matching, and indexing problems. We propose a linear time algorithm for single pattern matching, and randomized linear time algorithms for multiple pattern matching and indexing. We also define three types of periods, called full period, initial period, and general period. We propose O(n) time, O(nlog⁡log⁡n) time, and O(nlog⁡n) time algorithms for finding all the full periods, initial periods, and general periods of a string of length n, respectively. Our efficient algorithms use a representation of the Cartesian tree, called parent-distance representation.

KW - Cartesian tree matching

KW - Indexing

KW - Parent-distance representation

KW - Pattern matching

KW - Periods

UR - http://www.scopus.com/inward/record.url?scp=85091201370&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2020.09.014

DO - 10.1016/j.tcs.2020.09.014

M3 - Article

AN - SCOPUS:85091201370

SN - 0304-3975

VL - 845

SP - 181

EP - 197

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

Finding patterns and periods in Cartesian tree matching

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this