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Pattern Matching on Run-Length Grammar-Compressed Strings in Linear Time

Authors Yuto Iguchi, Ryo Yoshinaka , Ayumi Shinohara

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • pattern matching
  • run-length straight-line programs
  • compression
  • suffix tree

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Abstract

Run-length straight-line programs (RLSLPs) are a technique for grammar-based compression, allowing any string to be represented with optimal space for δ, the substring complexity of the string. We address the compressed pattern matching problem for RLSLPs: Given a compressed text in RLSLP format and an uncompressed pattern, determine if the pattern appears in the text. This paper proposes an algorithm that solves this problem in linear time with respect to the size of the grammar and the length of the pattern.

Cite As Get BibTex

Yuto Iguchi, Ryo Yoshinaka, and Ayumi Shinohara. Pattern Matching on Run-Length Grammar-Compressed Strings in Linear Time. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.9

Author Details

Yuto Iguchi
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Ryo Yoshinaka
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Ayumi Shinohara
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

Funding

  • Yoshinaka, Ryo: JSPS KAKENHI 18K11150, 20H05703, 23K11325, 24H00697, 24K14827.
  • Shinohara, Ayumi: JSPS KAKENHI 21K11745.

Acknowledgements

We are grateful to the anonymous reviewers for their thorough review and helpful recommendations.

