Skip to main content
SpringerLink
Log in

Optimal Discretization Orders for Distance Geometry: A Theoretical Standpoint

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

Included in the following conference series:

Abstract

Distance geometry consists in embedding a simple weighted undirected graph \(G=(V,E,d)\) in a K-dimensional space so that all distances \(d_{uv}\), which are the weights on the edges of G, are satisfied by the positions assigned to its vertices. The search domain of this problem is generally continuous, but it can be discretized under certain assumptions, that are strongly related to the order given to the vertices of G. This paper formalizes the concept of optimal partial discretization order, and adapts a previously proposed algorithm with the aim of finding discretization orders that are also able to optimize a given set of objectives. The objectives are conceived for improving the structure of the discrete search domain, for its exploration to become more efficient.

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 EPUB and 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

References

  1. Bertsimas, D., Brown, D.B., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53(3), 464–501 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cassioli, A., Günlük, O., Lavor, C., Liberti, L.: Discretization vertex orders in distance geometry. Discrete Appl. Math. 197, 27–41 (2015). doi:10.1016/j.dam.2014.08.035

    Article  MathSciNet  Google Scholar 

  3. Costa, V., Mucherino, A., Lavor, C., Cassioli, A., Carvalho, L.M., Maculan, N.: Discretization orders for protein side chains. J. Global Optim. 60(2), 333–349 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gonçalves, D.S., Mucherino, A.: Discretization orders and efficient computation of cartesian coordinates for distance geometry. Optim. Lett. 8(7), 2111–2125 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cabalar, P.: Answer set; programming? In: Balduccini, M., Son, T.C. (eds.) Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning. LNCS, vol. 6565, pp. 334–343. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Lavor, C., Lee, J., Lee-St.John, A., Liberti, L., Mucherino, A., Sviridenko, M.: Discretization orders for distance geometry problems. Optim. Lett. 6(4), 783–796 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: The discretizable molecular distance geometry problem. Comput. Optim. Appl. 52, 115–146 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lavor, C., Liberti, L., Mucherino, A.: The interval branch-and-prune algorithm for the discretizable molecular distance geometry problem with inexact distances. J. Global Optim. 56(3), 855–871 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean distance geometry and applications. SIAM Rev. 56(1), 3–69 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liberti, L., Lavor, C., Mucherino, A., Maculan, N.: Molecular distance geometry methods: from continuous to discrete. Int. Trans. Oper. Res. 18(1), 33–51 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mucherino, A.: On the identification of discretization orders for distance geometry with intervals. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2013. LNCS, vol. 8085, pp. 231–238. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  13. Mucherino, A.: A pseudo de Bruijn graph representation for discretization orders for distance geometry. In: Ortuño, F., Rojas, I. (eds.) IWBBIO 2015, Part I. LNCS, vol. 9043, pp. 514–523. Springer, Heidelberg (2015)

    Google Scholar 

  14. Mucherino, A., Fuchs, M., Vasseur, X., Gratton, S.: Variable neighborhood search for robust optimization and applications to aerodynamics. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 230–237. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  15. Mucherino, A., Lavor, C., Liberti, L.: The discretizable distance geometry problem. Optim. Lett. 6(8), 1671–1686 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds.): Distance Geometry: Theory, Methods and Applications. Springer, New York (2013)

    Google Scholar 

  17. Saxe, J.: 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 (1979)

    Google Scholar 

Download references

Acknowledgments

I am thankful to Douglas S. Gonçalves and Leo Liberti for the fruitful discussions.

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

Corresponding author

Correspondence to Antonio Mucherino .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Mucherino, A. (2015). Optimal Discretization Orders for Distance Geometry: A Theoretical Standpoint. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26520-9_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation