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Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc. (Invited Talk)

Author Sharma V. Thankachan



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Sharma V. Thankachan
  • Department of Computer Science, University of Central Florida, Orlando, FL, USA

Acknowledgements

I want to thank my collaborators Rahul Shah and Arnab Ganguly.

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Sharma V. Thankachan. Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc. (Invited Talk). In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 3:1-3:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.CPM.2022.3

Abstract

In the past two decades, we have witnessed the design of various compact data structures for pattern matching over an indexed text [Navarro, 2016]. Popular indexes like the FM-index [Paolo Ferragina and Giovanni Manzini, 2005], compressed suffix arrays/trees [Roberto Grossi and Jeffrey Scott Vitter, 2005; Kunihiko Sadakane, 2007], the recent r-index [Travis Gagie et al., 2020; Takaaki Nishimoto and Yasuo Tabei, 2021], etc., capture the key functionalities of classic suffix arrays/trees [Udi Manber and Eugene W. Myers, 1993; Peter Weiner, 1973] in compact space. Mostly, they rely on the Burrows-Wheeler Transform (BWT) and its associated operations [Burrows and Wheeler, 1994]. However, compactly encoding some advanced suffix tree (ST) variants, like parameterized ST [Brenda S. Baker, 1993; S. Rao Kosaraju, 1995; Juan Mendivelso et al., 2020], order-isomorphic/preserving ST [Maxime Crochemore et al., 2016], two-dimensional ST [Raffaele Giancarlo, 1995; Dong Kyue Kim et al., 1998], etc. [Sung Gwan Park et al., 2019; Tetsuo Shibuya, 2000]- collectively known as suffix trees with missing suffix links [Richard Cole and Ramesh Hariharan, 2003], has been challenging. The previous techniques are not easily extendable because these variants do not hold some structural properties of the standard ST that enable compression. However, some limited progress has been made in these directions recently [Arnab Ganguly et al., 2017; Travis Gagie et al., 2017; Gianni Decaroli et al., 2017; Dhrumil Patel and Rahul Shah, 2021; Arnab Ganguly et al., 2021; Sung{-}Hwan Kim and Hwan{-}Gue Cho, 2021; Sung{-}Hwan Kim and Hwan{-}Gue Cho, 2021; Arnab Ganguly et al., 2017; Arnab Ganguly et al., 2022; Arnab Ganguly et al., 2021]. This talk will briefly survey them and highlight some interesting open problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Text Indexing
  • Suffix Trees
  • String Matching

