Document Open Access Logo

Set Parameterized Matching via Multi-Layer Hashing

Authors Moshe Lewenstein , Ely Porat

PDF

File

Thumbnail PDF
PDF
LIPIcs.CPM.2026.36.pdf
  • Filesize: 0.88 MB
  • 18 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • Set Parameterized Matching
  • Pattern Matching
  • Randomized Algorithms
  • Hashing
  • Parameterized Matching

Metrics

Abstract

We study the set parameterized matching problem, a generalization of the classical parameterized matching problem introduced by Baker [Baker, 1993; Baker, 1997]. In set parameterized matching, both the pattern and text are sequences where each position contains a set of characters rather than a single character. Two set-strings parameterized match if there exists a bijection between their alphabets that maps one to the other set-wise. Boussidan [Aaron Boussidan, 2025] introduced this problem for the case of equal-length set-strings. We present a randomized algorithm running in O(N + M) time with high probability, where N is the text size and M is the pattern size. Our approach employs a novel three-layer hashing scheme based on Karp-Rabin fingerprinting that addresses the challenges of (1) the size blowup in representations of the problem, (2) set-to-set matching, and (3) the dynamic nature of encodings of text substrings during pattern scanning.

Cite As Get BibTex

Moshe Lewenstein and Ely Porat. Set Parameterized Matching via Multi-Layer Hashing. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CPM.2026.36

Author Details

Moshe Lewenstein
  • Bar-Ilan University, Ramat Gan, Israel
Ely Porat
  • Bar-Ilan University, Ramat Gan, Israel

Funding

  • Lewenstein, Moshe: Work on this paper was supported by ISF grant # 2760/25 awarded by the Israel Science Foundation.

References

  1. Amihood Amir, Martin Farach, and S. Muthukrishnan. Alphabet dependence in parameterized matching. Information Processing Letters, 49(3):111-115, 1994. URL: https://doi.org/10.1016/0020-0190(94)90086-8.
  2. Amihood Amir and Gonzalo Navarro. Parameterized matching on non-linear structures. Information Processing Letters, 109(15):864-867, 2009. URL: https://doi.org/10.1016/J.IPL.2009.04.012.
  3. Alberto Apostolico, Péter L. Erdős, and Alpár Jüttner. Parameterized searching with mismatches for run-length encoded strings. Theoretical Computer Science, 454:23-29, 2012. URL: https://doi.org/10.1016/J.TCS.2012.03.018.
  4. Alberto Apostolico, Péter L. Erdős, and Moshe Lewenstein. Parameterized matching with mismatches. Journal of Discrete Algorithms, 5(1):135-140, 2007. URL: https://doi.org/10.1016/J.JDA.2006.03.014.
  5. Alberto Apostolico and Raffaele Giancarlo. Periodicity and repetitions in parameterized strings. Discrete Applied Mathematics, 156(9):1389-1398, 2008. URL: https://doi.org/10.1016/J.DAM.2006.11.017.
  6. Brenda S. Baker. A program for identifying duplicated code. In Computing Science and Statistics: Proceedings of the 24th Symposium on the Interface, 1992. Google Scholar
  7. Brenda S. Baker. A theory of parameterized pattern matching: Algorithms and applications. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing (STOC), pages 71-80, 1993. URL: https://doi.org/10.1145/167088.167115.
  8. Brenda S. Baker. Parameterized duplication in strings: Algorithms and an application to software maintenance. SIAM Journal on Computing, 26(5):1343-1362, 1997. URL: https://doi.org/10.1137/S0097539793246707.
  9. Brenda S. Baker. Parameterized diff. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 854-855. SIAM, 1999. URL: http://dl.acm.org/citation.cfm?id=314500.314968.
  10. Richard Beal and Donald A. Adjeroh. Compressed parameterized pattern matching. Theor. Comput. Sci., 609:129-142, 2016. URL: https://doi.org/10.1016/J.TCS.2015.09.015.
  11. Pierre Bourhis, Aaron Boussidan, and Philippe Gambette. On distances between words with parameters. In 34th Annual Symposium on Combinatorial Pattern Matching, CPM 2023, volume 259 of LIPIcs, pages 6:1-6:23, 2023. URL: https://doi.org/10.4230/LIPIcs.CPM.2023.6.
  12. Aaron Boussidan. Comparaison automatique de pièces de théâtre à l’aide de distances d’édition et d’alignement. Phd dissertation, Gustave Eiffel University, 2025. Google Scholar
  13. Richard Cole, Carmit Hazay, Moshe Lewenstein, and Dekel Tsur. Two-dimensional parameterized matching. ACM Transactions on Algorithms, 11(2):12, 2014. Google Scholar
  14. S. Deguchi, F. Higashijima, H. Bannai, S. Inenaga, and M. Takeda. Parameterized suffix arrays for binary strings. In Proceedings of the Prague Stringology Conference, pages 84-94, 2008. Google Scholar
  15. Arnab Ganguly, Wing-Kai Hon, Kunihiko Sadakane, Rahul Shah, Sharma V. Thankachan, and Y. Yang. Space-efficient dictionaries for parameterized and order-preserving pattern matching. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016), volume 54 of Leibniz International Proceedings in Informatics (LIPIcs), pages 2:1-2:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/LIPIcs.CPM.2016.2.
  16. Arnab Ganguly, Rahul Shah, and Sharma V. Thankachan. pBWT: Achieving succinct data structures for parameterized pattern matching and related problems. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 397-407. SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974782.25.
  17. R. Garg, R. Prasad, and S. Agarwal. Fast parameterized word matching on compressed text. In International Conference on Computer and Communication Technology (ICCCT), pages 317-321. IEEE, 2014. Google Scholar
  18. Carmit Hazay, Moshe Lewenstein, and Dina Sokol. Approximate parameterized matching. ACM Transactions on Algorithms, 3(3):29, 2007. URL: https://doi.org/10.1145/1273340.1273345.
  19. Richard M. Karp and Michael O. Rabin. Efficient randomized pattern-matching algorithms. IBM J. Res. Dev., 31(2):249-260, 1987. URL: https://doi.org/10.1147/RD.312.0249.
  20. Orgad Keller, Tsvi Kopelowitz, and Moshe Lewenstein. On the longest common parameterized subsequence. Theoretical Computer Science, 410(51):5347-5353, 2009. URL: https://doi.org/10.1016/J.TCS.2009.09.011.
  21. R. Khetan, S. Agarwal, and R. Prasad. An efficient approach towards compressed parameterized word matching using wavelet tree. Journal of Information and Optimization Sciences, 37(2):285-301, 2016. Google Scholar
  22. I. Lee, J. Mendivelso, and Yoan J. Pinzón. δγ-parameterized matching. In String Processing and Information Retrieval (SPIRE), volume 5280 of LNCS, pages 236-248, 2008. Google Scholar
  23. Moshe Lewenstein. Parameterized matching. In Encyclopedia of Algorithms, pages 635-638. Springer, 2008. URL: https://doi.org/10.1007/978-0-387-30162-4_282.
  24. Juan Mendivelso, Sharma V. Thankachan, and Yoan J. Pinzón. A brief history of parameterized matching problems. Discrete Applied Mathematics, 274:103-115, 2020. URL: https://doi.org/10.1016/J.DAM.2018.07.017.
  25. Tetsuo Shibuya. Generalization of a suffix tree for RNA structural pattern matching. Algorithmica, 39(1):1-19, 2004. URL: https://doi.org/10.1007/S00453-003-1067-9.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact