Skip to main content

Diverse Palindromic Factorization Is NP-complete

  • Conference paper
  • First Online:
Developments in Language Theory (DLT 2015)

Abstract

We prove that it is NP-complete to decide whether a given string can be factored into palindromes that are each unique in the factorization.

T. Gagie and S.J. Puglisi—Supported by grants 268324, 258308 and 284598 from the Academy of Finland.

M. Piątkowski—Supported by a research fellowship within the project “Enhancing Educational Potential of Nicolaus Copernicus University in the Disciplines of Mathematical and Natural Sciences” (project no. POKL.04.01.01-00-081/10).

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alitabbi, A., Iliopoulos, C.S., Rahman, M.S.: Maximal palindromic factorization. In: Proceedings of the Prague Stringology Conference (PSC), pp. 70–77 (2013)

    Google Scholar 

  2. Fernau, H., Manea, F., Mercaş, R., Schmid, M.L.: Pattern matching with variables: fast algorithms and new hardness results. In: Proceedings of the 32nd Symposium on Theoretical Aspects of Computer Science (STACS), pp. 302–315 (2015)

    Google Scholar 

  3. Fici, G., Gagie, T., Kärkkäinen, J., Kempa, D.: A subquadratic algorithm for minimum palindromic factorization. Journal of Discrete Algorithms 28, 41–48 (2014)

    Article  MathSciNet  Google Scholar 

  4. Frid, A.E., Puzynina, S., Zamboni, L.: On palindromic factorization of words. Advances in Applied Mathematics 50(5), 737–748 (2013)

    Article  MathSciNet  Google Scholar 

  5. Gawrychowski, P., Uznański, P.: Tight tradeoffs for approximating palindromes in streams. Technical Report 1410.6433, arxiv.org (2014)

    Google Scholar 

  6. I, T., Sugimoto, S., Inenaga, S., Bannai, H., Takeda, M.: Computing palindromic factorizations and palindromic covers on-line. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds.) CPM 2014. LNCS, vol. 8486, pp. 150–161. Springer, Heidelberg (2014)

    Google Scholar 

  7. Kosolobov, D., Rubinchik, M., Shur, A.M.: Pal\(^\text{ k }\) is linear recognizable online. In: Italiano, G.F., Margaria-Steffen, T., Pokorný, J., Quisquater, J.-J., Wattenhofer, R. (eds.) SOFSEM 2015-Testing. LNCS, vol. 8939, pp. 289–301. Springer, Heidelberg (2015)

    Google Scholar 

  8. Ravsky, O.: On the palindromic decomposition of binary words. Journal of Automata, Languages and Combinatorics 8(1), 75–83 (2003)

    MathSciNet  Google Scholar 

  9. Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Slisenko, A.O. (ed.) Structures in Constructive Mathematics and Mathematical Logic, Part II, pp. 115–125 (1968)

    Google Scholar 

  10. Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Transactions on Information Theory 22(3), 337–343 (1977)

    Article  MathSciNet  Google Scholar 

  11. Ziv, J., Lempel, A.: Compression of individual sequences via variable-rate coding. IEEE Transactions on Information Theory 24(5), 530–536 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Travis Gagie .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Bannai, H. et al. (2015). Diverse Palindromic Factorization Is NP-complete. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21500-6_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics