On the Maximum Number of Distinct Palindromic Sub-arrays

Mahalingam, Kalpana; Pandoh, Palak

doi:10.1007/978-3-030-13435-8_32

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…In this section, we find the maximum number of non-empty distinct HV-palindromes in a 2D word w of size (m, n). It was proved in [1] and [23] that there are at most n palindromes in a 1D word of length n and at most 2n + ⌊ n 2 ⌋ − 1 palindromes in a two-row array of size (2, n) respectively. Further, it was conjectured in [3] that the number of HV-palindromes in any 2D word of size (2, n) is less than or equal to 2n.…”

Section: 1mentioning

confidence: 99%

“…In this section find the maximum number of palindromes in a 2D palindrome and the maximum number of HV-palindromes in a HV-palindrome of size (m, n). We recall the following result from [23].…”

Section: Corollary 52 the Maximum Number Of Hv-palindromes In Anymentioning

confidence: 99%

“…An algorithm for finding maximal 2D palindromes was given in [11]. The maximum and the least number of 2D palindromic sub-arrays in a given array was studied in [3,23] and [24] respectively.…”

Section: Introductionmentioning

confidence: 99%

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On the least number of palindromes in two-dimensional words

Mahalingam

Pandoh

Krithivasan

2020

Theoretical Computer Science

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Section: 1mentioning

confidence: 99%

Section: Corollary 52 the Maximum Number Of Hv-palindromes In Anymentioning

confidence: 99%

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On the least number of palindromes in two-dimensional words

Mahalingam

Pandoh

Krithivasan

2020

Theoretical Computer Science

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“…[3]. The maximum and the least number of 2D palindromic sub-arrays in a given array was studied in [2,15] and [16], respectively. Palindromic subsequences, i.e., scattered palindromic subwords, in words were studied recently in [4,10].…”

Section: Introductionmentioning

confidence: 99%

Counting scattered palindromes in a finite word

Mahalingam¹,

Pandoh²

2021

Preprint

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We investigate the scattered palindromic subwords in a finite word. We start by characterizing the words with the least number of scattered palindromic subwords. Then, we give an upper bound for the total number of palindromic subwords in a word of length n in terms of Fibonacci number Fn by proving that at most Fn new scattered palindromic subwords can be created on the concatenation of a letter to a word of length n − 1. We propose a conjecture on the maximum number of scattered palindromic subwords in a word of length n with q distinct letters. We support the conjecture by showing its validity for words where q ≥ n 2 .

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“…In this paper we address two different kinds of 2-dimensional (2D) palindromes, each having different symmetry requirements. 2D palindromes have been given a lot of attention in recent literature [1,2,3,4].…”

Section: Introductionmentioning

confidence: 99%

2-Dimensional Palindromes with $k$ Mismatches

Sokol¹

2020

Preprint

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This paper extends the problem of 2-dimensional palindrome search into the area of approximate matching. Using the Hamming distance as the measure, we search for 2D palindromes that allow up to k mismatches. We consider two different definitions of 2D palindromes and describe efficient algorithms for both of them. The first definition implies a square, while the second definition (also known as a centrosymmetric factor ), can be any rectangular shape. Given a text of size n × m, the time complexity of the first algorithm is O(nm(log m + log n + k)) and for the second algorithm it is O(nm(log m + k) + occ) where occ is the size of the output.

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On the Maximum Number of Distinct Palindromic Sub-arrays

Cited by 6 publications

References 15 publications

On the least number of palindromes in two-dimensional words

On the least number of palindromes in two-dimensional words

Counting scattered palindromes in a finite word

2-Dimensional Palindromes with $k$ Mismatches

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