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A DNA Algorithm for the Hamiltonian Path Problem Using Microfluidic Systems

  • Lucas Ledesma
  • Juan Pazos
  • Alfonso Rodríguez-Patón
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2950)

Abstract

This paper describes the design of a linear time DNA algorithm for the Hamiltonian Path Problem (HPP) suited for parallel implementation using a microfluidic system. This bioalgorithm was inspired by the algorithm contained in [16] within the tissue P systems model. The algorithm is not based on the usual brute force generate/test technique, but builds the space solution gradually. The possible solutions/paths are built step by step by exploring the graph according to a breadth-first search so that only the paths that represent permutations of the set of vertices, and which, therefore, do not have repeated vertices (a vertex is only added to a path if this vertex is not already present) are extended. This simple distributed DNA algorithm has only two operations: concatenation (append) and sequence separation (filter). The HPP is resolved autonomously by the system, without the need for external control or manipulation. In this paper, we also note other possible bioalgorithms and the relationship of the implicit model used to solve the HPP to other abstract theoretical distributed DNA computing models (test tube distributed systems, grammar systems, parallel automata).

Keywords

Hamiltonian Path Hamiltonian Path Problem Grammar System Biomolecular Computation Append Operation 
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.

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References

  1. 1.
    Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Amos, M., Gibbons, A., Hodgson, D.: Error-resistant implementation of DNA computation. In: Proceedings of the Second Annual Meeting on DNA Based Computers, held at Princeton University, June 10-12 (1996)Google Scholar
  3. 3.
    Andronescu, M., Dees, D., Slaybaugh, L., Zhao, Y., Condon, A., Cohen, B., Skiena, S.: Algorithms for testing that DNA word designs avoid unwanted secondary structure. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 92–104. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Castellanos, J., Martín-Vide, C., Mitrana, V., Sempere, J.: Solving NP-complete problems with networks of evolutionary processors. In: Proc. of the 6th International Work-Conference on Artificial and Natural Neural Networks, IWANN. LNCS, vol. 2048, pp. 621–628 (2001)Google Scholar
  5. 5.
    Chiu, D.T., Pezzoli, E., Wu, H., Stroock, A.D., Whitesides, G.M.: Using threedimensional microfluidic networks for solving computationally hard problems. PNAS 98(6), 2961–2966 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Csuhaj-Varju, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems. A Grammatical Approach to Distribution and Cooperation. Gordon and Breach, London (1994)zbMATHGoogle Scholar
  7. 7.
    Csuhaj-Varju, E., Kari, L., Păun, G.: Test tube distributed systems based on splicing. Computers and AI 15(2-3), 211–232 (1996)zbMATHGoogle Scholar
  8. 8.
    Csuhaj-Varju, E., Freund, R., Kari, L., Păun, G.: DNA computing based on splicing: universality results. In: Proc. First Annual Pacific Symp. on Biocomputing, Hawaii, pp. 179–190 (1996)Google Scholar
  9. 9.
    Dassow, J., Martín-Vide, C., Păun, G., Rodríguez-Patón, A.: Conditional concatenation. Fundamenta Informaticae 44(4), 353–372 (2000)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Freund, R., Freund, F.: Test tube systems or how to bake a DNA cake. Acta Cybernetica 12(4), 445–459 (1996)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Gehani, A., Reif, J.H.: Microflow bio-molecular computation. Biosystems 52(1-3), 197–216 (1999)CrossRefGoogle Scholar
  12. 12.
    Gloor, G., Kari, L., Gaasenbeek, M., Yu, S.: Towards a DNA solution to the shortest common superstring problem. In: 4th Int. Meeting on DNA-Based Computing, Baltimore, Penns (June 1998)Google Scholar
  13. 13.
    Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bull. Math. Biology 49, 737–759 (1987)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Head, T.: Hamiltonian Paths and Double Stranded DNA. In: Păun, G. (ed.) Computing with Bio- Molecules. Theory and Experiments, pp. 80–92. World Scientific, Singapore (1998)Google Scholar
  15. 15.
    Manz, A., Harrison, D.J., Verpoorte, E.M.J., Fettinger, J.C., Paulus, A., Ludi, H., Widmer, H.M.: Planar chips technology for miniaturization and integration of separation techniques into monitoring systems: “Capillary electrophoresis on a chip. J. Chromatogr. 593, 253–258 (1992)CrossRefGoogle Scholar
  16. 16.
    Martín-Vide, C., Păun, G., Pazos, J., Rodríguez-Patón, A.: Tissue P systems. Theoretical Computer Science 296(2), 295–326 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    McCaskill, J.S.: Optically programming DNA computing in microflow reactors. Biosystems 59(2), 125–138 (2001)CrossRefGoogle Scholar
  18. 18.
    Morimoto, N., Arita, M., Suyama, A.: Solid phase DNA solution to the Hamiltonian path problem. In: Proceedings of the 3rd DIMACS Workshop on DNA Based Computers, The University of Pennsylvania pp. 83–92 (June 1997)Google Scholar
  19. 19.
    Păun, G., Thierrin, G.: Multiset processing by means of systems of finite state transducers. In: Boldt, O., Jürgensen, H. (eds.) WIA 1999. LNCS, vol. 2214, pp. 140–157. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  20. 20.
    Selvaganapathy, P.R., Carlen, E.T., Mastrangelo, C.H.: Recent Progress in Microfluidic Devices for Nucleic Acid and Antibody Assays. Proceedings of the IEEE 91(6), 954–973 (2003)CrossRefGoogle Scholar
  21. 21.
    Verpoorte, E., De Rooij, N.F.: Microfluidics Meets MEMS. Proceedings of the IEEE 91(6), 930–953 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Lucas Ledesma
    • 1
  • Juan Pazos
    • 1
  • Alfonso Rodríguez-Patón
    • 1
  1. 1.Facultad de InformáticaUniversidad Politécnica de MadridBoadilla del Monte, MadridSpain

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