Counting Palindromes in Substrings

Rubinchik, Mikhail; Shur, Arseny M.

doi:10.1007/978-3-319-67428-5_25

Cited by 14 publications

(14 citation statements)

References 18 publications

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“…We also consider a special case of this problem when the dictionary D is the set of all squares (i.e., strings of the form U U ) in T . The case that D is the set of palindromes in T was considered by Rubinchik and Shur in [21]. For the dictionary D = {aa, aaaa, abba, c}, we have:…”

Section: Countdistinctmentioning

confidence: 99%

Counting Distinct Patterns in Internal Dictionary Matching

Charalampopoulos¹,

Kociumaka²,

Mohamed³

et al. 2020

Preprint

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We consider the problem of preprocessing a text T of length n and a dictionary D in order to be able to efficiently answer queries CountDistinct(i, j), that is, given i and j return the number of patterns from D that occur in the fragment T [i . . j]. The dictionary is internal in the sense that each pattern in D is given as a fragment of T . This way, the dictionary takes space proportional to the number of patterns d = |D| rather than their total length, which could be Θ(n•d). An Õ(n+d)-size 1 data structure that answers CountDistinct(i, j) queries O(log n)-approximately in Õ(1) time was recently proposed in a work that introduced internal dictionary matching [ISAAC 2019]. Here we present an Õ(n+d)-size data structure that answers CountDistinct(i, j) queries 2-approximately in Õ(1) time. Using range queries, for any m, we give an Õ(min(nd/m, n 2 /m 2 ) + d)-size data structure that answers CountDistinct(i, j) queries exactly in Õ(m) time. We also consider the special case when the dictionary consists of all square factors of the string. We design an O(n log 2 n)-size data structure that allows us to count distinct squares in a text fragment T [i . . j] in O(log n) time.

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Section: Countdistinctmentioning

confidence: 99%

Counting Distinct Patterns in Internal Dictionary Matching

Charalampopoulos¹,

Kociumaka²,

Mohamed³

et al. 2020

Preprint

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“…Let us consider the following operations on J , where I is an interval: insert(I): J := J ∪ {I}; delete(I): J := J \ {I} for I ∈ J ; and count, which returns | J |. It is folklore knowledge that all these operations can be performed efficiently using a static range tree (sometimes called a segment tree; see [12]). In Appendix A, we prove the following lemma for completeness.…”

Section: Fact 22 ([2]mentioning

confidence: 99%

Efficient Representation and Counting of Antipower Factors in Words

Kociumaka

Radoszewski

Rytter

et al. 2019

Language and Automata Theory and Applications

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A k-antipower (for k ≥ 2) is a concatenation of k pairwise distinct words of the same length. The study of antipower factors of a word was initiated by Fici et al. (ICALP 2016) and first algorithms for computing antipower factors were presented by Badkobeh et al. (Inf. Process. Lett., 2018). We address two open problems posed by Badkobeh et al. Our main results are algorithms for counting and reporting factors of a word which are k-antipowers. They work in O(nk log k) time and O(nk log k + C) time, respectively, where C is the number of reported factors. For k = o( n/ log n), this improves the time complexity of O(n 2 /k) of the solution by Badkobeh et al. Our main algorithmic tools are runs and gapped repeats.We also present an improved data structure that checks, for a given factor of a word and an integer k, if the factor is a k-antipower.

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“…Our data structure provides a general framework for solving problems related to the internal structure of the string. The case of palindromes has already been studied in [30], where authors proposed a data structure of size O(n log n) that returns the number of all distinct palindromes in T [i . .…”

Section: Introductionmentioning

confidence: 99%