Palindromic trees for a sliding window and its applications

Takuya Mieno, Kiichi Watanabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Research output: Contribution to journalArticlepeer-review

Abstract

The palindromic tree (a.k.a. eertree) for a string S of length n is a tree-like data structure that represents the set of all distinct palindromic substrings of S, using O(n) space [Rubinchik and Shur, 2018]. It is known that, when S is over an alphabet of size σ and is given in an online manner, then the palindromic tree of S can be constructed in O(nlog⁡σ) time with O(n) space. In this paper, we consider the sliding window version of the problem: For a sliding window of length at most d, we present two versions of an algorithm which maintains the palindromic tree of size O(d) for every sliding window S[i..j] over S, where 1≤j−i+1≤d. The first version works in O(nlog⁡σ) time with O(d) space where σ≤d is the maximum number of distinct characters in the windows, and the second one works in O(n+dσ) time with (d+2)σ+O(d) space. We also show how our algorithms can be applied to efficient computation of minimal unique palindromic substrings (MUPS) and minimal absent palindromic words (MAPW) for a sliding window.

Original languageEnglish
Article number106174
JournalInformation Processing Letters
Volume173
DOIs
Publication statusPublished - Jan 2022

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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