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References

  1. Brenda S. Baker. A theory of parameterized pattern matching: algorithms and applications. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, May 16-18, 1993, San Diego, CA, USA, pages 71-80, 1993. URL: https://doi.org/10.1145/167088.167115.
  2. Michael Burrows and David Wheeler. A block-sorting lossless data compression algorithm. In Digital SRC Research Report. Citeseer, 1994. Google Scholar
  3. Richard Cole and Ramesh Hariharan. Faster suffix tree construction with missing suffix links. SIAM J. Comput., 33(1):26-42, 2003. URL: https://doi.org/10.1137/S0097539701424465.
  4. Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Marcin Kubica, Alessio Langiu, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, and Tomasz Walen. Order-preserving indexing. Theor. Comput. Sci., 638:122-135, 2016. URL: https://doi.org/10.1016/j.tcs.2015.06.050.
  5. Gianni Decaroli, Travis Gagie, and Giovanni Manzini. A compact index for order-preserving pattern matching. In 2017 Data Compression Conference, DCC 2017, Snowbird, UT, USA, April 4-7, 2017, pages 72-81, 2017. URL: https://doi.org/10.1109/DCC.2017.35.
  6. Paolo Ferragina and Giovanni Manzini. Indexing compressed text. J. ACM, 52(4):552-581, 2005. URL: https://doi.org/10.1145/1082036.1082039.
  7. Travis Gagie, Giovanni Manzini, and Rossano Venturini. An encoding for order-preserving matching. In 25th Annual European Symposium on Algorithms, ESA 2017, September 4-6, 2017, Vienna, Austria, pages 38:1-38:15, 2017. URL: https://doi.org/10.4230/LIPIcs.ESA.2017.38.
  8. Travis Gagie, Gonzalo Navarro, and Nicola Prezza. Fully functional suffix trees and optimal text searching in bwt-runs bounded space. J. ACM, 67(1):2:1-2:54, 2020. URL: https://doi.org/10.1145/3375890.
  9. Arnab Ganguly, Wing-Kai Hon, Kunihiko Sadakane, Rahul Shah, Sharma V. Thankachan, and Yilin Yang. A framework for designing space-efficient dictionaries for parameterized and order-preserving matching. Theor. Comput. Sci., 854:52-62, 2021. URL: https://doi.org/10.1016/j.tcs.2020.11.036.
  10. Arnab Ganguly, Dhrumil Patel, Rahul Shah, and Sharma V. Thankachan. LF successor: Compact space indexing for order-isomorphic pattern matching. In 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12-16, 2021, Glasgow, Scotland (Virtual Conference), volume 198 of LIPIcs, pages 71:1-71:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.71.
  11. 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 2017, Barcelona, Spain, January 16-19, pages 397-407, 2017. URL: https://doi.org/10.1137/1.9781611974782.25.
  12. Arnab Ganguly, Rahul Shah, and Sharma V. Thankachan. Structural pattern matching - succinctly. In Yoshio Okamoto and Takeshi Tokuyama, editors, 28th International Symposium on Algorithms and Computation, ISAAC 2017, December 9-12, 2017, Phuket, Thailand, volume 92 of LIPIcs, pages 35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2017.35.
  13. Arnab Ganguly, Rahul Shah, and Sharma V. Thankachan. Fully functional parameterized suffix trees in compact space. In 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, July 4-8, 2022, Paris, France, LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  14. Raffaele Giancarlo. A generalization of the suffix tree to square matrices, with applications. SIAM J. Comput., 24(3):520-562, 1995. URL: https://doi.org/10.1137/S0097539792231982.
  15. Roberto Grossi and Jeffrey Scott Vitter. Compressed suffix arrays and suffix trees with applications to text indexing and string matching. SIAM J. Comput., 35(2):378-407, 2005. URL: https://doi.org/10.1137/S0097539702402354.
  16. Dong Kyue Kim, Yoo Ah Kim, and Kunsoo Park. Constructing suffix arrays for multi-dimensional matrices. In Martin Farach-Colton, editor, Combinatorial Pattern Matching, 9th Annual Symposium, CPM 98, Piscataway, New Jersey, USA, July 20-22, 1998, Proceedings, volume 1448 of Lecture Notes in Computer Science, pages 126-139. Springer, 1998. URL: https://doi.org/10.1007/BFb0030786.
  17. Sung-Hwan Kim and Hwan-Gue Cho. A compact index for cartesian tree matching. In Pawel Gawrychowski and Tatiana Starikovskaya, editors, 32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021, July 5-7, 2021, Wrocław, Poland, volume 191 of LIPIcs, pages 18:1-18:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.CPM.2021.18.
  18. Sung-Hwan Kim and Hwan-Gue Cho. Simpler fm-index for parameterized string matching. Inf. Process. Lett., 165:106026, 2021. URL: https://doi.org/10.1016/j.ipl.2020.106026.
  19. S. Rao Kosaraju. Faster algorithms for the construction of parameterized suffix trees (preliminary version). In 36th Annual Symposium on Foundations of Computer Science, Milwaukee, Wisconsin, 23-25 October 1995, pages 631-637, 1995. URL: https://doi.org/10.1109/SFCS.1995.492664.
  20. Udi Manber and Eugene W. Myers. Suffix arrays: A new method for on-line string searches. SIAM J. Comput., 22(5):935-948, 1993. URL: https://doi.org/10.1137/0222058.
  21. Juan Mendivelso, Sharma V. Thankachan, and Yoan J. Pinzón. A brief history of parameterized matching problems. Discret. Appl. Math., 274:103-115, 2020. URL: https://doi.org/10.1016/j.dam.2018.07.017.
  22. Gonzalo Navarro. Compact data structures: A practical approach. Cambridge University Press, 2016. Google Scholar
  23. Takaaki Nishimoto and Yasuo Tabei. Optimal-time queries on bwt-runs compressed indexes. In Nikhil Bansal, Emanuela Merelli, and James Worrell, editors, 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12-16, 2021, Glasgow, Scotland (Virtual Conference), volume 198 of LIPIcs, pages 101:1-101:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.101.
  24. Sung Gwan Park, Amihood Amir, Gad M. Landau, and Kunsoo Park. Cartesian tree matching and indexing. In Nadia Pisanti and Solon P. Pissis, editors, 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019, June 18-20, 2019, Pisa, Italy, volume 128 of LIPIcs, pages 16:1-16:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.CPM.2019.16.
  25. Dhrumil Patel and Rahul Shah. Inverse suffix array queries for 2-dimensional pattern matching in near-compact space. In Hee-Kap Ahn and Kunihiko Sadakane, editors, 32nd International Symposium on Algorithms and Computation, ISAAC 2021, December 6-8, 2021, Fukuoka, Japan, volume 212 of LIPIcs, pages 60:1-60:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2021.60.
  26. Kunihiko Sadakane. Compressed suffix trees with full functionality. Theory Comput. Syst., 41(4):589-607, 2007. URL: https://doi.org/10.1007/s00224-006-1198-x.
  27. Tetsuo Shibuya. Generalization of a suffix tree for RNA structural pattern matching. In Algorithm Theory - SWAT 2000, 7th Scandinavian Workshop on Algorithm Theory, Bergen, Norway, July 5-7, 2000, Proceedings, pages 393-406, 2000. URL: https://doi.org/10.1007/3-540-44985-X_34.
  28. Peter Weiner. Linear pattern matching algorithms. In 14th Annual Symposium on Switching and Automata Theory, Iowa City, Iowa, USA, October 15-17, 1973, pages 1-11, 1973. URL: https://doi.org/10.1109/SWAT.1973.13.
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