Minimal Unique Substrings and Minimal Absent Words in a Sliding Window

Takuya Mieno, Yuki Kuhara, Tooru Akagi, Yuta Fujishige, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

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

Abstract

A substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. A string w is called a minimal absent word (MAW) of T if w does not occur in T and any proper substring of w occurs in T. In this paper, we study the problems of computing MUSs and MAWs in a sliding window over a given string T. We first show how the set of MUSs can change in a sliding window over T, and present an-time and O(d)-space algorithm to compute MUSs in a sliding window of width d over T, where is the maximum number of distinct characters in every window. We then give tight upper and lower bounds on the maximum number of changes in the set of MAWs in a sliding window over T. Our bounds improve on the previous results in Crochemore et al. (2017).

Original languageEnglish
Title of host publicationSOFSEM 2020
Subtitle of host publicationTheory and Practice of Computer Science - 46th International Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2020, Proceedings
EditorsAlexander Chatzigeorgiou, Riccardo Dondi, Herodotos Herodotou, Christos Kapoutsis, Yannis Manolopoulos, George A. Papadopoulos, Florian Sikora
PublisherSpringer
Pages148-160
Number of pages13
ISBN (Print)9783030389185
DOIs
Publication statusPublished - Jan 1 2020
Event46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020 - Limassol, Cyprus
Duration: Jan 20 2020Jan 24 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12011 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020
CountryCyprus
CityLimassol
Period1/20/201/24/20

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Mieno, T., Kuhara, Y., Akagi, T., Fujishige, Y., Nakashima, Y., Inenaga, S., Bannai, H., & Takeda, M. (2020). Minimal Unique Substrings and Minimal Absent Words in a Sliding Window. In A. Chatzigeorgiou, R. Dondi, H. Herodotou, C. Kapoutsis, Y. Manolopoulos, G. A. Papadopoulos, & F. Sikora (Eds.), SOFSEM 2020: Theory and Practice of Computer Science - 46th International Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2020, Proceedings (pp. 148-160). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12011 LNCS). Springer. https://doi.org/10.1007/978-3-030-38919-2_13