Skip to main content
SpringerLink
Log in

Solving the Set-Splitting Problem in Sticker-Based Model and the Lipton-Adelmann Model

  • Conference paper
  • First Online:
Parallel and Distributed Processing and Applications (ISPA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2745))

Abstract

Adleman wrote the first paper in which it was demonstrated that DNA (DeoxyriboNucleic Acid) strands could be applied for dealing with solutions to an instance of the NP-complete Hamiltonian path problem (HPP). Lipton wrote the second paper in which it was shown that the Adleman techniques could also be used to solving the NP-complete satisfiability (SAT) problem (the first NP-complete problem). Adleman and his co-authors proposed sticker for enhancing the Adleman-Lipton model. In the paper, it is proved how to apply sticker in the sticker-based model for constructing solution space of DNA for the set-splitting problem and how to apply DNA operations in the Adleman-Lipton model to solve that problem from solution space of sticker.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. R. Sinden. DNA Structure and Function. Academic Press, 1994.

    Google Scholar 

  2. L. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021–1024, Nov. 11, 1994.

    Article  Google Scholar 

  3. R. J. Lipton. DNA solution of hard computational problems. Science, 268:542:545, 1995.

    Article  Google Scholar 

  4. Q. Quyang, P.D. Kaplan, S. Liu, and A. Libchaber. DNA solution of the maximal clique problem. Science, 278:446–449, 1997.

    Article  Google Scholar 

  5. M. Arita, A. Suyama, and M. Hagiya. A heuristic approach for Hamiltonian path problem with molecules. Proceedings of 2nd Genetic Programming (GP-97), 1997, pp. 457–462.

    Google Scholar 

  6. N. Morimoto, M. Arita, and A. Suyama. Solid phase DNA solution to the Hamiltonian path problem. DIMACS (Series in Discrete Mathematics and Theoretical Computer Science), Vol. 48, 1999, pp. 93–206.

    Google Scholar 

  7. A. Narayanan, and S. Zorbala. DNA algorithms for computing shortest paths. In Genetic Programming 1998: Proceedings of the Third Annual Conference, J. R. Koza et al. (Eds), 1998, pp. 718–724.

    Google Scholar 

  8. S.-Y. Shin, B.-T. Zhang, and S.-S. Jun. Solving traveling salesman problems using molecular programming. Proceedings of the 1999 Congress on Evolutionary Computation (CEC99), vol. 2, pp. 994–1000, 1999.

    Article  Google Scholar 

  9. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to algorithms.

    Google Scholar 

  10. M. R. Garey, and D. S. Johnson. Computer and intractability. Freeman, San Fransico, CA, 1979.

    Google Scholar 

  11. D. Boneh, C. Dunworth, R. J. Lipton and J. Sgall. On the computational Power of DNA. In Discrete Applied Mathematics, Special Issue on Computational Molecular Biology, Vol. 71 (1996), pp. 79–94.

    Article  MATH  MathSciNet  Google Scholar 

  12. L. M. Adleman. On constructing a molecular computer. DNA Based Computers, Eds. R. Lipton and E. Baum, DIMACS: series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society. 1–21 (1996)

    Google Scholar 

  13. M. Amos. “DNA Computation”, Ph.D. Thesis, department of computer science, the University of Warwick, 1997.

    Google Scholar 

  14. S. Roweis, E. Winfree, R. Burgoyne, N. V. Chelyapov, M. F. Goodman, Paul W.K. Rothemund and L. M. Adleman. “A Sticker Based Model for DNA Computation”. 2nd annual workshop on DNA Computing, Princeton University. Eds. L. Landweber and E. Baum, DIMACS: series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society. 1–29 (1999).

    Google Scholar 

  15. M.J. Perez-Jimenez and F. Sancho-Caparrini. “Solving Knapsack Problems in a Sticker Based Model”. 7nd annual workshop on DNA Computing, DIMACS: series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, 2001.

