Document Open Access Logo

A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

Authors Anadi Agrawal, Paweł Gawrychowski

PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2020.4.pdf
  • Filesize: 446 kB
  • 12 pages

Document Identifiers

Author Details

Anadi Agrawal
  • Institute of Computer Science, University of Wrocław, Poland
Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland

Cite As Get BibTex

Anadi Agrawal and Paweł Gawrychowski. A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.4

Abstract

The Longest Common Increasing Subsequence (LCIS) is a variant of the classical Longest Common Subsequence (LCS), in which we additionally require the common subsequence to be strictly increasing. While the well-known "Four Russians" technique can be used to find LCS in subquadratic time, it does not seem directly applicable to LCIS. Recently, Duraj [STACS 2020] used a completely different method based on the combinatorial properties of LCIS to design an 𝒪(n²(log log n)²/log^{1/6}n) time algorithm. We show that an approach based on exploiting tabulation (more involved than "Four Russians") can be used to construct an asymptotically faster 𝒪(n² log log n/√{log n}) time algorithm. As our solution avoids using the specific combinatorial properties of LCIS, it can be also adapted for the Longest Common Weakly Increasing Subsequence (LCWIS).

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Longest Common Increasing Subsequence
  • Four Russians

Metrics

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

References

  1. Amir Abboud, Arturs Backurs, and Virginia Vassilevska Williams. Tight hardness results for LCS and other sequence similarity measures. In 56th FOCS, pages 59-78, 2015. Google Scholar
  2. Amir Abboud and Karl Bringmann. Tighter connections between formula-SAT and shaving logs. In 45th ICALP, pages 8:1-8:18, 2018. Google Scholar
  3. Vladimir Arlazarov, Yefim Dinitz, M. A. Kronrod, and Igor Faradžev. On economical construction of the transitive closure of an oriented graph. Doklady Akademii Nauk, 194:487–488, 1970. Google Scholar
  4. Jon Louis Bentley and Andrew Chi-Chih Yao. An almost optimal algorithm for unbounded searching. Inf. Process. Lett., 5(3):82-87, 1976. Google Scholar
  5. Philip Bille and Martin Farach-Colton. Fast and compact regular expression matching. Theor. Comput. Sci., 409(3):486-496, 2008. Google Scholar
  6. Philip Bille and Mikkel Thorup. Faster regular expression matching. In 36th ICALP, pages 171-182, 2009. Google Scholar
  7. Karl Bringmann and Marvin Künnemann. Quadratic conditional lower bounds for string problems and dynamic time warping. In 56th FOCS, pages 79-97, 2015. Google Scholar
  8. Mark R. Brown and Robert Endre Tarjan. A fast merging algorithm. J. ACM, 26(2):211-226, 1979. Google Scholar
  9. Lech Duraj. A sub-quadratic algorithm for the longest common increasing subsequence problem. In 37th STACS, pages 41:1-41:18, 2020. Google Scholar
  10. Lech Duraj, Marvin Künnemann, and Adam Polak. Tight conditional lower bounds for longest common increasing subsequence. Algorithmica, 81(10):3968-3992, 2019. Google Scholar
  11. Szymon Grabowski. New tabulation and sparse dynamic programming based techniques for sequence similarity problems. Discret. Appl. Math., 212:96-103, 2016. Google Scholar
  12. Scott Huddleston and Kurt Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-184, 1982. Google Scholar
  13. Martin Kutz, Gerth Stølting Brodal, Kanela Kaligosi, and Irit Katriel. Faster algorithms for computing longest common increasing subsequences. J. Discrete Algorithms, 9(4):314-325, 2011. Google Scholar
  14. Eugene W. Myers. A four Russians algorithm for regular expression pattern matching. J. ACM, 39(2):430-448, 1992. Google Scholar
  15. Adam Polak. Why is it hard to beat 𝒪(n²) for longest common weakly increasing subsequence? Inf. Process. Lett., 132:1-5, 2018. Google Scholar
  16. Yoshifumi Sakai. A linear space algorithm for computing a longest common increasing subsequence. Inf. Process. Lett., 99(5):203-207, 2006. Google Scholar
  17. Robert A. Wagner and Michael J. Fischer. The string-to-string correction problem. J. ACM, 21(1):168-173, 1974. Google Scholar
  18. R. Ryan Williams. Faster all-pairs shortest paths via circuit complexity. SIAM J. Comput., 47(5):1965-1985, 2018. Google Scholar
  19. I-Hsuan Yang, Chien-Pin Huang, and Kun-Mao Chao. A fast algorithm for computing a longest common increasing subsequence. Inf. Process. Lett., 93(5):249-253, 2005. Google Scholar
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 About DROPS Imprint Privacy Contact