Double-Ended Palindromic Trees in Linear Time
Abstract
The palindromic tree (a.k.a. eertree) is a data structure that provides access to all palindromic substrings of a string. In this paper, we propose a dynamic version of eertree, called double-ended eertree, which supports online operations on the stored string, including double-ended queue operations, counting distinct palindromic substrings, and finding the longest palindromic prefix/suffix. At the heart of our construction, we identify a new class of substring occurrences, called surfaces, that are palindromic substring occurrences that are neither prefixes nor suffixes of any other palindromic substring occurrences, which is of independent interest. Surfaces characterize the link structure of all palindromic substrings in the eertree, thereby allowing a linear-time implementation of double-ended eertrees through a linear-time maintenance of surfaces.
Keywords
Cite
@article{arxiv.2210.02292,
title = {Double-Ended Palindromic Trees in Linear Time},
author = {Qisheng Wang and Ming Yang and Xinrui Zhu},
journal= {arXiv preprint arXiv:2210.02292},
year = {2025}
}
Comments
Full version, 64 pages, 2 tables, 17 algorithms. Title changed, abstract improved, some proofs simplified, the persistent part removed for simplicity