Document Open Access Logo

Compressed Dictionary Matching on Run-Length Encoded Strings

Authors Philip Bille , Inge Li Gørtz , Simon J. Puglisi , Simon R. Tarnow

PDF

File

Thumbnail PDF
PDF
LIPIcs.CPM.2025.21.pdf
  • Filesize: 0.73 MB
  • 16 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Dictionary matching
  • run-length encoding
  • compressed pattern matching

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Given a set of pattern strings 𝒫 = {P₁, P₂,… P_k} and a text string S, the classic dictionary matching problem is to report all occurrences of each pattern in S. We study the dictionary problem in the compressed setting, where the pattern strings and the text string are compressed using run-length encoding, and the goal is to solve the problem without decompression and achieve efficient time and space in the size of the compressed strings. Let m and n be the total length of the patterns 𝒫 and the length of the text string S, respectively, and let  ̅m and  ̅n be the total number of runs in the run-length encoding of the patterns in 𝒫 and S, respectively. Our main result is an algorithm that achieves O(( ̅m +  ̅n)log log m + occ) expected time, and O( ̅m) space, where occ is the total number of occurrences of patterns in S. This is the first non-trivial solution to the problem. Since any solution must read the input, our time bound is optimal within an log log m factor. We introduce several new techniques to achieve our bounds, including a new compressed representation of the classic Aho-Corasick automaton and a new efficient string index that supports fast queries in run-length encoded strings.

Cite As Get BibTex

Philip Bille, Inge Li Gørtz, Simon J. Puglisi, and Simon R. Tarnow. Compressed Dictionary Matching on Run-Length Encoded Strings. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.21

Author Details

Philip Bille
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark
Inge Li Gørtz
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark
Simon J. Puglisi
  • Helsinki Institute for Information Technology (HIIT), Finland
  • Department of Computer Science, University of Helsinki, Finland
Simon R. Tarnow
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark

Funding

  • Bille, Philip: Danish Research Council grant DFF-8021-002498.
  • Gørtz, Inge Li: Danish Research Council grant DFF-8021-002498.

References

  1. Alfred V. Aho and Margaret J. Corasick. Efficient string matching: An aid to bibliographic search. Commun. ACM, 18(6):333-340, 1975. URL: https://doi.org/10.1145/360825.360855.
  2. Stephen Alstrup and Jacob Holm. Improved algorithms for finding level ancestors in dynamic trees. In Proc. 27th ICALP, pages 73-84, 2000. URL: https://doi.org/10.1007/3-540-45022-X_8.
  3. Stephen Alstrup, Thore Husfeldt, and Theis Rauhe. Marked ancestor problems. In Proc. 39th FOCS, pages 534-544, 1998. URL: https://doi.org/10.1109/SFCS.1998.743504.
  4. Amihood Amir and Gary Benson. Efficient two-dimensional compressed matching. In Proc. 2nd DCC, pages 279-288, 1992. URL: https://doi.org/10.1109/DCC.1992.227453.
  5. Amihood Amir, Gary Benson, and Martin Farach. Optimal two-dimensional compressed matching. J. Algorithms, 24(2):354-379, 1997. URL: https://doi.org/10.1006/JAGM.1997.0860.
  6. Amihood Amir and Martin Farach. Adaptive dictionary matching. In Proc. 32nd FOCS, pages 760-766, 1991. URL: https://doi.org/10.1109/SFCS.1991.185445.
  7. Amihood Amir, Martin Farach, Zvi Galil, Raffaele Giancarlo, and Kunsoo Park. Dynamic dictionary matching. J. Comput. Syst. Sci., 49(2):208-222, 1994. URL: https://doi.org/10.1016/S0022-0000(05)80047-9.
  8. Amihood Amir, Martin Farach, Ramana M. Idury, Johannes A. La Poutré, and Alejandro A. Schäffer. Improved dynamic dictionary matching. Inf. Comput., 119(2):258-282, 1995. URL: https://doi.org/10.1006/INCO.1995.1090.
  9. 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(6):2123-2157, 2019. URL: https://doi.org/10.1007/S00453-018-0526-2.
  10. Amihood Amir, Gad M. Landau, and Dina Sokol. Inplace run-length 2d compressed search. Theor. Comput. Sci., 290(3):1361-1383, 2003. URL: https://doi.org/10.1016/S0304-3975(02)00041-5.
  11. Amihood Amir, Avivit Levy, Ely Porat, and B. Riva Shalom. Dictionary matching with one gap. In Proc. 25th CPM, pages 11-20, 2014. URL: https://doi.org/10.1007/978-3-319-07566-2_2.
  12. Amihood Amir, Avivit Levy, Ely Porat, and B. Riva Shalom. Dictionary matching with a few gaps. Theor. Comput. Sci., 589:34-46, 2015. URL: https://doi.org/10.1016/J.TCS.2015.04.011.
  13. Amihood Amir, Moshe Lewenstein, and Ely Porat. Faster algorithms for string matching with k mismatches. J. Algorithms, 50(2):257-275, 2004. URL: https://doi.org/10.1016/S0196-6774(03)00097-X.
  14. Arne Andersson and Stefan Nilsson. A new efficient radix sort. In Proc. 35th FOCS, pages 714-721, 1994. URL: https://doi.org/10.1109/SFCS.1994.365721.
  15. Alberto Apostolico, Gad M. Landau, and Steven Skiena. Matching for run-length encoded strings. J. Complex., 15(1):4-16, 1999. URL: https://doi.org/10.1006/JCOM.1998.0493.
  16. Tanver Athar, Carl Barton, Widmer Bland, Jia Gao, Costas S. Iliopoulos, Chang Liu, and Solon P. Pissis. Fast circular dictionary-matching algorithm. Math. Struct. Comput. Sci., 27(2):143-156, 2017. URL: https://doi.org/10.1017/S0960129515000134.
  17. Arturs Backurs and Piotr Indyk. Which regular expression patterns are hard to match? In Proc. 57th FOCS, pages 457-466, 2016. URL: https://doi.org/10.1109/FOCS.2016.56.
  18. Djamal Belazzougui. Succinct dictionary matching with no slowdown. In Proc. 21st CPM, pages 88-100, 2010. URL: https://doi.org/10.1007/978-3-642-13509-5_9.
  19. Djamal Belazzougui. Worst-case efficient single and multiple string matching on packed texts in the word-ram model. J. Discrete Algorithms, 14:91-106, 2012. URL: https://doi.org/10.1016/J.JDA.2011.12.011.
  20. Omer Berkman and Uzi Vishkin. Finding level-ancestors in trees. J. Comput. Syst. Sci., 48(2):214-230, 1994. URL: https://doi.org/10.1016/S0022-0000(05)80002-9.
  21. Philip Bille, Inge Li Gørtz, Hjalte Wedel Vildhøj, and David Kofoed Wind. String matching with variable length gaps. Theoret. Comput. Sci., 443:25-34, 2012. URL: https://doi.org/10.1016/J.TCS.2012.03.029.
  22. Philip Bille and Mikkel Thorup. Regular expression matching with multi-strings and intervals. In Proc. 21st SODA, 2010. Google Scholar
  23. William I. Chang and Eugene L. Lawler. Sublinear approximate string matching and biological applications. Algorithmica, 12(4):327-344, 1994. URL: https://doi.org/10.1007/BF01185431.
  24. Bernard Chazelle. Computing on a free tree via complexity-preserving mappings. Algorithmica, 2:337-361, 1987. URL: https://doi.org/10.1007/BF01840366.
  25. Raphaël Clifford, Allyx Fontaine, Ely Porat, Benjamin Sach, and Tatiana Starikovskaya. Dictionary matching in a stream. In Proc. 23rd ESA, pages 361-372, 2015. URL: https://doi.org/10.1007/978-3-662-48350-3_31.
  26. Richard Cole, Lee-Ad Gottlieb, and Moshe Lewenstein. Dictionary matching and indexing with errors and don't cares. In Proc. 36th STOC, pages 91-100, 2004. URL: https://doi.org/10.1145/1007352.1007374.
  27. Beate Commentz-Walter. A string matching algorithm fast on the average. In Hermann A. Maurer, editor, Proc. 6th ICALP, volume 71, pages 118-132, 1979. URL: https://doi.org/10.1007/3-540-09510-1_10.
  28. Paul F. Dietz. Fully persistent arrays (extended array). In Proc. 1st WADS, pages 67-74, 1989. URL: https://doi.org/10.1007/3-540-51542-9_8.
  29. Paul F. Dietz. Finding level-ancestors in dynamic trees. In Proc. 2nd WADS, pages 32-40, 1991. URL: https://doi.org/10.1007/BFB0028247.
  30. Mohamed Y. Eltabakh, Wing-Kai Hon, Rahul Shah, Walid G. Aref, and Jeffrey Scott Vitter. The sbc-tree: an index for run-length compressed sequences. In Proc. 11th EDBT, pages 523-534, 2008. URL: https://doi.org/10.1145/1353343.1353407.
  31. Paolo Ferragina and Fabrizio Luccio. Dynamic dictionary matching in external memory. Inf. Comput., 146(2):85-99, 1998. URL: https://doi.org/10.1006/INCO.1998.2733.
  32. Paolo Ferragina and S. Muthukrishnan. Efficient dynamic method-lookup for object oriented languages (extended abstract). In Proc. 4th ESA, pages 107-120, 1996. URL: https://doi.org/10.1007/3-540-61680-2_50.
  33. Johannes Fischer, Travis Gagie, Pawel Gawrychowski, and Tomasz Kociumaka. Approximating LZ77 via small-space multiple-pattern matching. In Proc. 23rd ESA, pages 533-544, 2015. URL: https://doi.org/10.1007/978-3-662-48350-3_45.
  34. Johannes Fischer, Travis Gagie, Paweł Gawrychowski, and Tomasz Kociumaka. Approximating lz77 via small-space multiple-pattern matching. In Proc. 23rd ESA, pages 533-544, 2015. Google Scholar
  35. Michael L. Fredman, János Komlós, and Endre Szemerédi. Storing a sparse table with O(1) worst case access time. In Proc. 23rd FOCS, pages 165-169, 1982. URL: https://doi.org/10.1109/SFCS.1982.39.
  36. Arnab Ganguly, Wing-Kai Hon, and Rahul Shah. A framework for dynamic parameterized dictionary matching. In Proc. 15th SWAT, pages 10:1-10:14, 2016. URL: https://doi.org/10.4230/LIPICS.SWAT.2016.10.
  37. Shay Golan and Ely Porat. Real-time streaming multi-pattern search for constant alphabet. In Proc. 25th ESA, pages 41:1-41:15, 2017. URL: https://doi.org/10.4230/LIPICS.ESA.2017.41.
  38. Yijie Han. Deterministic sorting in o(nloglogn) time and linear space. J. Algorithms, 50(1):96-105, 2004. URL: https://doi.org/10.1016/J.JALGOR.2003.09.001.
  39. Wing-Kai Hon, Tsung-Han Ku, Rahul Shah, Sharma V. Thankachan, and Jeffrey Scott Vitter. Faster compressed dictionary matching. Theor. Comput. Sci., 475:113-119, 2013. URL: https://doi.org/10.1016/J.TCS.2012.10.050.
  40. Tomohiro I, Takaaki Nishimoto, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Compressed automata for dictionary matching. Theor. Comput. Sci., 578:30-41, 2015. URL: https://doi.org/10.1016/J.TCS.2015.01.019.
  41. Takuya Kida, Masayuki Takeda, Ayumi Shinohara, Masamichi Miyazaki, and Setsuo Arikawa. Multiple pattern matching in LZW compressed text. In Proceedings of the 8th Data Compression Conference, pages 103-112, 1998. URL: https://doi.org/10.1109/DCC.1998.672136.
  42. Donald E. Knuth, James H. Morris Jr., and Vaughan R. Pratt. Fast pattern matching in strings. SIAM J. Comput., 6(2):323-350, 1977. URL: https://doi.org/10.1137/0206024.
  43. Tsvi Kopelowitz, Ely Porat, and Yaron Rozen. Succinct online dictionary matching with improved worst-case guarantees. In Proc. 27th CPM, pages 6:1-6:13, 2016. URL: https://doi.org/10.4230/LIPICS.CPM.2016.6.
  44. S. Muthukrishnan and Martin Müller. Time and space efficient method-lookup for object-oriented programs (extended abstract). In Proc. 7th SODA, pages 42-51, 1996. URL: http://dl.acm.org/citation.cfm?id=313852.313882.
  45. Gonzalo Navarro. A guided tour to approximate string matching. ACM Comput. Surv., 33(1):31-88, 2001. URL: https://doi.org/10.1145/375360.375365.
  46. Yoshifumi Sakai. Computing the longest common subsequence of two run-length encoded strings. In Proc. 23rd ISAAC, pages 197-206, 2012. URL: https://doi.org/10.1007/978-3-642-35261-4_23.
  47. Dan E. Willard. Log-logarithmic worst-case range queries are possible in space theta(n). Inf. Process. Lett., 17(2):81-84, 1983. URL: https://doi.org/10.1016/0020-0190(83)90075-3.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact