Document Open Access Logo

Approximation Algorithms for the Longest Run Subsequence Problem

Authors Yuichi Asahiro , Hiroshi Eto , Mingyang Gong, Jesper Jansson , Guohui Lin , Eiji Miyano , Hirotaka Ono , Shunichi Tanaka

PDF

File

Thumbnail PDF
PDF
LIPIcs.CPM.2023.2.pdf
  • Filesize: 0.79 MB
  • 12 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Longest run subsequence problem
  • bounded occurrence
  • approximation algorithm

Metrics

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

Abstract

We study the approximability of the Longest Run Subsequence problem (LRS for short). For a string S = s_1 ⋯ s_n over an alphabet Σ, a run of a symbol σ ∈ Σ in S is a maximal substring of consecutive occurrences of σ. A run subsequence S' of S is a sequence in which every symbol σ ∈ Σ occurs in at most one run. Given a string S, the goal of LRS is to find a longest run subsequence S^* of S such that the length |S^*| is maximized over all the run subsequences of S. It is known that LRS is APX-hard even if each symbol has at most two occurrences in the input string, and that LRS admits a polynomial-time k-approximation algorithm if the number of occurrences of every symbol in the input string is bounded by k. In this paper, we design a polynomial-time (k+1)/2-approximation algorithm for LRS under the k-occurrence constraint on input strings. For the case k = 2, we further improve the approximation ratio from 3/2 to 4/3.

Cite As Get BibTex

Yuichi Asahiro, Hiroshi Eto, Mingyang Gong, Jesper Jansson, Guohui Lin, Eiji Miyano, Hirotaka Ono, and Shunichi Tanaka. Approximation Algorithms for the Longest Run Subsequence Problem. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CPM.2023.2

Author Details

Yuichi Asahiro
  • Kyushu Sangyo University, Fukuoka, Japan
Hiroshi Eto
  • Kyushu Institute of Technology, Iizuka, Japan
Mingyang Gong
  • Uniersity of Alberta, Edmonton, Canada
Jesper Jansson
  • Kyoto University, Kyoto, Japan
Guohui Lin
  • Uniersity of Alberta, Edmonton, Canada
Eiji Miyano
  • Kyushu Institute of Technology, Iizuka, Japan
Hirotaka Ono
  • Nagoya University, Nagoya, Japan
Shunichi Tanaka
  • Kyushu Institute of Technology, Iizuka, Japan

Funding

This work is partially supported by NSERC Canada, and JSPS KAKENHI Grant Numbers JP17K00024, JP20H05967, JP21K11755, JP21K19765, JP22H00513, JP22H03550, and JP22K11915.

Acknowledgements

The authors would like to thank the anonymous reviewers for their suggestions and detailed comments that helped to improve the presentation of the paper.

References

  1. Paola Alimonti and Viggo Kann. Some APX-completeness results for cubic graphs. Theor. Comput. Sci., 237(1-2):123-134, 2000. URL: https://doi.org/10.1016/S0304-3975(98)00158-3.
  2. Yuichi Asahiro, Jesper Jansson, Guohui Lin, Eiji Miyano, Hirotaka Ono, and Tadatoshi Utashima. Polynomial-time equivalences and refined algorithms for longest common subsequence variants. In Hideo Bannai and Jan Holub, editors, 33rd Annual Symposium on Combinatorial Pattern Matching, CPM 2022, June 27-29, 2022, Prague, Czech Republic, volume 223 of LIPIcs, pages 15:1-15:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.CPM.2022.15.
  3. Mauro Castelli, Riccardo Dondi, Giancarlo Mauri, and Italo Zoppis. The longest filled common subsequence problem. In Juha Kärkkäinen, Jakub Radoszewski, and Wojciech Rytter, editors, 28th Annual Symposium on Combinatorial Pattern Matching, CPM 2017, July 4-6, 2017, Warsaw, Poland, volume 78 of LIPIcs, pages 14:1-14:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.CPM.2017.14.
  4. Mauro Castelli, Riccardo Dondi, Giancarlo Mauri, and Italo Zoppis. Comparing incomplete sequences via longest common subsequence. Theor. Comput. Sci., 796:272-285, 2019. URL: https://doi.org/10.1016/j.tcs.2019.09.022.
  5. Riccardo Dondi and Florian Sikora. The longest run subsequence problem: Further complexity results. 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 14:1-14:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.CPM.2021.14.
  6. Martin Grötschel, Michael Jünger, and Gerhard Reinelt. A cutting plane algorithm for the linear ordering problem. Oper. Res., 32(6):1195-1220, 1984. URL: https://doi.org/10.1287/opre.32.6.1195.
  7. Haitao Jiang, Chunfang Zheng, David Sankoff, and Binhai Zhu. Scaffold filling under the breakpoint and related distances. IEEE ACM Trans. Comput. Biol. Bioinform., 9(4):1220-1229, 2012. URL: https://doi.org/10.1109/TCBB.2012.57.
  8. Junwei Luo, Yawei Wei, Mengna Lyu, Zhengjiang Wu, Xiaoyan Liu, Huimin Luo, and Chaokun Yan. A comprehensive review of scaffolding methods in genome assembly. Briefings Bioinform., 22(5), 2021. URL: https://doi.org/10.1093/bib/bbab033.
  9. Adriana Muñoz, Chunfang Zheng, Qian Zhu, Victor A. Albert, Steve Rounsley, and David Sankoff. Scaffold filling, contig fusion and comparative gene order inference. BMC Bioinform., 11:304, 2010. URL: https://doi.org/10.1186/1471-2105-11-304.
  10. F. Sanger, G.M. Air, B.G. Barrell, N.L. Brown, A.R. Coulson, J.C. Fiddes, C.A. Hutchison III, P.M. Slocombe, and M. Smith. Nucleotide sequence of bacteriophage ϕx174 DNA. Nature, 265:687-695, 1977. Google Scholar
  11. Sven Schrinner, Manish Goel, Michael Wulfert, Philipp Spohr, Korbinian Schneeberger, and Gunnar W. Klau. The longest run subsequence problem. In Carl Kingsford and Nadia Pisanti, editors, 20th International Workshop on Algorithms in Bioinformatics, WABI 2020, September 7-9, 2020, Pisa, Italy (Virtual Conference), volume 172 of LIPIcs, pages 6:1-6:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.WABI.2020.6.
  12. Sven Schrinner, Manish Goel, Michael Wulfert, Philipp Spohr, Korbinian Schneeberger, and Gunnar W. Klau. Using the longest run subsequence problem within homology-based scaffolding. Algorithms Mol. Biol., 16(1):11, 2021. URL: https://doi.org/10.1186/s13015-021-00191-8.
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