Skip to main content
SpringerLink
Log in

A Space Efficient Algorithm for LCIS Problem

  • Conference paper
  • First Online:
Security, Privacy, and Anonymity in Computation, Communication, and Storage (SpaCCS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10656))

  • 1668 Accesses

Abstract

This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common increasing subsequence of sizes n and m respectively, in time O(nm) using additional \(\min \{n,m\}\,+\,1\) space.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abboud, A., Backurs, A., Williams, V.V.: Quadratic-time hardness of LCS and other sequence similarity measures. In: Proceedings of the 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2015), pp. 59–78 (2015)

    Google Scholar 

  2. Abboud, A., Hansen, T.D., Williams, V.V., Williams, R.: Simulating branching programs with edit distance and friends or: a polylog shaved is a lower bound made. In: Proceedings of the 48th Annual ACM Symposium on Symposium on Theory of Computing (STOC 2016), pp. 375–388 (2016)

    Google Scholar 

  3. Backurs, A., Indyk, P.: Edit distance cannot be computed in strongly subquadratic time (unless SETH is false). In: Proceedings of the 47th Annual ACM Symposium on Theory of Computing (STOC 2015), pp. 51–58 (2015)

    Google Scholar 

  4. Backurs, A., Indyk, P.: Which regular expression patterns are hard to match? In: Proceedings of the 57th Annual Symposium on Foundations of Computer Science, (FOCS 2016), pp. 457–466 (2016)

    Google Scholar 

  5. Backurs, A., Tzamos, C.: Improving viterbi is hard: better runtimes imply faster clique algorithms. In: Proceedings of the 34th International Conference on Machine Learning (ICML 2017), pp. 311–321 (2017)

    Google Scholar 

  6. Chan, W., Zhang, Y., Fung, S.P.Y., Ye, D., Zhu, H.: Efficient algorithms for finding a longest common increasing subsequence. J. Comb. Optim. 13, 277–288 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cygan, M., Mucha, M., Wegrzycki, K., Wlodarczyk, M.: On problems equivalent to (min, +)-convolution. In: Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), pp. 22:1–15 (2017)

    Google Scholar 

  8. Hirschberg, D.S.: A linear space algorithm for computing maximal common subsequences. Commun. ACM 18(6), 341–343 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kutz, M., Brodal, G.S., Kaligosi, K., Katriel, I.: Faster algorithms for computing longest common increasing subsequences. J. Discrete Algorithms 9, 314–325 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sakai, Y.: A linear space algorithm for computing a longest common increasing subsequence. Inf. Process. Lett. 99, 203–207 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yang, I.H., Huang, C.P., Chao, K.M.: A fast algorithm for computing a longest common increasing subsequence. Inf. Process. Lett. 93(5), 249–253 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgment

This work was supported in part by the Quanzhou Foundation of Science and Technology under Grant No.2013Z38, Fujian Provincial Key Laboratory of Data-Intensive Computing and Fujian University Laboratory of Intelligent Computing and Information Processing.

Author information

Authors and Affiliations

  1. Quanzhou Normal University, Quanzhou, 362000, China

    Daxin Zhu

  2. Fujian University of Technology, Fuzhou, 350108, China

    Xiaodong Wang

Authors
  1. Daxin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaodong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaodong Wang .

Editor information

Editors and Affiliations

  1. Guangzhou University , Guangzhou, China

    Guojun Wang

  2. Edith Kinney Gaylord Presidential Professor, University of Oklahoma, Norman, Oklahoma, USA

    Mohammed Atiquzzaman

  3. Aalto University, Espoo, Finland

    Zheng Yan

  4. University of Texas at San Antonio, San Antonio, Texas, USA

    Kim-Kwang Raymond Choo

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zhu, D., Wang, X. (2017). A Space Efficient Algorithm for LCIS Problem. In: Wang, G., Atiquzzaman, M., Yan, Z., Choo, KK. (eds) Security, Privacy, and Anonymity in Computation, Communication, and Storage. SpaCCS 2017. Lecture Notes in Computer Science(), vol 10656. Springer, Cham. https://doi.org/10.1007/978-3-319-72389-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-72389-1_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72388-4

  • Online ISBN: 978-3-319-72389-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation