Skip to main content
Book cover

International Conference on Geometric Science of Information

GSI 2013: Geometric Science of Information pp 231–238Cite as

On the Identification of Discretization Orders for Distance Geometry with Intervals

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNIP,volume 8085)

Abstract

The discretization of instances of the distance geometry problem is possible when some particular assumptions are satisfied. When molecules are concerned, such assumptions strongly depend on the order in which the atoms of the molecule are considered. When the chemical composition of the molecule is known, as it is the case for the proteins, a general order can be identified for an entire class of instances. However, when this information is not available, ad-hoc orders need to be found for every considered instance. In this paper, the problem of finding discretization orders for distance geometry problems with intervals is formalized, and an algorithm for its solution is presented.

Keywords

  • Protein Backbone
  • Reference Distance
  • Distance Geometry
  • Exact Distance
  • Weighted Undirected Graph

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: 10.1007/978-3-642-40020-9_24
  • Chapter length: 8 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   89.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-40020-9
  • 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   119.99
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alipanahi, B., Krislock, N., Ghodsi, A., Wolkowicz, H., Donaldson, L., Li, M.: Determining Protein Structures from NOESY Distance Constraints by Semidefinite Programming. Journal of Computational Biology 20(4), 296–310 (2013)

    MathSciNet  CrossRef  Google Scholar 

  2. Biswas, P., Lian, T., Wang, T., Ye, Y.: Semidefinite Programming based Algorithms for Sensor Network Localization. ACM Transactions in Sensor Networks 2, 188–220 (2006)

    CrossRef  Google Scholar 

  3. Carvalho, R.S., Lavor, C., Protti, F.: Extending the Geometric Build-Up Algorithm for the Molecular Distance Geometry Problem. Information Processing Letters 108, 234–237 (2008)

    MathSciNet  CrossRef  Google Scholar 

  4. Crippen, G.M., Havel, T.F.: Distance Geometry and Molecular Conformation. John Wiley & Sons, New York (1988)

    MATH  Google Scholar 

  5. Costa, V., Mucherino, A., Lavor, C., Carvalho, L.M., Maculan, N.: On Suitable Orders for Discretizing Molecular Distance Geometry Problems related to Protein Side Chains. In: IEEE Conference Proceedings, Federated Conference on Computer Science and Information Systems (FedCSIS 2012), Workshop on Computational Optimization (WCO 2012), Wroclaw, Poland, pp. 397–402 (2012)

    Google Scholar 

  6. Dong, Q., Wu, Z.: A linear-time Algorithm for Solving the Molecular Distance Geometry Problem with Exact Inter-Atomic Distances. Journal of Global Optimization 22, 365–375 (2002)

    MathSciNet  MATH  CrossRef  Google Scholar 

  7. Dong, Q., Wu, Z.: A Geometric Build-Up Algorithm for Solving the Molecular Distance Geometry Problem with Sparse Distance Data. Journal of Global Optimization 26, 321–333 (2003)

    MathSciNet  MATH  CrossRef  Google Scholar 

  8. Krislock, N., Wolkowicz, H.: Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions. SIAM Journal on Optimization 20, 2679–2708 (2010)

    MathSciNet  MATH  CrossRef  Google Scholar 

  9. Lavor, C., Lee, J., John, A.L.-S., Liberti, L., Mucherino, A., Sviridenko, M.: Discretization Orders for Distance Geometry Problems. Optimization Letters 6(4), 783–796 (2012)

    MathSciNet  MATH  CrossRef  Google Scholar 

  10. Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: Recent Advances on the Discretizable Molecular Distance Geometry Problem. European Journal of Operational Research 219, 698–706 (2012)

    MathSciNet  MATH  CrossRef  Google Scholar 

  11. Lavor, C., Liberti, L., Mucherino, A.: The interval, Branch-and-Prune Algorithm for the Discretizable Molecular Distance Geometry Problem with Inexact Distances. To appear in Journal of Global Optimization (2013)

    Google Scholar 

  12. Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean Distance Geometry and Applications. To appear in SIAM Review (2013)

    Google Scholar 

  13. Malliavin, T.E., Mucherino, A., Nilges, M.: Distance Geometry in Structural Biology: New Perspectives. In: [17], pp. 329–350 (2013)

    Google Scholar 

  14. Moré, J.J., Wu, Z.: Global Continuation for Distance Geometry Problems. SIAM Journal on Optimization 7, 814–836 (1997)

    MathSciNet  MATH  CrossRef  Google Scholar 

  15. Moré, J.J., Wu, Z.: Distance Geometry Optimization for Protein Structures. Journal of Global Optimimization 15, 219–223 (1999)

    MATH  CrossRef  Google Scholar 

  16. Mucherino, A., Lavor, C., Liberti, L.: The Discretizable Distance Geometry Problem. Optimization Letters 6(8), 1671–1686 (2012)

    MathSciNet  MATH  CrossRef  Google Scholar 

  17. Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds.): Distance Geometry: Theory, Methods and Applications, 410 pages. Springer (2013)

    Google Scholar 

  18. Mucherino, A., Lavor, C., Malliavin, T., Liberti, L., Nilges, M., Maculan, N.: Influence of Pruning Devices on the Solution of Molecular Distance Geometry Problems. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 206–217. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Antonio Mucherino

Authors
  1. Antonio Mucherino
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Sony Computer Science Laboratories Inc, Tokyo, Japan

    Frank Nielsen

  2. Thales Land Air Systems, 91470, Limours, France

    Frédéric Barbaresco

Rights and permissions

Reprints and Permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mucherino, A. (2013). On the Identification of Discretization Orders for Distance Geometry with Intervals. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40020-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40019-3

  • Online ISBN: 978-3-642-40020-9

  • eBook Packages: Computer ScienceComputer Science (R0)