Reconstructing a String from its Lyndon Arrays

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F18%3A00313940" target="_blank" >RIV/68407700:21240/18:00313940 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.tcs.2017.04.008" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2017.04.008</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2017.04.008" target="_blank" >10.1016/j.tcs.2017.04.008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reconstructing a String from its Lyndon Arrays

Popis výsledku v původním jazyce

Given a string x = x[1.. n] on an ordered alphabet of size σ , the Lyndon array λ = λx [1..n] of x is an array of positive integers such that λ[i], 1 <= i <= n, is the length of the maximal Lyndon word over the ordering of that begins at position i in x. The Lyndon array has recently attracted considerable attention due to its pivotal role in establishing the long-standing conjecture that ρ (n ) < n, where ρ ( n) is the maximum number of maximal periodicities (runs) in any string of length n. Here we first describe two linear-time algorithms that, given a valid Lyndon array λ, compute a corresponding string — one for an alphabet of size n, the other for a smaller alphabet. We go on to describe another linear-time algorithm that determines whether or not a given integer array is a Lyndon array of some string. Finally we show how σ Lyndon arrays λ = {λ1 = λ, λ2 , . . . , λσ } corresponding to σ “rotations” of the alphabet can be used to determine uniquely the string x on such that λx = λ.

Název v anglickém jazyce

Reconstructing a String from its Lyndon Arrays

Popis výsledku anglicky

Given a string x = x[1.. n] on an ordered alphabet of size σ , the Lyndon array λ = λx [1..n] of x is an array of positive integers such that λ[i], 1 <= i <= n, is the length of the maximal Lyndon word over the ordering of that begins at position i in x. The Lyndon array has recently attracted considerable attention due to its pivotal role in establishing the long-standing conjecture that ρ (n ) < n, where ρ ( n) is the maximum number of maximal periodicities (runs) in any string of length n. Here we first describe two linear-time algorithms that, given a valid Lyndon array λ, compute a corresponding string — one for an alphabet of size n, the other for a smaller alphabet. We go on to describe another linear-time algorithm that determines whether or not a given integer array is a Lyndon array of some string. Finally we show how σ Lyndon arrays λ = {λ1 = λ, λ2 , . . . , λσ } corresponding to σ “rotations” of the alphabet can be used to determine uniquely the string x on such that λx = λ.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

1879-2294

Svazek periodika

710

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

8

Strana od-do

44-51

Kód UT WoS článku

000424958900006

EID výsledku v databázi Scopus

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