On reverse engineering the Lyndon tree

Yuto Nakashima, Takuya Takagi, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

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

3 Citations (Scopus)

Abstract

We consider the problem of reverse engineering the Lyndon tree, i.e., given a full binary ordered tree T with n leaves as input, compute a string w of length n for which it’s Lyndon tree is isomorphic to the input tree. Although the problem is easy and solvable in linear time when assuming a binary alphabet or when there is no limit on the alphabet size, how to efficiently find the smallest alphabet size for a solution string is not known. We show several new observations concerning this problem. Namely, we show that: 1) For any full binary ordered tree T, there exists a solution string w over an alphabet of size at most h + 1, where h is the height of T. 2) For any positive n, there exists a full binary ordered tree T with n leaves, s.t. the smallest alphabet size of the solution string for T is ⌊n2 ⌋ + 1.

Original languageEnglish
Title of host publicationProceedings of the Prague Stringology Conference, PSC 2017
EditorsJan Holub, Jan Zdarek
PublisherPrague Stringology Club
Pages108-117
Number of pages10
ISBN (Electronic)9788001061930
Publication statusPublished - 2017
Event21st Prague Stringology Conference, PSC 2017 - Prague, Czech Republic
Duration: Aug 28 2017Aug 30 2017

Publication series

NameProceedings of the Prague Stringology Conference, PSC 2017

Conference

Conference21st Prague Stringology Conference, PSC 2017
CountryCzech Republic
CityPrague
Period8/28/178/30/17

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On reverse engineering the Lyndon tree'. Together they form a unique fingerprint.

Cite this