TY - GEN

T1 - On reverse engineering the Lyndon tree

AU - Nakashima, Yuto

AU - Takagi, Takuya

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

N1 - Publisher Copyright:
© Czech Technical University in Prague, Czech Republic.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:85048277401

T3 - Proceedings of the Prague Stringology Conference, PSC 2017

SP - 108

EP - 117

BT - Proceedings of the Prague Stringology Conference, PSC 2017

A2 - Holub, Jan

A2 - Zdarek, Jan

PB - Prague Stringology Club

T2 - 21st Prague Stringology Conference, PSC 2017

Y2 - 28 August 2017 through 30 August 2017

ER -