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Shortest Cover After Edit

Authors Kazuki Mitani, Takuya Mieno , Kazuhisa Seto , Takashi Horiyama

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Author Details

Kazuki Mitani
  • Graduate School of Information Science and Technology, Hokkaido University, Japan
Takuya Mieno
  • Department of Computer and Network Engineering, University of Electro-Communications, Tokyo, Japan
Kazuhisa Seto
  • Faculty of Information Science and Technology, Hokkaido University, Japan
Takashi Horiyama
  • Faculty of Information Science and Technology, Hokkaido University, Japan

Funding

  • Mieno, Takuya: JSPS KAKENHI Grant Numbers JP22K21273 and JP23H04381
  • Seto, Kazuhisa: JSPS KAKENHI Grant Number JP22H00513
  • Horiyama, Takashi: JSPS KAKENHI Grant Number JP20H05964

Cite AsGet BibTex

Kazuki Mitani, Takuya Mieno, Kazuhisa Seto, and Takashi Horiyama. Shortest Cover After Edit. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CPM.2024.24

Abstract

This paper investigates the (quasi-)periodicity of a string when the string is edited. A string C is called a cover (as known as a quasi-period) of a string T if each character of T lies within some occurrence of C. By definition, a cover of T must be a border of T; that is, it occurs both as a prefix and as a suffix of T. In this paper, we focus on the changes in the longest border and the shortest cover of a string when the string is edited only once. We propose a data structure of size O(n) that computes the longest border and the shortest cover of the string in O(𝓁 log n) time after an edit operation (either insertion, deletion, or substitution of some string) is applied to the input string T of length n, where 𝓁 is the length of the string being inserted or substituted. The data structure can be constructed in O(n) time given string T.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • string algorithm
  • border
  • cover
  • quasi-periodicity
  • dynamic string

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References

  1. Paniz Abedin, Sahar Hooshmand, Arnab Ganguly, and Sharma V. Thankachan. The heaviest induced ancestors problem revisited. In Annual Symposium on Combinatorial Pattern Matching, CPM 2018, July 2-4, 2018 - Qingdao, China, volume 105 of LIPIcs, pages 20:1-20:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPICS.CPM.2018.20.
  2. Amihood Amir, Itai Boneh, Panagiotis Charalampopoulos, and Eitan Kondratovsky. Repetition detection in a dynamic string. In 27th Annual European Symposium on Algorithms, ESA 2019, September 9-11, 2019, Munich/Garching, Germany, volume 144 of LIPIcs, pages 5:1-5:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPICS.ESA.2019.5.
  3. Amihood Amir, Panagiotis Charalampopoulos, Costas S. Iliopoulos, Solon P. Pissis, and Jakub Radoszewski. Longest common factor after one edit operation. In String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Palermo, Italy, September 26-29, 2017, Proceedings, volume 10508 of Lecture Notes in Computer Science, pages 14-26. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-67428-5_2.
  4. Amihood Amir, Panagiotis Charalampopoulos, Solon P. Pissis, and Jakub Radoszewski. Dynamic and internal longest common substring. Algorithmica, 82(12):3707-3743, 2020. URL: https://doi.org/10.1007/S00453-020-00744-0.
  5. Alberto Apostolico and Andrzej Ehrenfeucht. Efficient detection of quasiperiodicities in strings. Technical Report 90.5, The Leonadro Fibonacci Institute, Trento, Italy, 1990. Google Scholar
  6. Alberto Apostolico and Andrzej Ehrenfeucht. Efficient detection of quasiperiodicities in strings. Theor. Comput. Sci., 119(2):247-265, 1993. URL: https://doi.org/10.1016/0304-3975(93)90159-Q.
  7. Alberto Apostolico, Martin Farach, and Costas S. Iliopoulos. Optimal superprimitivity testing for strings. Inf. Process. Lett., 39(1):17-20, 1991. URL: https://doi.org/10.1016/0020-0190(91)90056-N.
  8. Michael A. Bender and Martin Farach-Colton. The LCA problem revisited. In LATIN 2000: Theoretical Informatics, 4th Latin American Symposium, Punta del Este, Uruguay, April 10-14, 2000, Proceedings, volume 1776 of Lecture Notes in Computer Science, pages 88-94. Springer, 2000. URL: https://doi.org/10.1007/10719839_9.
  9. Dany Breslauer. An on-line string superprimitivity test. Inf. Process. Lett., 44(6):345-347, 1992. URL: https://doi.org/10.1016/0020-0190(92)90111-8.
  10. Panagiotis Charalampopoulos, Pawel Gawrychowski, and Karol Pokorski. Dynamic longest common substring in polylogarithmic time. In 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 27:1-27:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPICS.ICALP.2020.27.
  11. Panagiotis Charalampopoulos, Tomasz Kociumaka, and Philip Wellnitz. Faster approximate pattern matching: A unified approach. CoRR, abs/2004.08350, 2020. URL: https://arxiv.org/abs/2004.08350.
  12. Mitsuru Funakoshi and Takuya Mieno. Minimal unique palindromic substrings after single-character substitution. In String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Lille, France, October 4-6, 2021, Proceedings, volume 12944 of Lecture Notes in Computer Science, pages 33-46. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-86692-1_4.
  13. Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Computing longest palindromic substring after single-character or block-wise edits. Theor. Comput. Sci., 859:116-133, 2021. URL: https://doi.org/10.1016/J.TCS.2021.01.014.
  14. Pawel Gawrychowski, Jakub Radoszewski, and Tatiana Starikovskaya. Quasi-periodicity in streams. In 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019, June 18-20, 2019, Pisa, Italy, volume 128 of LIPIcs, pages 22:1-22:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPICS.CPM.2019.22.
  15. Dan Gusfield. Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology. Cambridge University Press, 1997. URL: https://doi.org/10.1017/CBO9780511574931.
  16. Marek Karpinski, Wojciech Rytter, and Ayumi Shinohara. An efficient pattern-matching algorithm for strings with short descriptions. Nord. J. Comput., 4(2):172-186, 1997. Google Scholar
  17. Donald E. Knuth, James H. Morris Jr., and Vaughan R. Pratt. Fast pattern matching in strings. SIAM J. Comput., 6(2):323-350, 1977. URL: https://doi.org/10.1137/0206024.
  18. Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, and Tomasz Walen. Internal pattern matching queries in a text and applications. CoRR, abs/1311.6235, 2023. URL: https://doi.org/10.48550/arXiv.1311.6235.
  19. Michael G. Main and Richard J. Lorentz. An O(n log n) algorithm for finding all repetitions in a string. J. Algorithms, 5(3):422-432, 1984. URL: https://doi.org/10.1016/0196-6774(84)90021-X.
  20. Neerja Mhaskar and W. F. Smyth. String covering: A survey. Fundam. Informaticae, 190(1):17-45, 2022. URL: https://doi.org/10.3233/FI-222164.
  21. Takuya Mieno and Mitsuru Funakoshi. Data structures for computing unique palindromes in static and non-static strings. Algorithmica, 2023. URL: https://doi.org/10.1007/s00453-023-01170-8.
  22. Dennis W. G. Moore and William F. Smyth. An optimal algorithm to compute all the covers of a string. Inf. Process. Lett., 50(5):239-246, 1994. URL: https://doi.org/10.1016/0020-0190(94)00045-X.
  23. Yuki Urabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Longest Lyndon substring after edit. In Annual Symposium on Combinatorial Pattern Matching, CPM 2018, July 2-4, 2018 - Qingdao, China, volume 105 of LIPIcs, pages 19:1-19:10. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPICS.CPM.2018.19.
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