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Improved Circular Dictionary Matching

Author Nicola Cotumaccio

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LIPIcs.CPM.2025.18.pdf
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ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Circular pattern matching
  • dictionary matching
  • suffix tree
  • compressed suffix tree
  • suffix array
  • LCP array
  • Burrows-Wheeler Transform
  • FM-index

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Abstract

The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back to its first character. The circular dictionary matching problem is motivated by applications in bioinformatics and computational geometry.
In 2011, Hon et al. [ISAAC 2011] showed how to efficiently solve circular dictionary matching queries within compressed space by building on Mantaci et al.’s eBWT and Sadakane’s compressed suffix tree. The proposed solution is based on the assumption that the strings in the dictionary are all distinct and non-periodic, no string is a circular rotation of some other string, and the strings in the dictionary have similar lengths.
In this paper, we consider arbitrary dictionaries, and we show how to solve circular dictionary matching queries in O((m + occ) log n) time within compressed space using n log σ (1 + o(1)) + O(n) + O(d log n) bits, where n is the total length of the dictionary, m is the length of the pattern, occ is the number of occurrences, d is the number of strings in the dictionary and σ is the size of the alphabet. Our solution is based on an extension of the suffix array to arbitrary dictionaries and a sampling mechanism for the LCP array of a dictionary inspired by recent results in graph indexing and compression.

Cite As Get BibTex

Nicola Cotumaccio. Improved Circular Dictionary Matching. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.18

Author Details

Nicola Cotumaccio
  • University of Helsinki, Finland

Funding

Funded by the Helsinki Institute for Information Technology (HIIT).

Acknowledgements

I would like to thank Kunihiko Sadakane for introducing me to the topic.

References

  1. Alfred V. Aho and Margaret J. Corasick. Efficient string matching: an aid to bibliographic search. Commun. ACM, 18(6):333-340, June 1975. URL: https://doi.org/10.1145/360825.360855.
  2. Jarno Alanko, Nicola Cotumaccio, and Nicola Prezza. Linear-time minimization of Wheeler DFAs. In 2022 Data Compression Conference (DCC), pages 53-62. IEEE, 2022. URL: https://doi.org/10.1109/DCC52660.2022.00013.
  3. Jarno Alanko, Giovanna D'Agostino, Alberto Policriti, and Nicola Prezza. Regular languages meet prefix sorting. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 911-930. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.55.
  4. Jarno N Alanko, Davide Cenzato, Nicola Cotumaccio, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza. Computing the LCP array of a labeled graph. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. Google Scholar
  5. Amihood Amir, Tsvi Kopelowitz, Avivit Levy, Seth Pettie, Ely Porat, and B Riva Shalom. Mind the gap! Online dictionary matching with one gap. Algorithmica, 81:2123-2157, 2019. URL: https://doi.org/10.1007/S00453-018-0526-2.
  6. Amihood Amir, Avivit Levy, Ely Porat, and B Riva Shalom. Dictionary matching with a few gaps. Theoretical Computer Science, 589:34-46, 2015. URL: https://doi.org/10.1016/J.TCS.2015.04.011.
  7. Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piątkowski. Constructing the bijective and the extended Burrows-Wheeler transform in linear time. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  8. Djamal Belazzougui. Succinct dictionary matching with no slowdown. In Amihood Amir and Laxmi Parida, editors, Combinatorial Pattern Matching, pages 88-100, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-13509-5_9.
  9. Djamal Belazzougui, Fabio Cunial, Juha Kärkkäinen, and Veli Mäkinen. Linear-time string indexing and analysis in small space. ACM Transactions on Algorithms (TALG), 16(2):1-54, 2020. URL: https://doi.org/10.1145/3381417.
  10. Silvia Bonomo, Sabrina Mantaci, Antonio Restivo, Giovanna Rosone, and Marinella Sciortino. Sorting conjugates and suffixes of words in a multiset. International Journal of Foundations of Computer Science, 25(08):1161-1175, 2014. Google Scholar
  11. Christina Boucher, Davide Cenzato, Zsuzsanna Lipták, Massimiliano Rossi, and Marinella Sciortino. Computing the original eBWT faster, simpler, and with less memory. In Thierry Lecroq and Hélène Touzet, editors, String Processing and Information Retrieval, pages 129-142, Cham, 2021. Springer International Publishing. URL: https://doi.org/10.1007/978-3-030-86692-1_11.
  12. Michael Burrows and David J. Wheeler. A block-sorting lossless data compression algorithm. Technical report, Systems Research Center, 1994. Google Scholar
  13. Davide Cenzato, Veronica Guerrini, Zsuzsanna Lipták, and Giovanna Rosone. Computing the optimal BWT of very large string collections. In 2023 Data Compression Conference (DCC), pages 71-80, 2023. URL: https://doi.org/10.1109/DCC55655.2023.00015.
  14. Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. Internal dictionary matching. Algorithmica, 83(7):2142-2169, 2021. URL: https://doi.org/10.1007/S00453-021-00821-Y.
  15. Panagiotis Charalampopoulos, Tomasz Kociumaka, Jakub Radoszewski, Solon P Pissis, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Approximate circular pattern matching. In ESA 2022-30th Annual European Symposium on Algorithms, 2022. Google Scholar
  16. Raphaël Clifford, Allyx Fontaine, Ely Porat, Benjamin Sach, and Tatiana Starikovskaya. Dictionary matching in a stream. In Algorithms-ESA 2015: 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, pages 361-372. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-48350-3_31.
  17. Alessio Conte, Nicola Cotumaccio, Travis Gagie, Giovanni Manzini, Nicola Prezza, and Marinella Sciortino. Computing matching statistics on Wheeler DFAs. In 2023 Data Compression Conference (DCC), pages 150-159, 2023. URL: https://doi.org/10.1109/DCC55655.2023.00023.
  18. Nicola Cotumaccio. Graphs can be succinctly indexed for pattern matching in O(| E| ²+| V| ^5/2) time. In 2022 Data Compression Conference (DCC), pages 272-281, 2022. URL: https://doi.org/10.1109/DCC52660.2022.00035.
  19. Nicola Cotumaccio. Prefix sorting DFAs: A recursive algorithm. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Schloss-Dagstuhl-Leibniz Zentrum für Informatik, 2023. Google Scholar
  20. Nicola Cotumaccio. A Myhill-Nerode theorem for generalized automata, with applications to pattern matching and compression. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. Google Scholar
  21. Nicola Cotumaccio. Improved circular dictionary matching, 2025. URL: https://arxiv.org/abs/2504.03394.
  22. Nicola Cotumaccio, Giovanna D’Agostino, Alberto Policriti, and Nicola Prezza. Co-lexicographically ordering automata and regular languages - part I. J. ACM, 70(4), August 2023. URL: https://doi.org/10.1145/3607471.
  23. Nicola Cotumaccio, Travis Gagie, Dominik Köppl, and Nicola Prezza. Space-time trade-offs for the LCP array of Wheeler DFAs. In Franco Maria Nardini, Nadia Pisanti, and Rossano Venturini, editors, String Processing and Information Retrieval, pages 143-156, Cham, 2023. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-43980-3_12.
  24. Nicola Cotumaccio and Nicola Prezza. On indexing and compressing finite automata. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2585-2599. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.153.
