Longest common Abelian factors and large alphabets

Golnaz Badkobeh, Travis Gagie, Szymon Grabowski, Yuto Nakashima, Simon J. Puglisi, Shiho Sugimoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings
EditorsShunsuke Inenaga, Kunihiko Sadakane, Tetsuya Sakai
PublisherSpringer Verlag
Pages254-259
Number of pages6
ISBN (Print)9783319460482
DOIs
Publication statusPublished - Jan 1 2016
Event23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016 - Beppu, Japan
Duration: Oct 18 2016Oct 20 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9954 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016
CountryJapan
CityBeppu
Period10/18/1610/20/16

Fingerprint

Strings
Join
Equality
Testing

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Badkobeh, G., Gagie, T., Grabowski, S., Nakashima, Y., Puglisi, S. J., & Sugimoto, S. (2016). Longest common Abelian factors and large alphabets. In S. Inenaga, K. Sadakane, & T. Sakai (Eds.), String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings (pp. 254-259). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9954 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-46049-9_24

Longest common Abelian factors and large alphabets. / Badkobeh, Golnaz; Gagie, Travis; Grabowski, Szymon; Nakashima, Yuto; Puglisi, Simon J.; Sugimoto, Shiho.

String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings. ed. / Shunsuke Inenaga; Kunihiko Sadakane; Tetsuya Sakai. Springer Verlag, 2016. p. 254-259 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9954 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Badkobeh, G, Gagie, T, Grabowski, S, Nakashima, Y, Puglisi, SJ & Sugimoto, S 2016, Longest common Abelian factors and large alphabets. in S Inenaga, K Sadakane & T Sakai (eds), String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9954 LNCS, Springer Verlag, pp. 254-259, 23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016, Beppu, Japan, 10/18/16. https://doi.org/10.1007/978-3-319-46049-9_24
Badkobeh G, Gagie T, Grabowski S, Nakashima Y, Puglisi SJ, Sugimoto S. Longest common Abelian factors and large alphabets. In Inenaga S, Sadakane K, Sakai T, editors, String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings. Springer Verlag. 2016. p. 254-259. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-46049-9_24
Badkobeh, Golnaz ; Gagie, Travis ; Grabowski, Szymon ; Nakashima, Yuto ; Puglisi, Simon J. ; Sugimoto, Shiho. / Longest common Abelian factors and large alphabets. String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings. editor / Shunsuke Inenaga ; Kunihiko Sadakane ; Tetsuya Sakai. Springer Verlag, 2016. pp. 254-259 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{abaca58ead754f51805cd92032e7d72f,
title = "Longest common Abelian factors and large alphabets",
abstract = "Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).",
author = "Golnaz Badkobeh and Travis Gagie and Szymon Grabowski and Yuto Nakashima and Puglisi, {Simon J.} and Shiho Sugimoto",
year = "2016",
month = "1",
day = "1",
doi = "10.1007/978-3-319-46049-9_24",
language = "English",
isbn = "9783319460482",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "254--259",
editor = "Shunsuke Inenaga and Kunihiko Sadakane and Tetsuya Sakai",
booktitle = "String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings",
address = "Germany",

}

TY - GEN

T1 - Longest common Abelian factors and large alphabets

AU - Badkobeh, Golnaz

AU - Gagie, Travis

AU - Grabowski, Szymon

AU - Nakashima, Yuto

AU - Puglisi, Simon J.

AU - Sugimoto, Shiho

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

AB - Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

UR - http://www.scopus.com/inward/record.url?scp=84989948571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989948571&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46049-9_24

DO - 10.1007/978-3-319-46049-9_24

M3 - Conference contribution

AN - SCOPUS:84989948571

SN - 9783319460482

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

SP - 254

EP - 259

BT - String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings

A2 - Inenaga, Shunsuke

A2 - Sadakane, Kunihiko

A2 - Sakai, Tetsuya

PB - Springer Verlag

ER -