Document Open Access Logo

Quasi-Linear-Time Algorithm for Longest Common Circular Factor

Authors Mai Alzamel , Maxime Crochemore , Costas S. Iliopoulos , Tomasz Kociumaka , Jakub Radoszewski , Wojciech Rytter , Juliusz Straszyński , Tomasz Waleń , Wiktor Zuba

PDF
Thumbnail PDF

File

LIPIcs.CPM.2019.25.pdf
  • Filesize: 0.6 MB
  • 14 pages

Document Identifiers

Author Details

Mai Alzamel
  • Department of Informatics, King’s College London, UK
  • Department of Computer Science, King Saud University, Riyadh, Saudi Arabia
Maxime Crochemore
  • Department of Informatics, King’s College London, UK
  • Laboratoire d\'Informatique Gaspard-Monge, Université Paris-Est, Marne-la-Vallée, France
Costas S. Iliopoulos
  • Department of Informatics, King’s College London, UK
Tomasz Kociumaka
  • Institute of Informatics, University of Warsaw, Poland
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel
Jakub Radoszewski
  • Institute of Informatics, University of Warsaw, Poland
Wojciech Rytter
  • Institute of Informatics, University of Warsaw, Poland
Juliusz Straszyński
  • Institute of Informatics, University of Warsaw, Poland
Tomasz Waleń
  • Institute of Informatics, University of Warsaw, Poland
Wiktor Zuba
  • Institute of Informatics, University of Warsaw, Poland

Funding

  • Kociumaka, Tomasz: Supported by ISF grants no. 824/17 and 1278/16 and by an ERC grant MPM under the EU's Horizon 2020 Research and Innovation Programme (grant no. 683064).
  • Radoszewski, Jakub: Supported by the “Algorithms for text processing with errors and uncertainties” project carried out within the HOMING programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.
  • Straszyński, Juliusz: Supported by the “Algorithms for text processing with errors and uncertainties” project carried out within the HOMING programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.
  • Waleń, Tomasz: https://www.mimuw.edu.pl/~walen

Cite AsGet BibTex

Mai Alzamel, Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, and Wiktor Zuba. Quasi-Linear-Time Algorithm for Longest Common Circular Factor. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.CPM.2019.25

Abstract

We introduce the Longest Common Circular Factor (LCCF) problem in which, given strings S and T of length at most n, we are to compute the longest factor of S whose cyclic shift occurs as a factor of T. It is a new similarity measure, an extension of the classic Longest Common Factor. We show how to solve the LCCF problem in O(n log^4 n) time using O(n log^2 n) space.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • longest common factor
  • circular pattern matching
  • internal pattern matching
  • intersection of hyperrectangles

Metrics

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

Related Versions

References

  1. Amihood Amir, Gad M. Landau, Moshe Lewenstein, and Dina Sokol. Dynamic text and static pattern matching. ACM Transactions on Algorithms, 3(2):19, 2007. URL: http://dx.doi.org/10.1145/1240233.1240242.
  2. Alberto Apostolico, Maxime Crochemore, Martin Farach-Colton, Zvi Galil, and S. Muthukrishnan. 40 years of suffix trees. Communications of the ACM, 59(4):66-73, 2016. URL: http://dx.doi.org/10.1145/2810036.
  3. Tanver Athar, Carl Barton, Widmer Bland, Jia Gao, Costas S. Iliopoulos, Chang Liu, and Solon P. Pissis. Fast circular dictionary-matching algorithm. Mathematical Structures in Computer Science, 27(2):143-156, 2017. URL: http://dx.doi.org/10.1017/S0960129515000134.
  4. Md. Aashikur Rahman Azim, Costas S. Iliopoulos, Mohammad Sohel Rahman, and M. Samiruzzaman. A fast and lightweight filter-based algorithm for circular pattern matching. In Pierre Baldi and Wei Wang, editors, 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics, BCB 2014, pages 621-622. ACM, 2014. URL: http://dx.doi.org/10.1145/2649387.2660804.
  5. Hideo Bannai, Tomohiro I, Shunsuke Inenaga, Yuto Nakashima, Masayuki Takeda, and Kazuya Tsuruta. The "Runs" Theorem. SIAM Journal on Computing, 46(5):1501-1514, 2017. URL: http://dx.doi.org/10.1137/15M1011032.
  6. Carl Barton, Costas S. Iliopoulos, and Solon P. Pissis. Fast algorithms for approximate circular string matching. Algorithms for Molecular Biology, 9:9, 2014. URL: http://dx.doi.org/10.1186/1748-7188-9-9.
  7. Carl Barton, Costas S. Iliopoulos, and Solon P. Pissis. Average-Case Optimal Approximate Circular String Matching. In Adrian-Horia Dediu, Enrico Formenti, Carlos Martín-Vide, and Bianca Truthe, editors, Language and Automata Theory and Applications, LATA 2015, volume 8977 of LNCS, pages 85-96. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-319-15579-1_6.
  8. Or Birenzwige, Shay Golan, and Ely Porat. Locally Consistent Parsing for Text Indexing in Small Space. ArXiv preprint, 2018. URL: http://arxiv.org/abs/1812.00359.
  9. Domenico Cantone, Simone Faro, and Arianna Pavone. Sequence Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations. ArXiv preprint, 2018. URL: http://arxiv.org/abs/1812.00421.
  10. Kuei-Hao Chen, Guan-Shieng Huang, and Richard Chia-Tung Lee. Bit-Parallel Algorithms for Exact Circular String Matching. The Computer Journal, 57(5):731-743, 2014. URL: http://dx.doi.org/10.1093/comjnl/bxt023.
  11. Da-Jung Cho, Yo-Sub Han, and Hwee Kim. Alignment with non-overlapping inversions and translocations on two strings. Theoretical Computer Science, 575:90-101, 2015. URL: http://dx.doi.org/10.1016/j.tcs.2014.10.036.
  12. Maxime Crochemore, Christophe Hancart, and Thierry Lecroq. Algorithms on strings. Cambridge University Press, 2007. URL: http://dx.doi.org/10.1017/cbo9780511546853.
  13. Maxime Crochemore, Costas S. Iliopoulos, Marcin Kubica, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. Extracting powers and periods in a word from its runs structure. Theoretical Computer Science, 521:29-41, 2014. URL: http://dx.doi.org/10.1016/j.tcs.2013.11.018.
  14. Herbert Edelsbrunner. A new approach to rectangle intersections, Part I. International Journal of Computer Mathematics, 13(3-4):209-219, 1983. URL: http://dx.doi.org/10.1080/00207168308803364.
  15. Martin Farach-Colton, Paolo Ferragina, and S. Muthukrishnan. On the sorting-complexity of suffix tree construction. Journal of the ACM, 47(6):987-1011, 2000. URL: http://dx.doi.org/10.1145/355541.355547.
  16. Nathan J. Fine and Herbert S. Wilf. Uniqueness Theorems for Periodic Functions. Proceedings of the American Mathematical Society, 16:109-114, 1965. URL: http://dx.doi.org/10.1090/S0002-9939-1965-0174934-9.
  17. Kimmo Fredriksson and Szymon Grabowski. Average-optimal string matching. Journal of Discrete Algorithms, 7(4):579-594, 2009. URL: http://dx.doi.org/10.1016/j.jda.2008.09.001.
  18. Kimmo Fredriksson and Gonzalo Navarro. Average-optimal single and multiple approximate string matching. ACM Journal of Experimental Algorithmics, 9:1.4:1-1.4:47, 2004. URL: http://dx.doi.org/10.1145/1005813.1041513.
