Document Open Access Logo

Exploring the Gap Between LCS and LCStr

Authors Shay Golan , Matan Kraus , Ely Porat , B. Riva Shalom

PDF

File

Thumbnail PDF
PDF
LIPIcs.CPM.2026.27.pdf
  • Filesize: 1.29 MB
  • 21 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Longest Common Subsequence
  • Longest Common Substring
  • Conditional Lower Bound

Metrics

Abstract

The Longest Common Subsequence (LCS) problem and the Longest Common Substring (LCStr) problem are classical string problems with broad theoretical and practical significance. The former has a quadratic conditional lower bound [FOCS, 2015], while the latter admits a linear-time solution.
In this paper, we study a natural variation of these problems, the Longest Common Subsequence-Substring (LCSS) problem. The LCSS problem seeks the longest string that is simultaneously a subsequence of one input string and a substring of the other. This variant bridges LCS and LCStr, raising intriguing algorithmic questions: Does the complexity of computing LCSS interpolate between the linear time of LCStr and the quadratic time of LCS? What about approximability? We also examine a natural extension of LCSS to multiple strings, parameterizing the balance between subsequence and substring requirements.
Our results reveal several insights. First, under the SETH conjecture, the inherent complexity of LCSS is quadratic, similar to LCS. In contrast, we provide a linear-time approximation for LCSS. Finally, for the multi-string variant, unlike both problems, we design a quadratic-time algorithm, uncovering deeper structural properties of the problem.
By studying the complexity of the LCSS problem, we aim to gain some understanding of what influences whether a variant of the LCS problem behaves more like the standard LCS or like LCStr. Our findings suggest that hybrid constraints can create computational "sweet spots," where problems become more tractable than their pure counterparts. This opens a broader research direction in constraint-mediated algorithm design.
Beyond LCSS itself, our work highlights unexpected connections between subsequence and substring constraints, advancing the theoretical understanding of string problems and laying the foundation for new algorithmic techniques and complexity-theoretic insights in the rich space between classical string comparison paradigms.

Cite As Get BibTex

Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom. Exploring the Gap Between LCS and LCStr. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CPM.2026.27

Author Details

Shay Golan
  • Ariel University, Israel
Matan Kraus
  • Bar-Ilan University, Ramat Gan, Israel
Ely Porat
  • Bar-Ilan University, Ramat Gan, Israel
B. Riva Shalom
  • Shenkar College, Ramat Gan, Israel

Funding

  • Golan, Shay: partially supported by Israel Science Foundation grant 810/21.
  • Kraus, Matan: supported by the ISF grant no. 1926/19, by the BSF grant 2018364, and by the ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).
  • Porat, Ely: supported by the ISF grant no. 1926/19, by the BSF grant 2018364, and by the ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).

References

  1. Amir Abboud, Arturs Backurs, and Virginia Vassilevska Williams. Tight hardness results for LCS and other sequence similarity measures. In 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, pages 59-78, 2015. URL: https://doi.org/10.1109/FOCS.2015.14.
  2. Amir Abboud, Thomas Dueholm Hansen, Virginia Vassilevska Williams, and Ryan Williams. Simulating branching programs with edit distance and friends: or: a polylog shaved is a lower bound made. In Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing, STOC '16, pages 375-388, New York, NY, USA, 2016. Association for Computing Machinery. URL: https://doi.org/10.1145/2897518.2897653.
  3. Amir Abboud and Aviad Rubinstein. Fast and Deterministic Constant Factor Approximation Algorithms for LCS Imply New Circuit Lower Bounds. In Anna R. Karlin, editor, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018), volume 94 of Leibniz International Proceedings in Informatics (LIPIcs), pages 35:1-35:14, Dagstuhl, Germany, 2018. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ITCS.2018.35.
  4. Amir Abboud, Ryan Williams, and Huacheng Yu. More applications of the polynomial method to algorithm design. In Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms, pages 218-230. SIAM, 2014. Google Scholar
  5. Shyan Akmal and Virginia Vassilevska Williams. Improved approximation for longest common subsequence over small alphabets. 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 13:1-13:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.13.
  6. Mai Alzamel, Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszynski, Tomasz Walen, and Wiktor Zuba. Quasi-linear-time algorithm for longest common circular factor. 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 25:1-25:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.CPM.2019.25.
  7. Amihood Amir and Itai Boneh. Locally maximal common factors as a tool for efficient dynamic string algorithms. 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 11:1-11:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.CPM.2018.11.
  8. Amihood Amir, Panagiotis Charalampopoulos, Costas S Iliopoulos, Solon P Pissis, and Jakub Radoszewski. Longest common factor after one edit operation. In International Symposium on String Processing and Information Retrieval, pages 14-26. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-67428-5_2.
  9. Amihood Amir, Panagiotis Charalampopoulos, Solon P. Pissis, and Jakub Radoszewski. Longest common substring made fully dynamic. In Michael A. Bender, Ola Svensson, and Grzegorz Herman, editors, 27th Annual European Symposium on Algorithms, ESA 2019, September 9-11, 2019, Munich/Garching, Germany, volume 144 of LIPIcs, pages 6:1-6:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.ESA.2019.6.
  10. Amihood Amir, Zvi Gotthilf, and B. Riva Shalom. Weighted LCS. J. Discrete Algorithms, 8(3):273-281, 2010. URL: https://doi.org/10.1016/J.JDA.2010.02.001.
  11. Amihood Amir, Tzvika Hartman, Oren Kapah, B. Riva Shalom, and Dekel Tsur. Generalized LCS. Theor. Comput. Sci., 409(3):438-449, 2008. URL: https://doi.org/10.1016/J.TCS.2008.08.037.
  12. 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.
  13. Hsing-Yen Ann, Chang-Biau Yang, and Chiou-Ting Tseng. Efficient polynomial-time algorithms for the constrained LCS problem with strings exclusion. Journal of Combinatorial Optimization, 28(4):800-813, 2014. URL: https://doi.org/10.1007/S10878-012-9588-2.
  14. Alberto Apostolico. Improving the worst-case performance of the Hunt-Szymanski strategy for the longest common subsequence of two strings. Information Processing Letters, 23(2):63-69, 1986. URL: https://doi.org/10.1016/0020-0190(86)90044-X.
  15. Alberto Apostolico and Concettina Guerra. The longest common subsequence problem revisited. Algorithmica, 2:315-336, 1987. URL: https://doi.org/10.1007/BF01840365.
  16. Sang Won Bae and Inbok Lee. On finding a longest common palindromic subsequence. Theoretical Computer Science, 710:29-34, 2018. URL: https://doi.org/10.1016/J.TCS.2017.02.018.
