Inferring strings from Lyndon factorization

Yuto Nakashima, Takashi Okabe, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The Lyndon factorization of a string w is a unique factorization ℓ1p1,…,ℓmpm of w such that 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,pm)) 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 ℓ1p1,…,ℓmpm 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
Pages (from-to)147-156
Number of pages10
JournalTheoretical Computer Science
Publication statusPublished - Aug 15 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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