On Longest Common Property Preserved Substring Queries

Kazuki Kai, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Tomasz Kociumaka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


We revisit the problem of longest common property preserving substring queries introduced by Ayad et al. (SPIRE 2018, arXiv 2018). We consider a generalized and unified on-line setting, where we are given a set X of k strings of total length n that can be pre-processed so that, given a query string y and a positive integer (Formula presented), we can determine the longest substring of y that satisfies some specific property and is common to at least (Formula presented) strings in X. Ayad et al. considered the longest square-free substring in an on-line setting and the longest periodic and palindromic substring in an off-line setting. In this paper, we give efficient solutions in the on-line setting for finding the longest common square, periodic, palindromic, and Lyndon substrings. More precisely, we show that X can be pre-processed in O(n) time resulting in a data structure of O(n) size that answers queries in (Formula presented) time and O(1) working space, where (Formula presented) is the size of the alphabet, and the common substring must be a square, a periodic substring, a palindrome, or a Lyndon word.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 26th International Symposium, SPIRE 2019, Proceedings
EditorsNieves R. Brisaboa, Simon J. Puglisi
Number of pages13
ISBN (Print)9783030326852
Publication statusPublished - 2019
Event26th International Symposium on String Processing and Information Retrieval, SPIRE 2019 - Segovia, Spain
Duration: Oct 7 2019Oct 9 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11811 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th International Symposium on String Processing and Information Retrieval, SPIRE 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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