  25. Nicola Cotumaccio and Catia Trubiani. Convex Petri nets. In Michael Köhler-Bussmeier, Daniel Moldt, and Heiko Rölke, editors, Proceedings of the International Workshop on Petri Nets and Software Engineering 2024 co-located with the 45th International Conference on Application and Theory of Petri Nets and Concurrency (PETRI NETS 2024), June 24 - 25, 2024, Geneva, Switzerland, volume 3730 of CEUR Workshop Proceedings. CEUR-WS.org, 2024. URL: https://ceur-ws.org/Vol-3730/poster1.pdf.
  26. Jonathan A Eisen. Environmental shotgun sequencing: its potential and challenges for studying the hidden world of microbes. PLoS biology, 5(3):e82, 2007. Google Scholar
  27. Paolo Ferragina and Giovanni Manzini. Indexing compressed text. J. ACM, 52(4):552-581, July 2005. URL: https://doi.org/10.1145/1082036.1082039.
  28. Johannes Fischer and Volker Heun. Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM Journal on Computing, 40(2):465-492, 2011. URL: https://doi.org/10.1137/090779759.
  29. Travis Gagie, Giovanni Manzini, and Jouni Sirén. Wheeler graphs: A framework for BWT-based data structures. Theoretical computer science, 698:67-78, 2017. URL: https://doi.org/10.1016/J.TCS.2017.06.016.
  30. Paweł Gawrychowski and Tatiana Starikovskaya. Streaming dictionary matching with mismatches. Algorithmica, pages 1-21, 2019. Google Scholar
  31. Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, and Ely Porat. Dynamic dictionary matching in the online model. In Algorithms and Data Structures: 16th International Symposium, WADS 2019, Edmonton, AB, Canada, August 5-7, 2019, Proceedings 16, pages 409-422. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-24766-9_30.
  32. Wing-Kai Hon, Tsung-Han Ku, Chen-Hua Lu, Rahul Shah, and Sharma V. Thankachan. Efficient algorithm for circular Burrows-Wheeler transform. In Juha Kärkkäinen and Jens Stoye, editors, Combinatorial Pattern Matching, pages 257-268, Berlin, Heidelberg, 2012. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-31265-6_21.
  33. Wing-Kai Hon, Tsung-Han Ku, Rahul Shah, and Sharma V. Thankachan. Space-efficient construction algorithm for the circular suffix tree. In Johannes Fischer and Peter Sanders, editors, Combinatorial Pattern Matching, pages 142-152, Berlin, Heidelberg, 2013. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-38905-4_15.
  34. Wing-Kai Hon, Tsung-Han Ku, Rahul Shah, Sharma V. Thankachan, and Jeffrey Scott Vitter. Faster compressed dictionary matching. Theoretical Computer Science, 475:113-119, 2013. URL: https://doi.org/10.1016/j.tcs.2012.10.050.
  35. Wing-Kai Hon, Tak-Wah Lam, Rahul Shah, Sharma V Thankachan, Hing-Fung Ting, and Yilin Yang. Dictionary matching with a bounded gap in pattern or in text. Algorithmica, 80:698-713, 2018. URL: https://doi.org/10.1007/S00453-017-0288-2.
  36. Wing-Kai Hon, Chen-Hua Lu, Rahul Shah, and Sharma V Thankachan. Succinct indexes for circular patterns. In Algorithms and Computation: 22nd International Symposium, ISAAC 2011, Yokohama, Japan, December 5-8, 2011. Proceedings 22, pages 673-682. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-25591-5_69.
  37. Costas S Iliopoulos, Solon P Pissis, and M Sohel Rahman. Searching and indexing circular patterns. Algorithms for Next-Generation Sequencing Data: Techniques, Approaches, and Applications, pages 77-90, 2017. URL: https://doi.org/10.1007/978-3-319-59826-0_3.
  38. Costas S. Iliopoulos and M. Sohel Rahman. Indexing circular patterns. In Shin-ichi Nakano and Md. Saidur Rahman, editors, WALCOM: Algorithms and Computation, pages 46-57, Berlin, Heidelberg, 2008. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-540-77891-2_5.
  39. M. Lothaire. Combinatorics on words, volume 17. Cambridge university press, 1997. Google Scholar
  40. Sabrina Mantaci, Antonio Restivo, Giovanna Rosone, and Marinella Sciortino. An extension of the Burrows-Wheeler transform. Theoretical Computer Science, 387(3):298-312, 2007. URL: https://doi.org/10.1016/J.TCS.2007.07.014.
  41. J Ian Munro, Gonzalo Navarro, and Yakov Nekrich. Space-efficient construction of compressed indexes in deterministic linear time. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 408-424. SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974782.26.
  42. Gonzalo Navarro. Compact Data Structures: A Practical Approach. Cambridge University Press, 2016. Google Scholar
  43. Ge Nong, Sen Zhang, and Wai Hong Chan. Two efficient algorithms for linear time suffix array construction. IEEE Transactions on Computers, 60(10):1471-1484, 2011. URL: https://doi.org/10.1109/TC.2010.188.
  44. Enno Ohlebusch, Simon Gog, and Adrian Kügel. Computing matching statistics and maximal exact matches on compressed full-text indexes. In Edgar Chavez and Stefano Lonardi, editors, String Processing and Information Retrieval, pages 347-358, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-16321-0_36.
  45. Kunihiko Sadakane. Compressed suffix trees with full functionality. Theor. Comp. Sys., 41(4):589-607, December 2007. URL: https://doi.org/10.1007/s00224-006-1198-x.
  46. Carola Simon and Rolf Daniel. Metagenomic analyses: past and future trends. Applied and environmental microbiology, 77(4):1153-1161, 2011. Google Scholar
  47. Blair L Strang and Nigel D Stow. Circularization of the herpes simplex virus type 1 genome upon lytic infection. Journal of virology, 79(19):12487-12494, 2005. Google Scholar
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