  19. Szymon Grabowski, Tomasz Kociumaka, and Jakub Radoszewski. On Abelian Longest Common Factor with and without RLE. Fundamenta Informaticae, 163(3):225-244, 2018. URL: http://dx.doi.org/10.3233/FI-2018-1740.
  20. Tommi Hirvola and Jorma Tarhio. Bit-Parallel Approximate Matching of Circular Strings with k Mismatches. ACM Journal of Experimental Algorithmics, 22:1.5:1-1.5:22, 2017. URL: http://dx.doi.org/10.1145/3129536.
  21. Costas S. Iliopoulos, Solon P. Pissis, and M. Sohel Rahman. Searching and Indexing Circular Patterns. In Mourad Elloumi, editor, Algorithms for Next-Generation Sequencing Data, Techniques, Approaches, and Applications, pages 77-90. Springer, 2017. URL: http://dx.doi.org/10.1007/978-3-319-59826-0_3.
  22. Costas S. Iliopoulos and M. Sohel Rahman. Indexing Circular Patterns. In Shin-Ichi Nakano and Md. Saidur Rahman, editors, Algorithms and Computation, WALCOM 2008, volume 4921 of LNCS, pages 46-57. Springer, 2008. URL: http://dx.doi.org/10.1007/978-3-540-77891-2_5.
  23. Dominik Kempa and Tomasz Kociumaka. String synchronizing sets: Sublinear-time BWT construction and optimal LCE data structure. In Edith Cohen, editor, 51st Annual ACM Symposium on Theory of Computing, STOC 2019. ACM, 2019. URL: http://dx.doi.org/10.1145/3313276.3316368.
  24. Tomasz Kociumaka. Efficient Data Structures for Internal Queries in Texts. PhD thesis, University of Warsaw, October 2018. URL: https://www.mimuw.edu.pl/~kociumaka/files/phd.pdf.
  25. Tomasz Kociumaka, Marcin Kubica, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. A Linear Time Algorithm for Seeds Computation. ArXiv preprint, 2019. URL: http://arxiv.org/abs/1107.2422v2.
  26. Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. Efficient Data Structures for the Factor Periodicity Problem. In Liliana Calderón-Benavides, Cristina N. González-Caro, Edgar Chávez, and Nivio Ziviani, editors, String Processing and Information Retrieval, SPIRE 2012, volume 7608 of LNCS, pages 284-294. Springer, 2012. URL: http://dx.doi.org/10.1007/978-3-642-34109-0_30.
  27. Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. Internal Pattern Matching Queries in a Text and Applications. In Piotr Indyk, editor, 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, pages 532-551. SIAM, 2015. URL: http://dx.doi.org/10.1137/1.9781611973730.36.
  28. Jie Lin and Donald A. Adjeroh. All-Against-All Circular Pattern Matching. The Computer Journal, 55(7):897-906, 2012. URL: http://dx.doi.org/10.1093/comjnl/bxr126.
  29. Jie Lin, Yue Jiang, and Don Adjeroh. Circular Pattern Discovery. The Computer Journal, 58(5):1061-1073, 2015. URL: http://dx.doi.org/10.1093/comjnl/bxu009.
  30. Udi Manber and Eugene W. Myers. Suffix Arrays: A New Method for On-Line String Searches. SIAM Journal on Computing, 22(5):935-948, 1993. URL: http://dx.doi.org/10.1137/0222058.
  31. Hideaki Ogiwara, Takashi Kohno, Hirofumi Nakanishi, Kazuhiro Nagayama, Masanori Sato, and Jun Yokota. Unbalanced translocation, a major chromosome alteration causing loss of heterozygosity in human lung cancer. Oncogene, 27(35):4788-4797, 2008. URL: http://dx.doi.org/10.1038/onc.2008.113.
  32. Robert Susik, Szymon Grabowski, and Sebastian Deorowicz. Fast and Simple Circular Pattern Matching. In Aleksandra Gruca, Tadeusz Czachórski, and Stanisław Kozielski, editors, Man-Machine Interactions, ICMMI 2013, volume 242 of Advances in Intelligent Systems and Computing, pages 537-544. Springer, 2013. URL: http://dx.doi.org/10.1007/978-3-319-02309-0_59.
  33. Dorothy Warburton. De novo balanced chromosome rearrangements and extra marker chromosomes identified at prenatal diagnosis: clinical significance and distribution of breakpoints. The American Journal of Human Genetics, 49(5):995-1013, 1991. URL: http://www.ncbi.nlm.nih.gov/pubmed/1928105.
  34. Brooke Weckselblatt, Karen E. Hermetz, and M. Katharine Rudd. Unbalanced translocations arise from diverse mutational mechanisms including chromothripsis. Genome Research, 25(7):937-947, 2015. URL: http://dx.doi.org/10.1101/gr.191247.115.
  35. Peter Weiner. Linear Pattern Matching Algorithms. In 14th Annual Symposium on Switching and Automata Theory, SWAT 1973, pages 1-11, Washington, DC, USA, 1973. IEEE Computer Society. URL: http://dx.doi.org/10.1109/SWAT.1973.13.
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
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact