Solving the Discretizable Molecular Distance Geometry Problem by Multiple Realization Trees

Chapter

Abstract

The discretizable molecular distance geometry problem (DMDGP) is a subclass of the MDGP, where instances can be solved using a discrete algorithm called branch-and-prune (BP). We present an initial study showing that the BP algorithm can be used differently from its original form, where the initial atoms are fixed and the branches of the BP tree are generated until the last atom is reached. Particularly, we show that the use of multiple BP trees may explore the search space faster than the original BP.

Keywords

Distance geometry Branch-and-prune Realization tree 

References

  1. 1.
    Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne, P.E.: The protein data bank. Nucleic Acids Res. 28, 235–242 (2000)Google Scholar
  2. 2.
    Crippen, G., Havel, T.: Distance Geometry and Molecular Conformation. Wiley, New York (1988)Google Scholar
  3. 3.
    Dong, Q., Wu, Z.: A linear-time algorithm for solving the molecular distance geometry problem with exact interatomic distances. J. Global Optim. 22, 365–375 (2002)Google Scholar
  4. 4.
    Lavor, C., Liberti, L., Maculan, N.: Molecular distance geometry problem. Encyclopedia of Optimization, pp. 2305–2311, 2nd edn. Springer, New York (2009)Google Scholar
  5. 5.
    Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: The discretizable molecular distance geometry problem. Comput. Optim. Appl. 52, 115–146 (2012)Google Scholar
  6. 6.
    Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: Recent advances on the discretizable molecular distance geometry problem. Eur. J. Oper. Res. 219, 698–706 (2012)Google Scholar
  7. 7.
    Liberti, L., Lavor, C., Maculan, N.: A branch-and-prune algorithm for the molecular distance geometry problem. Int. Trans. Oper. Res. 15, 1–17 (2008)Google Scholar
  8. 8.
    Liberti, L., Lavor, C., Mucherino, A., Maculan, N.: Molecular distance geometry methods: from continuous to discrete. Int. Trans. Oper. Res. 18, 33–51 (2010)Google Scholar
  9. 9.
    Mucherino, A., Lavor, C., Liberti, L.,  Talbi, E.-G.: A parallel version of the branch and prune algorithm for the molecular distance geometry problem. In: IEEE Conference Proceedings, ACS/IEEE International Conference on Computer Systems and Applications (AICCSA10), pp. 1–6. Hammamet, Tunisia (2010)Google Scholar
  10. 10.
    Nucci, P.: Heuristicas para o problema molecular de geometria de distancias aplicado a proteinas. Undergraduate Dissertation, Fluminense Federal UniversityGoogle Scholar
  11. 11.
    Saxe, J.B.: Embeddability of weighted graphs in k-space is strongly NP-hard. In: Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp. 480–489. Monticello, IL (1979)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Pedro Nucci
    • 1
  • Loana Tito Nogueira
    • 2
  • Carlile Lavor
    • 3
  1. 1.Navy Arsenal of Rio de JaneiroBrazilian NavyRio de JaneiroBrazil
  2. 2.Instituto de ComputaçãoUniversidade Federal FluminenseRio de JaneiroBrazil
  3. 3.IMECC-UNICAMPCampinas-SPRio de JaneiroBrazil

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