Efficient computation of longest single-arm-gapped palindromes in a string

Narisada, Shintaro; Hendrian, Diptarama; Narisawa, Kazuyuki; Inenaga, Shunsuke; Shinohara, Ayumi

doi:10.1016/j.tcs.2019.10.025

Cited by 2 publications

(1 citation statement)

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“…Palindromes are strings that read the same forward and backward. Finding palindromic structures in a given string is a fundamental task in string processing, and thus it has extensively been studied (e.g., see [1][2][3][4][5][6][7][8][9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Computing palindromes and suffix trees of dynamic trees

Funakoshi,

Mieno,

Nakashima

et al. 2024

Preprint

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We consider the problems of computing maximal palindromes and distinct palindromes in an edge-labeled rooted tree where each edge is labeled by a single character. Such a tree is a natural generalization of a string, which can be seen as a single-path tree. There is a linear time offline algorithm to compute maximal palindromes and distinct palindromes in a given (static) tree whose edge-labels are drawn from a linearly-sortable alphabet [Mieno et al., ISAAC 2022]. In this paper, we tackle problems of palindrome enumeration on dynamic trees which support leaf additions and leaf deletions. We propose the first sub-quadratic algorithms to enumerate palindromes in a dynamic tree whose edge-labels are drawn from a general ordered alphabet. Our algorithm computes all maximal palindromes in O(N log h) time and all distinct palindromes in O(N log h + N log s) time with O(N) working space, where N is the number of edges in the tree, h is the height of the tree, and s is the number of distinct characters appearing in the tree. Furthermore, as a by-product, we present an O(N log N)-time online algorithm to construct the suffix tree of the input tree, which is of independent interest.

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