    Google Scholar 

  16. G. Paun, G. Rozenberg and A. Salomaa. DNA Computing: New Computing Paradigms. Springer-Verlag, New York, 1998. ISBN: 3-540-64196-3.

    MATH  Google Scholar 

  17. W.-L. Chang and M. Guo. “Solving the Dominating-set Problem in Adleman-Lipton’s Model”. The Third International Conference on Parallel and Distributed Computing, Applications and Technologies, Japan, 2002, pp. 167–172.

    Google Scholar 

  18. W.-L. Chang and M. Guo. “Solving the Clique Problem and the Vertex Cover Problem in Adleman-Lipton’s Model”. IASTED International Conference, Networks, Parallel and Distributed Processing, and Applications, Japan, 2002, pp. 431–436.

    Google Scholar 

  19. W.-L. Chang, M. Guo. “Solving NP-Complete Problem in the Adleman-Lipton Model”. The Proceedings of 2002 International Conference on Computer and Information Technology, Japan, 2002, pp. 157–162.

    Google Scholar 

  20. W.-L. Chang and M. Guo. “Resolving the 3-Dimensional Matching Problem and the Set Packing Problem in Adleman-Lipton’s Model”. IASTED International Conference, Networks, Parallel and Distributed Processing, and Applications, Japan, 2002, pp. 455–460.

    Google Scholar 

  21. Bin Fu. “Volume Bounded Molecular Computation”. Ph.D. Thesis, Department of Computer Science, Yale University, 1997.

    Google Scholar 

  22. Ravinderjit S. Braich, Clifford Johnson, Paul W.K. Rothemund, Darryl Hwang, Nickolas Chelyapov and Leonard M. Adleman. “Solution of a satisfiability problem on a gel-based DNA computer”. Proceedings of the 6th International Conference on DNA Computation in the Springer-Verlag Lecture Notes in Computer Science series.

    Google Scholar 

  23. Kalim Mir. “A restricted genetic alphabet for DNA computing”. Eric B. Baum and Laura F. Landweber, editors. DNA Based Computers II: DIMACS Workshop, June 10–12, 1996, volume 44 of DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Providence, RI, 1998, pp. 243–246.

    Google Scholar 

  24. A. R. Cukras, Dirk Faulhammer, Richard J. Lipton, and Laura F. Landweber. “Chess games: A model for RNA-based computation”. In Proceedings of the 4th DIMACS Meeting on DNA Based Computers, held at the University of Pennsylvania, June 16–19, 1998, pp. 27–37.

    Google Scholar 

  25. W.-L. Chang and M. Guo. “Using Sticker for Solving the Dominating-set Problem in the Adleman-Lipton Model”. IEICE Transaction on Information System, 2003, accepted.

    Google Scholar 

  26. W.-L. Chang and M. Guo. “Solving the Set-basis Problem in Sticker-based Model and the Adleman-Lipton Model”. It was submitted to the 2003 International Conference on Parallel Processing (ICPP2003), Kaohsiung, Taiwan, Republic of China.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Management, Southern Taiwan University of Technology, Tainan, 701, Taiwan R.O.C.

    Weng-Long Chang & Michael Ho

  2. Department of Computer Software, The University of Aizu, Aizu-Wakamatsu City, Fukushima, 965-8580, Japan

    Minyi Guo

Authors
  1. Weng-Long Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Minyi Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Software, The University of Aizu, Aizu-Wakamatsu City, Fukushima, 965-8580, Japan

    Minyi Guo

  2. Department of Computer Science, St. Francis Xavier University, Antigonish, NS, B2G 2W5, Canada

    Laurence Tianruo Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chang, WL., Guo, M., Ho, M. (2003). Solving the Set-Splitting Problem in Sticker-Based Model and the Lipton-Adelmann Model. In: Guo, M., Yang, L.T. (eds) Parallel and Distributed Processing and Applications. ISPA 2003. Lecture Notes in Computer Science, vol 2745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37619-4_20

Download citation

  • DOI: https://doi.org/10.1007/3-540-37619-4_20

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40523-8

  • Online ISBN: 978-3-540-37619-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation