Inferring strings from Lyndon factorization

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

4 Citations (Scopus)

Abstract

The Lyndon factorization of a string w is a unique factorization ℓp11,⋯, ℓpmm of w s.t. ℓ1,⋯, ℓm is a sequence of Lyndon words that is monotonically decreasing in lexicographic order. In this paper, we consider the reverse-engineering problem on Lyndon factorization: Given a sequence S = ((s1, p1),⋯, (sm, p m)) of ordered pairs of positive integers, find a string w whose Lyndon factorization corresponds to the input sequence S, i.e., the Lyndon factorization of w is in a form of ℓp11,⋯, ℓpmm with |ℓi| = si for all 1 ≤ i ≤ m. Firstly, we show that there exists a simple O(n)-time algorithm if the size of the alphabet is unbounded, where n is the length of the output string. Secondly, we present an O(n)-time algorithm to compute a string over an alphabet of the smallest size. Thirdly, we show how to compute only the size of the smallest alphabet in O(m) time. Fourthly, we give an O(m)-time algorithm to compute an O(m)-size representation of a string over an alphabet of the smallest size. Finally, we propose an efficient algorithm to enumerate all strings whose Lyndon factorizations correspond to S.

Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings
PublisherSpringer Verlag
Pages565-576
Number of pages12
EditionPART 2
ISBN (Print)9783662444641
DOIs
Publication statusPublished - Jan 1 2014
Event39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014 - Budapest, Hungary
Duration: Aug 25 2014Aug 29 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume8635 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014
CountryHungary
CityBudapest
Period8/25/148/29/14

Fingerprint

Factorization
Strings
Lyndon Words
Unique factorisation
Lexicographic Order
Ordered pair
Reverse engineering
Reverse Engineering
Efficient Algorithms
Integer
Output

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Nakashima, Y., Okabe, T., Tomohiro, I., Inenaga, S., Bannai, H., & Takeda, M. (2014). Inferring strings from Lyndon factorization. In Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings (PART 2 ed., pp. 565-576). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8635 LNCS, No. PART 2). Springer Verlag. https://doi.org/10.1007/978-3-662-44465-8_48

Inferring strings from Lyndon factorization. / Nakashima, Yuto; Okabe, Takashi; Tomohiro, I.; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2. ed. Springer Verlag, 2014. p. 565-576 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8635 LNCS, No. PART 2).

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

Nakashima, Y, Okabe, T, Tomohiro, I, Inenaga, S, Bannai, H & Takeda, M 2014, Inferring strings from Lyndon factorization. in Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 8635 LNCS, Springer Verlag, pp. 565-576, 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, Budapest, Hungary, 8/25/14. https://doi.org/10.1007/978-3-662-44465-8_48
Nakashima Y, Okabe T, Tomohiro I, Inenaga S, Bannai H, Takeda M. Inferring strings from Lyndon factorization. In Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2 ed. Springer Verlag. 2014. p. 565-576. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). https://doi.org/10.1007/978-3-662-44465-8_48
Nakashima, Yuto ; Okabe, Takashi ; Tomohiro, I. ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki. / Inferring strings from Lyndon factorization. Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2. ed. Springer Verlag, 2014. pp. 565-576 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).
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