References

  1. Amihood Amir and Gary Benson. Efficient two-dimensional compressed matching. In Data Compression Conference, 1992., pages 279-288, 1992. URL: https://doi.org/10.1109/DCC.1992.227453.
  2. Amihood Amir, Gary Benson, and Martin Farach. Let sleeping files lie: Pattern matching in Z-compressed files. Journal of Computer and System Sciences, 52(2):299-307, 1996. URL: https://doi.org/10.1006/jcss.1996.0023.
  3. Philip Bille, Gad M. Landau, Rajeev Raman, Kunihiko Sadakane, Srinivasa Rao Satti, and Oren Weimann. Random access to grammar-compressed strings and trees. SIAM Journal on Computing, 44(3):513-539, 2015. URL: https://doi.org/10.1137/130936889.
  4. Martin Farach and Mikkel Thorup. String matching in Lempel-Ziv compressed strings. Algorithmica, 20(4):388-404, 1998. URL: https://doi.org/10.1007/PL00009202.
  5. Simone Faro and Thierry Lecroq. The exact online string matching problem: A review of the most recent results. ACM Comput. Surv., 45(2), March 2013. URL: https://doi.org/10.1145/2431211.2431212.
  6. Moses Ganardi and Paweł Gawrychowski. Pattern matching on grammar-compressed strings in linear time. In Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2833-2846, 2022. URL: https://doi.org/10.1137/1.9781611977073.110.
  7. Moses Ganardi, Artur Jeż, and Markus Lohrey. Balancing straight-line programs. J. ACM, 68(4), June 2021. URL: https://doi.org/10.1145/3457389.
  8. Paweł Gawrychowski. Pattern matching in Lempel-Ziv compressed strings: Fast, simple, and deterministic. In Algorithms - ESA 2011, pages 421-432, 2011. URL: https://doi.org/10.1007/978-3-642-23719-5_36.
  9. Paweł Gawrychowski. Optimal pattern matching in LZW compressed strings. ACM Trans. Algorithms, 9(3), June 2013. URL: https://doi.org/10.1145/2483699.2483705.
  10. Keisuke Goto, Hideo Bannai, Shunsuke Inenaga, and Masayuki Takeda. Fast q-gram mining on SLP compressed strings. Journal of Discrete Algorithms, 18:89-99, 2013. URL: https://doi.org/10.1016/j.jda.2012.07.006.
  11. Dan Gusfield. Algorithms on strings, trees, and sequences: computer science and computational biology. Cambridge University Press, 1997. URL: https://doi.org/10.1017/CBO9780511574931.
  12. Marek Karpinski, Wojciech Rytter, and Ayumi Shinohara. Pattern-matching for strings with short descriptions. In Proc. The 6th Annual Symposium on Combinatorial Pattern Matching (CPM95), volume 937 of Lecture Notes in Computer Science, pages 205-214. Springer, 1995. URL: https://doi.org/10.1007/3-540-60044-2_44.
  13. Dominik Kempa and Tomasz Kociumaka. Collapsing the Hierarchy of Compressed Data Structures: Suffix Arrays in Optimal Compressed Space . In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 1877-1886, November 2023. URL: https://doi.org/10.1109/FOCS57990.2023.00114.
  14. Takuya Kida, Tetsuya Matsumoto, Yusuke Shibata, Masayuki Takeda, Ayumi Shinohara, and Setsuo Arikawa. Collage system: a unifying framework for compressed pattern matching. Theoretical Computer Science, 298(1):253-272, 2003. URL: https://doi.org/10.1016/S0304-3975(02)00426-7.
  15. Tomasz Kociumaka, Marcin Kubica, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. A linear-time algorithm for seeds computation. ACM Trans. Algorithms, 16(2), April 2020. URL: https://doi.org/10.1145/3386369.
  16. Tomasz Kociumaka, Gonzalo Navarro, and Francisco Olivares. Near-optimal search time in δ-optimal space. In LATIN 2022: Theoretical Informatics, pages 88-103, 2022. URL: https://doi.org/10.1007/978-3-031-20624-5_6.
  17. Tomasz Kociumaka, Gonzalo Navarro, and Nicola Prezza. Toward a definitive compressibility measure for repetitive sequences. IEEE Transactions on Information Theory, 69(4):2074-2092, 2023. URL: https://doi.org/10.1109/TIT.2022.3224382.
  18. Roman Kolpakov and Gregory Kucherov. Finding maximal repetitions in a word in linear time. In 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039), pages 596-604, 1999. URL: https://doi.org/10.1109/SFFCS.1999.814634.
  19. S. Rao Kosaraju. Pattern matching in compressed texts. In Foundations of Software Technology and Theoretical Computer Science, pages 349-362, 1995. URL: https://doi.org/10.1007/3-540-60692-0_60.
  20. Shuo Li, Jakub Pachocki, and Jakub Radoszewski. A note on the maximum number of k-powers in a finite word. The Electronic Journal of Combinatorics, 31(3), 2024. URL: https://doi.org/10.37236/11270.
  21. Markus Lohrey. Algorithmics on SLP-compressed strings: A survey. Groups - Complexity - Cryptology, 4(2):241-299, 2012. URL: https://doi.org/doi:10.1515/gcc-2012-0016.
  22. 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.
  23. Gonzalo Navarro. A guided tour to approximate string matching. ACM Computing Surveys, 33(1):31-88, 2001. URL: https://doi.org/10.1145/375360.375365.
  24. Gonzalo Navarro, Francisco Olivares, and Cristian Urbina. Balancing run-length straight-line programs. In String Processing and Information Retrieval, pages 117-131, 2022. URL: https://doi.org/10.1007/978-3-031-20643-6_9.
  25. Gonzalo Navarro and Cristian Urbina. Iterated straight-line programs. In LATIN 2024: Theoretical Informatics, pages 66-80, 2024. URL: https://doi.org/10.1007/978-3-031-55598-5_5.
  26. Takaaki Nishimoto, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Fully Dynamic Data Structure for LCE Queries in Compressed Space. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016), volume 58 of Leibniz International Proceedings in Informatics (LIPIcs), pages 72:1-72:14, 2016. URL: https://doi.org/10.4230/LIPIcs.MFCS.2016.72.
  27. Jakub Radoszewski. Linear Time Construction of Cover Suffix Tree and Applications. In 31st Annual European Symposium on Algorithms (ESA 2023), volume 274 of Leibniz International Proceedings in Informatics (LIPIcs), pages 89:1-89:17, 2023. URL: https://doi.org/10.4230/LIPIcs.ESA.2023.89.
  28. Wojciech Rytter. Grammar compression, LZ-encodings, and string algorithms with implicit input. In Automata, Languages and Programming (ICALP 2004), pages 15-27, 2004. URL: https://doi.org/10.1007/978-3-540-27836-8_5.
  29. Masayuki Takeda and Ayumi Shinohara. Pattern Matching on Compressed Text, in Encyclopedia of Algorithms, pages 1538-1542. Springer New York, 2016. URL: https://doi.org/10.1007/978-1-4939-2864-4_81.
  30. Esko Ukkonen. On-line construction of suffix trees. Algorithmica, 14:249-260, 1995. URL: https://doi.org/10.1007/BF01206331.
  31. Peter Weiner. Linear pattern matching algorithms. In 14th Annual Symposium on Switching and Automata Theory (SWAT 1973), pages 1-11, 1973. URL: https://doi.org/10.1109/SWAT.1973.13.
  32. Takanori Yamamoto, Hideo Bannai, Shunsuke Inenaga, and Masayuki Takeda. Faster subsequence and don't-care pattern matching on compressed texts. In Combinatorial Pattern Matching, pages 309-322, 2011. URL: https://doi.org/10.1007/978-3-642-21458-5_27.
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