Internal shortest absent word queries in constant time and linear space

Badkobeh, Golnaz; Charalampopoulos, Panagiotis; Kosolobov, Dmitry; Pissis, Solon P.

doi:10.1016/j.tcs.2022.04.029

Cited by 5 publications

(2 citation statements)

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“…Range queries concerning strings but not directly related to palindromes were also extensively studied in the literature, e.g., longest common subsequence [Tis08,Sak19,CGMW21,Sak22], longest common prefix [AAL + 14, GPST18, AGH + 20, MSST20], longest common substring [ACPR20], minimal and maximal suffixes [BGK + 16], minimal rotation [Koc16], approximate pattern matching [CKW20], dictionary matching [CKM + 21], shortest unique substring [AGPT20], and shortest absent word [BCKP22]. Counting the occurrences of a substring in another was studied in [KRRW15].…”

Section: Persisitent Data Structuresmentioning

confidence: 99%

Double-Ended Palindromic Trees: A Linear-Time Data Structure and Its Applications

Wang¹,

Yang²,

Zhu³

2022

Preprint

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The palindromic tree (a.k.a. eertree) is a linear-size data structure that provides access to all palindromic substrings of a string. In this paper, we propose a generalized version of eertree, called double-ended eertree, which supports linear-time online double-ended queue operations on the stored string. At the heart of our construction, is a class of substrings, called surfaces, of independent interest. Namely, surfaces are neither prefixes nor suffixes of any other palindromic substrings and characterize the link structure of all palindromic substrings in the eertree.As an application, we develop a framework for range queries involving palindromes on strings, including counting distinct palindromic substrings, and finding the longest palindromic substring, shortest unique palindromic substring and shortest absent palindrome of any substring. In particular, offline queries only use linear space. Apart from range queries, we enumerate palindromic rich strings with a given word in linear time on the length of the given word.

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Section: Persisitent Data Structuresmentioning

confidence: 99%

Double-Ended Palindromic Trees: A Linear-Time Data Structure and Its Applications

Wang¹,

Yang²,

Zhu³

2022

Preprint

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“…See [23] for an overview of internal queries. We also refer to [10,22,15,14,2,11] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Internal Longest Palindrome Queries in Optimal Time

Mitani¹,

Mieno²,

Seto³

et al. 2022

Preprint

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Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is one of the most important and classical problems regarding palindromic structures, that is, to compute the longest palindrome appearing in a string T of length n. The problem can be solved in O(n) time by the famous algorithm of Manacher [Journal of the ACM, 1975]. In this paper, we consider the problem in the internal model. The internal longest palindrome query is, given a substring T [i..j] of T as a query, to compute the longest palindrome appearing in T [i..j]. The best known data structure for this problem is the one proposed by Amir et al. [Algorithmica, 2020], which can answer any query in O(log n) time. In this paper, we propose a linear-size data structure that can answer any internal longest palindrome query in constant time. Also, given the input string T , our data structure can be constructed in O(n) time.

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