  17. Aranya Banerjee, Daniel Gibney, and Sharma V Thankachan. Longest common substring with gaps and related problems. In 32nd Annual European Symposium on Algorithms (ESA 2024), pages 16:1-16:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.ESA.2024.16.
  18. David Becerra, Juan Mendivelso, and Yoan Pinzón. A multiobjective optimization algorithm for the weighted lcs. Discrete Applied Mathematics, 212:37-47, 2016. URL: https://doi.org/10.1016/J.DAM.2015.11.005.
  19. Stav Ben-Nun, Shay Golan, Tomasz Kociumaka, and Matan Kraus. Time-space tradeoffs for finding a long common substring. In Inge Li Gørtz and Oren Weimann, editors, 31st Annual Symposium on Combinatorial Pattern Matching, CPM 2020, June 17-19, 2020, Copenhagen, Denmark, volume 161 of LIPIcs, pages 5:1-5:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.CPM.2020.5.
  20. Gary Benson, Avivit Levy, S. Maimoni, D. Noifeld, and B. Riva Shalom. Lcsk: A refined similarity measure. Theor. Comput. Sci., 638:11-26, 2016. URL: https://doi.org/10.1016/J.TCS.2015.11.026.
  21. Lasse Bergroth, Harri Hakonen, and Timo Raita. A survey of longest common subsequence algorithms. In Pablo de la Fuente, editor, Seventh International Symposium on String Processing and Information Retrieval, SPIRE 2000, A Coruña, Spain, September 27-29, 2000, pages 39-48. IEEE Computer Society, 2000. URL: https://doi.org/10.1109/SPIRE.2000.878178.
  22. Guillaume Blin, Paola Bonizzoni, Riccardo Dondi, and Florian Sikora. On the parameterized complexity of the repetition free longest common subsequence problem. Information Processing Letters, 112(7):272-276, 2012. URL: https://doi.org/10.1016/J.IPL.2011.12.009.
  23. Karl Bringman and Marvin Künnemann. Multivariate Fine-Grained Complexity of Longest Common Subsequence, pages 1216-1235. Society for Industrial and Applied Mathematics, 2018. URL: https://doi.org/10.1137/1.9781611975031.79.
  24. Karl Bringmann, Vincent Cohen-Addad, and Debarati Das. A linear-time n^0.4-approximation for longest common subsequence. ACM Trans. Algorithms, 19(1):9:1-9:24, 2023. URL: https://doi.org/10.1145/3568398.
  25. Karl Bringmann and Marvin Künnemann. Quadratic conditional lower bounds for string problems and dynamic time warping. In 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, pages 79-97. IEEE, 2015. URL: https://doi.org/10.1109/FOCS.2015.15.
  26. Mauro Castelli, Riccardo Dondi, Giancarlo Mauri, and Italo Zoppis. Comparing incomplete sequences via longest common subsequence. Theoretical Computer Science, 796:272-285, 2019. URL: https://doi.org/10.1016/J.TCS.2019.09.022.
  27. Wun-Tat Chan, Yong Zhang, Stanley PY Fung, Deshi Ye, and Hong Zhu. Efficient algorithms for finding a longest common increasing subsequence. Journal of Combinatorial Optimization, 13(3):277-288, 2007. URL: https://doi.org/10.1007/S10878-006-9031-7.
  28. Panagiotis Charalampopoulos, Pawel Gawrychowski, and Karol Pokorski. Dynamic longest common substring in polylogarithmic time. In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 27:1-27:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.27.
  29. Panagiotis Charalampopoulos, Tomasz Kociumaka, Solon P. Pissis, and Jakub Radoszewski. Faster algorithms for longest common substring. In Petra Mutzel, Rasmus Pagh, and Grzegorz Herman, editors, 29th Annual European Symposium on Algorithms, ESA 2021, September 6-8, 2021, Lisbon, Portugal (Virtual Conference), volume 204 of LIPIcs, pages 30:1-30:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ESA.2021.30.
  30. Debkumar Chowdhury, Kartik Sau, and Sanjukta Mishra. A new dna sequencing alignment methodology using the longest common subsequence technique. American Journal of Applied Mathematics and Computing, 1(3):5-9, 2020. Google Scholar
  31. Maxime Crochemore, Costas S. Iliopoulos, Alessio Langiu, and Filippo Mignosi. The longest common substring problem. Mathematical Structures in Computer Science, 27(2):277-295, 2017. URL: https://doi.org/10.1017/S0960129515000110.
  32. Maxime Crochemore and Ely Porat. Fast computation of a longest increasing subsequence and application. Information and Computation, 208(9):1054-1059, 2010. URL: https://doi.org/10.1016/j.ic.2010.04.003.
  33. Lisa De Mattéo, Yan Holtz, Vincent Ranwez, and Sèverine Bérard. Efficient algorithms for longest common subsequence of two bucket orders to speed up pairwise genetic map comparison. Plos one, 13(12):e0208838, 2018. Google Scholar
  34. Sebastian Deorowicz and Szymon Grabowski. Efficient algorithms for the longest common subsequence in k-length substrings. Inf. Process. Lett., 114(11):634-638, 2014. URL: https://doi.org/10.1016/J.IPL.2014.05.009.
  35. Thomas Derrien, Jordi Estellé, Santiago Marco Sola, David G Knowles, Emanuele Raineri, Roderic Guigó, and Paolo Ribeca. Fast computation and applications of genome mappability. PloS one, 7(1):e30377, 2012. Google Scholar
  36. Marko Djukanovic, Günther R Raidl, and Christian Blum. Anytime algorithms for the longest common palindromic subsequence problem. Computers & Operations Research, 114:104827, 2020. URL: https://doi.org/10.1016/J.COR.2019.104827.
  37. Lech Duraj, Marvin Künnemann, and Adam Polak. Tight conditional lower bounds for longest common increasing subsequence. Algorithmica, 81:3968-3992, 2019. URL: https://doi.org/10.1007/S00453-018-0485-7.
  38. David Eppstein, Zvi Galil, Raffaele Giancarlo, and Giuseppe F Italiano. Sparse dynamic programming i: linear cost functions. Journal of the ACM (JACM), 39(3):519-545, 1992. URL: https://doi.org/10.1145/146637.146650.
  39. Martin Farach-Colton, Paolo Ferragina, and Shanmugavelayutham Muthukrishnan. On the sorting-complexity of suffix tree construction. Journal of the ACM (JACM), 47(6):987-1011, 2000. URL: https://doi.org/10.1145/355541.355547.
  40. Effat Farhana and M Sohel Rahman. Doubly-constrained LCS and hybrid-constrained LCS problems revisited. Information Processing Letters, 112(13):562-565, 2012. URL: https://doi.org/10.1016/J.IPL.2012.04.007.
  41. Tomás Flouri, Emanuele Giaquinta, Kassian Kobert, and Esko Ukkonen. Longest common substrings with k mismatches. Information Processing Letters, 115(6-8):643-647, 2015. URL: https://doi.org/10.1016/J.IPL.2015.03.006.
  42. Darya Frolova, Helman Stern, and Sigal Berman. Most probable longest common subsequence for recognition of gesture character input. IEEE Transactions on Cybernetics, 43(3):871-880, 2013. URL: https://doi.org/10.1109/TSMCB.2012.2217324.
  43. Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Faster queries for longest substring palindrome after block edit. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019), pages 27:1-27:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.CPM.2019.27.
  44. Shafi Goldwasser and Dhiraj Holden. The Complexity of Problems in P Given Correlated Instances. In Christos H. Papadimitriou, editor, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017), volume 67 of Leibniz International Proceedings in Informatics (LIPIcs), pages 13:1-13:19, Dagstuhl, Germany, 2017. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ITCS.2017.13.
  45. Anna Gorbenko and Vladimir Popov. The longest common parameterized subsequence problem. Applied Mathematical Sciences, 6(58):2851-2855, 2012. Google Scholar
  46. Zvi Gotthilf, Danny Hermelin, and Moshe Lewenstein. Constrained lcs: hardness and approximation. In Combinatorial Pattern Matching: 19th Annual Symposium, CPM 2008, Pisa, Italy, June 18-20, 2008 Proceedings 19, pages 255-262. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-69068-9_24.
  47. Zvi Gotthilf and Moshe Lewenstein. Approximating constrained lcs. In International Symposium on String Processing and Information Retrieval, pages 164-172. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-75530-2_15.
  48. Dan Gusfield. Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology. Cambridge University Press, 1997. URL: https://doi.org/10.1017/CBO9780511574931.
  49. MohammadTaghi HajiAghayi, Masoud Seddighin, Saeedreza Seddighin, and Xiaorui Sun. Approximating longest common subsequence in linear time: Beating the n barrier. SIAM Journal on Computing, 51(4):1341-1367, 2022. Google Scholar
  50. Daniel S Hirschberg. Algorithms for the longest common subsequence problem. Journal of the ACM (JACM), 24(4):664-675, 1977. URL: https://doi.org/10.1145/322033.322044.
  51. Guo-Fong Huang, Chang-Biau Yang, Kuo-Tsung Tseng, and Kuo-Si Huang. Diagonal algorithms for the longest common subsequence problems with t-length and at least t-length substrings. In Proceedings of the 37th Workshop on Combinatorial Mathematics and Computation Theory, pages 119-127, 2020. Google Scholar
  52. Lucas Hui. A practical algorithm to find longest common substring in linear time. Computer Systems Science and Engineering, 15, March 2000. Google Scholar
  53. James W Hunt and Thomas G Szymanski. A fast algorithm for computing longest common subsequences. Communications of the ACM, 20(5):350-353, 1977. Google Scholar
  54. Costas Iliopoulos, M Sohel Rahman, and Wojciech Rytter. Algorithms for two versions of LCS problem for indeterminate strings. Journal of Combinatorial Mathematics and Combinatorial Computing, 71:155, 2009. Google Scholar
  55. Costas S Iliopoulos, Marcin Kubica, M Sohel Rahman, and Tomasz Waleń. Algorithms for computing the longest parameterized common subsequence. In Combinatorial Pattern Matching: 18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007. Proceedings 18, pages 265-273. Springer, 2007. Google Scholar
  56. Costas S Iliopoulos and M Sohel Rahman. Algorithms for computing variants of the longest common subsequence problem. Theoretical Computer Science, 395(2-3):255-267, 2008. URL: https://doi.org/10.1016/J.TCS.2008.01.009.
  57. Costas S Iliopoulos and M Sohel Rahman. New efficient algorithms for the LCS and constrained LCS problems. Information Processing Letters, 106(1):13-18, 2008. URL: https://doi.org/10.1016/J.IPL.2007.09.008.
  58. Costas S. Iliopoulos and M. Sohel Rahman. A new efficient algorithm for computing the longest common subsequence. Theor. Comp. Sys., 45(2):355-371, June 2009. URL: https://doi.org/10.1007/s00224-008-9101-6.
  59. R. Impagliazzo and R. Paturi. On the complexity of k-SAT. J. Comput. Syst. Sci., 62(2):367-375, 2001. URL: https://doi.org/10.1006/JCSS.2000.1727.
  60. R. Impagliazzo, R. Paturi, and F. Zane. Which problems have strongly exponential complexity? J. Comput. Syst. Sci., 63(4):512-530, 2001. URL: https://doi.org/10.1006/JCSS.2001.1774.
  61. Shunsuke Inenaga and Heikki Hyyrö. A hardness result and new algorithm for the longest common palindromic subsequence problem. Information Processing Letters, 129:11-15, 2018. URL: https://doi.org/10.1016/J.IPL.2017.08.006.
  62. Robert W. Irving and Campbell B. Fraser. Two algorithms for the longest common subsequence of three (or more) strings. In Alberto Apostolico, Maxime Crochemore, Zvi Galil, and Udi Manber, editors, Combinatorial Pattern Matching, pages 214-229. Springer Berlin Heidelberg, 1992. URL: https://doi.org/10.1007/3-540-56024-6_18.
  63. Orgad Keller, Tsvi Kopelowitz, and Moshe Lewenstein. On the longest common parameterized subsequence. Theoretical Computer Science, 410(51):5347-5353, 2009. URL: https://doi.org/10.1016/J.TCS.2009.09.011.
  64. Tomasz Kociumaka, Jakub Radoszewski, and Tatiana Starikovskaya. Longest common substring with approximately k mismatches. Algorithmica, 81(6):2633-2652, 2019. URL: https://doi.org/10.1007/S00453-019-00548-X.
  65. Tomasz Kociumaka, Tatiana Starikovskaya, and Hjalte Wedel Vildhøj. Sublinear space algorithms for the longest common substring problem. In European Symposium on Algorithms, pages 605-617. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-44777-2_50.
  66. Avivit Levy and B Riva Shalom. A comparative study of dictionary matching with gaps: limitations, techniques and challenges. Algorithmica, 84(3):590-638, 2022. URL: https://doi.org/10.1007/S00453-021-00851-6.
  67. Rao Li, Jyotishmoy Deka, and Kaushik Deka. An algorithm for the longest common subsequence and substring problem. Journal of Mathematics and Informatics, 25:77-81, 2023. URL: https://doi.org/10.22457/jmi.v25a08231.
  68. David Maier. The complexity of some problems on subsequences and supersequences. J. ACM, 25(2):322-336, April 1978. URL: https://doi.org/10.1145/322063.322075.
  69. Shay Mozes, Dekel Tsur, Oren Weimann, and Michal Ziv-Ukelson. Fast algorithms for computing tree lcs. Theoretical Computer Science, 410(43):4303-4314, 2009. String Algorithmics: Dedicated to Professor Maxime Crochemore on the occasion of his 60th birthday. URL: https://doi.org/10.1016/j.tcs.2009.07.011.
  70. Eugene W Myers. An O(ND) difference algorithm and its variations. Algorithmica, 1(1):251-266, 1986. URL: https://doi.org/10.1007/BF01840446.
  71. Narao Nakatsu, Yahiko Kambayashi, and Shuzo Yajima. A longest common subsequence algorithm suitable for similar text strings. Acta Informatica, 18:171-179, 1982. URL: https://doi.org/10.1007/BF00264437.
  72. Deena Nath, Jitendra Kurmi, and Vipin Rawat. A survey on longest common subsequence. International Journal for Research in Applied Science and Engineering Technology (IJRASET), 6:4552-4556, 2018. Google Scholar
  73. Negev Shekel Nosatzki. Approximating the longest common subsequence problem within a sub-polynomial factor in linear time. CoRR, abs/2112.08454, 2021. URL: https://arxiv.org/abs/2112.08454.
  74. Aviad Rubinstein and Zhao Song. Reducing approximate longest common subsequence to approximate edit distance. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1591-1600. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.98.
  75. Tatiana Starikovskaya and Hjalte Wedel Vildhøj. Time-space trade-offs for the longest common substring problem. In Combinatorial Pattern Matching: 24th Annual Symposium, CPM 2013, Bad Herrenalb, Germany, June 17-19, 2013. Proceedings 24, pages 223-234. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-38905-4_22.
  76. Sharma V Thankachan, Alberto Apostolico, and Srinivas Aluru. A provably efficient algorithm for the k-mismatch average common substring problem. Journal of Computational Biology, 23(6):472-482, 2016. URL: https://doi.org/10.1089/CMB.2015.0235.
  77. Robert A. Wagner and Michael J. Fischer. The string-to-string correction problem. J. ACM, 21:168-173, 1974. URL: https://doi.org/10.1145/321796.321811.
  78. Lusheng Wang and Binhai Zhu. Algorithms and hardness for the longest common subsequence of three strings and related problems. In Franco Maria Nardini, Nadia Pisanti, and Rossano Venturini, editors, String Processing and Information Retrieval, pages 367-380. Springer Nature Switzerland, 2023. URL: https://doi.org/10.1007/978-3-031-43980-3_30.
  79. Qingguo Wang, Mian Pan, Yi Shang, and Dmitry Korkin. A fast heuristic search algorithm for finding the longest common subsequence of multiple strings. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 24, pages 1287-1292, 2010. URL: https://doi.org/10.1609/AAAI.V24I1.7493.
  80. Y Wang. Longest common subsequence algorithms and applications in determining transposable genes. arXiv preprint arXiv:2301.03827, 2023. Google Scholar
  81. Peter Weiner. Linear pattern matching algorithms. In 14th Annual Symposium on Switching and Automata Theory (swat 1973), pages 1-11. IEEE, 1973. URL: https://doi.org/10.1109/SWAT.1973.13.
  82. Ryan Williams. A new algorithm for optimal 2-constraint satisfaction and its implications. Theoretical Computer Science, 348(2-3):357-365, 2005. URL: https://doi.org/10.1016/J.TCS.2005.09.023.
  83. Sun Wu, Udi Manber, Gene Myers, and Webb Miller. An O(NP) sequence comparison algorithm. Information Processing Letters, 35(6):317-323, 1990. URL: https://doi.org/10.1016/0020-0190(90)90035-V.
  84. Daxin Zhu, Lei Wang, Tinran Wang, and Xiaodong Wang. A space efficient algorithm for the longest common subsequence in k-length substrings. Theoretical Computer Science, 687:79-92, 2017. URL: https://doi.org/10.1016/J.TCS.2017.05.015.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact