Skip to main content
View expanded cover

Annual Symposium on Combinatorial Pattern Matching

CPM 2015: Combinatorial Pattern Matching pp 307–315Cite as

Greedy Conjecture for Strings of Length 4

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9133)

Abstract

In this short note, we prove that the greedy conjecture for the shortest common superstring problem is true for strings of length 4.

Keywords

  • Greedy Algorithm
  • Approximation Ratio
  • Travel Salesman Problem
  • Input String
  • Require Inequality

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-19929-0_26
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-19929-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)
Learn about institutional subscriptions

References

  1. Bellman, R.: Dynamic programming treatment of the travelling salesman problem. J. ACM (J.ACM) 9(1), 61–63 (1962)

    MATH  CrossRef  Google Scholar 

  2. Gallant, J., Maier, D., Storer, J.: On finding minimal length superstrings. J. Comput. Syst. Sci. 20(1), 50–58 (1980)

    MATH  MathSciNet  CrossRef  Google Scholar 

  3. Gevezes, T., Pitsoulis, L.: The shortest superstring problem. In: Rassias, T.M., Floudas, C.A., Butenko, S. (eds.) Optimization in Science and Engineering– In Honor of the 60th Birthday of Panos M. Pardalos, pp. 189–227. Springer, New York (2014)

    Google Scholar 

  4. Golovnev, A., Kulikov, A.S., Mihajlin, I.: Approximating shortest superstring problem using de bruijn graphs. In: Fischer, J., Sanders, P. (eds.) CPM 2013. LNCS, vol. 7922, pp. 120–129. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  5. Golovnev, A., Kulikov, A.S., Mihajlin, I.: Solving SCS for bounded length strings in fewer than \(2^n\) steps. Inf. Process. Lett. 114(8), 421–425 (2014)

    MATH  MathSciNet  CrossRef  Google Scholar 

  6. Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. J. Soc. Ind. Appl. Math. 10(1), 196–210 (1962)

    MATH  MathSciNet  CrossRef  Google Scholar 

  7. Karp, R.M.: Dynamic programming meets the principle of inclusion and exclusion. Oper. Res. Lett. 1(2), 49–51 (1982)

    MATH  MathSciNet  CrossRef  Google Scholar 

  8. Kohn, S., Gottlieb, A., Kohn, M.: A generating function approach to the traveling salesman problem. In: Proceedings of the 1977 annual conference. pp. 294–300. ACM (1977)

    Google Scholar 

  9. Laube, U., Weinard, M.: Conditional inequalities and the shortest common superstring problem. Int. J. Found. Comput. Sci. 17(1), 247–247 (2006)

    CrossRef  Google Scholar 

  10. Maier, D., Storer, J.A.: A note on the complexity of the superstring problem. Princeton University Technical report 233 (1977)

    Google Scholar 

  11. Mucha, M.: Lyndon words and short superstrings. In: Proceedings of the TwentyFourth Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 2013, Society for Industrial and Applied Mathematics (2013)

    Google Scholar 

  12. Ott, S.: Lower bounds for approximating shortest superstrings over an alphabet of size 2. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 55–64. Springer, Heidelberg (1999)

    CrossRef  Google Scholar 

  13. Tarhio, J., Ukkonen, E.: A greedy algorithm for constructing shortest common superstrings. In: Gruska, J., Rovan, B., Wiedermann, J. (eds.) MFCS 1986. LNCS, pp. 602–610. Springer, Heidelberg (1986)

    Google Scholar 

  14. Turner, J.: Approximation algorithms for the shortest common superstring problem. Inf. Comput. 83(1), 1–20 (1989)

    MATH  CrossRef  Google Scholar 

  15. Weinard, M., Schnitger, G.: On the greedy superstring conjecture. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 387–398. Springer, Heidelberg (2003)

    Google Scholar 

Download references

Acknowledgments

Research is partially supported by the Government of the Russian Federation (grant 14.Z50.31.0030) and Grant of the President of the Russian Federation (MK-6550.2015.1).

Author information

Authors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics, Saint Petersburg, Russia

    Alexander S. Kulikov & Evgeniy Sluzhaev

  2. St. Petersburg Academic University, Saint Petersburg, Russia

    Sergey Savinov & Evgeniy Sluzhaev

Authors
  1. Alexander S. Kulikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergey Savinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evgeniy Sluzhaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander S. Kulikov .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kulikov, A.S., Savinov, S., Sluzhaev, E. (2015). Greedy Conjecture for Strings of Length 4. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19929-0_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

  • eBook Packages: Computer ScienceComputer Science (R0)