Palindromic Trees for a Sliding Window and Its Applications
Takuya Mieno, Kiichi Watanabe, Yuto Nakashima, Shunsuke Inenaga, Hideo, Bannai, Masayuki Takeda

TL;DR
This paper develops algorithms for maintaining palindromic trees in sliding windows of a string, enabling efficient updates and applications to minimal unique palindromic substrings and absent palindromic words.
Contribution
It introduces two algorithms for maintaining palindromic trees in sliding windows with different time and space complexities, extending their applicability.
Findings
First algorithm operates in O(n log σ') time with O(d) space.
Second algorithm operates in O(n + dσ) time with (d+2)σ + O(d) space.
Algorithms enable efficient computation of MUPS and MAPW in sliding windows.
Abstract
The palindromic tree (a.k.a. eertree) for a string of length is a tree-like data structure that represents the set of all distinct palindromic substrings of , using space [Rubinchik and Shur, 2018]. It is known that, when is over an alphabet of size and is given in an online manner, then the palindromic tree of can be constructed in time with space. In this paper, we consider the sliding window version of the problem: For a sliding window of length at most , we present two versions of an algorithm which maintains the palindromic tree of size for every sliding window over , where . The first version works in time with space where is the maximum number of distinct characters in the windows, and the second one works in time with…
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Taxonomy
TopicsAlgorithms and Data Compression · semigroups and automata theory · DNA and Biological Computing
