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A Bitwise Approach to SCER Matching in Indeterminate Strings

Authors Simone Faro , Dominik Köppl , Thierry Lecroq , Francesco Pio Marino

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Subject Classification

ACM Subject Classification
  • Information systems → Information retrieval
Keywords
  • string matching
  • indeterminate strings
  • SCER matching

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Abstract

We study the problem of matching a determinate pattern against an indeterminate text of the same length n, where each text position is a set of possible characters drawn from an alphabet Σ of size σ. We study this matching problem under the order-preserving and parameterized matching setting. For that, we encode character sets by bit expressions using sum-free sequences. This encoding enables constant-time character comparisons and avoids explicit set operations. We present an optimal 𝒪(n) time algorithm for order-preserving matching and an 𝒪(n+(σ_p^x ⋅ σ_p^y) √{σ_p^x + σ_p^y}) time algorithm for parameterized matching, where σ_p^x and σ_p^y denote the number of distinct parameterized symbols in the pattern and the text, respectively. The proposed techniques significantly reduce overhead while maintaining exactness, offering practical performance improvements for pattern matching under uncertainty. Additionally, we extend the parameterized matching framework to allow mismatches, for which we present an algorithm with time complexity 𝒪(σ² n log n + n σ² √σ log(n σ)).

Cite As Get BibTex

Simone Faro, Dominik Köppl, Thierry Lecroq, and Francesco Pio Marino. A Bitwise Approach to SCER Matching in Indeterminate Strings. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CPM.2026.21

Author Details

Simone Faro
  • Department of Mathematics and Computer Science, University of Catania, Italy
Dominik Köppl
  • University of Yamanashi, Kofu, Japan
Thierry Lecroq
  • Univ Rouen Normandie, INSA Rouen Normandie, Université Le Havre Normandie, Normandie Univ, LITIS UR 4108, CNRS NormaSTIC FR 3638, IRIB, Rouen, France
Francesco Pio Marino
  • Department of Mathematics and Computer Science, University of Catania, Italy
  • Univ Rouen Normandie, INSA Rouen Normandie, Université Le Havre Normandie, Normandie Univ, LITIS UR 4108, CNRS NormaSTIC FR 3638, IRIB, Rouen, France

Funding

  • Köppl, Dominik: JSPS KAKENHI Grant Number 25K21150.

Supplementary Materials

References

  1. Alberto Apostolico, Peter Erdős, and Moshe Lewenstein. Parameterized matching with mismatches. J. Discrete Algorithms, 5:135-140, 2007. URL: https://doi.org/10.1016/j.jda.2006.03.014.
  2. Brenda S. Baker. A theory of parameterized pattern matching: algorithms and applications. In S. Rao Kosaraju, David S. Johnson, and Alok Aggarwal, editors, Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, May 16-18, 1993, San Diego, CA, USA, pages 71-80. ACM, 1993. URL: https://doi.org/10.1145/167088.167115.
  3. R.S. Bird. Two dimensional pattern matching. Information Processing Letters, 6(5):168-170, 1977. URL: https://doi.org/10.1016/0020-0190(77)90017-5.
  4. Elbert Oran Brigham. The Fast Fourier Transform. Prentice-Hall, Englewood Cliffs, N.J., 1974. Google Scholar
  5. Maxime Crochemore, Christophe Hancart, and Thierry Lecroq. Algorithms on Strings. Cambridge University Press, 2007. Google Scholar
  6. Hossein Dehghani, Thierry Lecroq, Neerja Mhaskar, and William F. Smyth. Practical KMP/BM style pattern-matching on indeterminate strings. Discrete Applied Mathematics, 370:22-33, 2025. URL: https://doi.org/10.1016/J.DAM.2025.02.032.
  7. Simone Faro, Dominik Köppl, Thierry Lecroq, and Francesco Pio Marino. marfra99x/SCER-ISM. Software, (visited on 2026-05-27). URL: https://github.com/marfra99x/SCER-ISM
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.26165
  8. Simone Faro, Francesco Pio Marino, and Arianna Pavone. Efficient online string matching based on characters distance text sampling. Algorithmica, 82(11):3390-3412, 2020. URL: https://doi.org/10.1007/S00453-020-00732-4.
  9. Simone Faro, Francesco Pio Marino, and Arianna Pavone. Improved characters distance sampling for online and offline text searching. Theoretical Computer Science, 946:113684, 2023. URL: https://doi.org/10.1016/J.TCS.2022.12.034.
  10. Simone Faro, Francesco Pio Marino, Arianna Pavone, and Antonio Scardace. Towards an efficient text sampling approach for exact and approximate matching. In Jan Holub and Jan Zdárek, editors, Prague Stringology Conference 2021, Prague, Czech Republic, August 30-31, 2021, pages 75-89. Czech Technical University in Prague, Faculty of Information Technology, Department of Theoretical Computer Science, 2021. URL: http://www.stringology.org/event/2021/p07.html.
  11. Paweł Gawrychowski, Samah Ghazawi, and Gad M. Landau. On indeterminate strings matching. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020), volume 161 of Leibniz International Proceedings in Informatics (LIPIcs), pages 14:1-14:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.CPM.2020.14.
  12. Dan Gusfield. Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. Cambridge University Press, 1997. Google Scholar
  13. Rui Henriques, Alexandre P. Francisco, Luís M. S. Russo, and Hideo Bannai. Order-preserving pattern matching indeterminate strings. In Gonzalo Navarro, David Sankoff, and Binhai Zhu, editors, Annual Symposium on Combinatorial Pattern Matching, CPM 2018, July 2-4, 2018 - Qingdao, China, volume 105 of LIPIcs, pages 2:1-2:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.CPM.2018.2.
  14. John E. Hopcroft and Richard M. Karp. An n^5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 2(4):225-231, 1973. URL: https://doi.org/10.1137/0202019.
  15. Tomohiro I, Shunsuke Inenaga, and Masayuki Takeda. Palindrome pattern matching. Theoretical Computer Science, 483:162-170, 2013. URL: https://doi.org/10.1016/J.TCS.2012.01.047.
  16. Harold W. Kuhn. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1-2):83-97, 1955. URL: https://doi.org/10.1002/nav.3800020109.
  17. Gonzalo Navarro and Mathieu Raffinot. Flexible Pattern Matching in Strings: Practical On-Line Search Algorithms for Texts and Biological Sequences. Cambridge University Press, 2002. URL: https://doi.org/10.1017/CBO9781316135228.
  18. Petr Procházka and Jan Holub. On-line searching in IUPAC nucleotide sequences. In Elisabetta De Maria, Ana L. N. Fred, and Hugo Gamboa, editors, Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019) - Volume 3: BIOINFORMATICS, Prague, Czech Republic, February 22-24, 2019, pages 66-77. SciTePress, 2019. URL: https://doi.org/10.5220/0007382900660077.
  19. M. Sohel Rahman, Costas S. Iliopoulos, and Laurent Mouchard. Pattern matching in degenerate DNA/RNA sequences. In M. Kaykobad and Md. Saidur Rahman, editors, Workshop on Algorithms and Computation 2007 - Proceedings of First WALCOM, 12 February 2007, Dhaka, Bangladesh, pages 109-120. Bangladesh Academy of Sciences (BAS), 2007. Google Scholar
  20. Apurba Saha, Iftekhar Hakim Kaowsar, Mahdi Hasnat Siyam, and M. Sohel Rahman. Algorithms for parameterized string matching with mismatches. arXiv, 2024. URL: https://doi.org/10.48550/arXiv.2412.00222.
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