IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00756943.html
   My bibliography  Save this paper

The Discretizable Distance Geometry Problem

Author

Listed:
  • Antonio Mucherino

    (GenScale - Scalable, Optimized and Parallel Algorithms for Genomics - Inria Rennes – Bretagne Atlantique - Inria - Institut National de Recherche en Informatique et en Automatique - IRISA-D7 - GESTION DES DONNÉES ET DE LA CONNAISSANCE - IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - UBS - Université de Bretagne Sud - ENS Rennes - École normale supérieure - Rennes - Inria - Institut National de Recherche en Informatique et en Automatique - Télécom Bretagne - CentraleSupélec - CNRS - Centre National de la Recherche Scientifique)

  • Carlile Lavor

    (IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil] - UNICAMP - Universidade Estadual de Campinas = University of Campinas)

  • Leo Liberti

    (LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce the Discretizable Distance Geometry Problem in R^3 (DDGP3), which consists in a subclass of instances of the Distance Geometry Problem for which an embedding in R^3 can be found by means of a discrete search. We show that the DDGP3 is a generalization of the Discretizable Molecular Distance Geometry Problem (DMDGP), and we discuss the main differences between the two problems. We prove that the DDGP3 is NP-hard and we extend the Branch & Prune (BP) algorithm, previously used for the DMDGP, for solving instances of the DDGP3. Protein graphs may or may not be in DMDGP and/or DDGP3 depending on vertex orders and edge density. We show experimentally that as distance thresholds decrease, PDB protein graphs which fail to be in the DMDGP still belong to DDGP3, which means that they can still be solved using a discrete search.

Suggested Citation

  • Antonio Mucherino & Carlile Lavor & Leo Liberti, 2012. "The Discretizable Distance Geometry Problem," Post-Print hal-00756943, HAL.
    • Handle: RePEc:hal:journl:hal-00756943
    DOI: 10.1007/s11590-011-0358-3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Felipe Fidalgo & Douglas S. Gonçalves & Carlile Lavor & Leo Liberti & Antonio Mucherino, 2018. "A symmetry-based splitting strategy for discretizable distance geometry problems," Journal of Global Optimization, Springer, vol. 71(4), pages 717-733, August.
    2. Lavor, Carlile & Souza, Michael & Carvalho, Luiz M. & Gonçalves, Douglas S. & Mucherino, Antonio, 2021. "Improving the sampling process in the interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    3. Farid Alizadeh & Douglas Gonçalves & Nathan Krislock & Leo Liberti, 2018. "Preface: Special issue dedicated to Distance Geometry," Journal of Global Optimization, Springer, vol. 72(1), pages 1-4, September.
    4. Simon J. L. Billinge & Phillip M. Duxbury & Douglas S. Gonçalves & Carlile Lavor & Antonio Mucherino, 2016. "Assigned and unassigned distance geometry: applications to biological molecules and nanostructures," 4OR, Springer, vol. 14(4), pages 337-376, December.
    5. Virginia Costa & Antonio Mucherino & Carlile Lavor & Andrea Cassioli & Luiz Carvalho & Nelson Maculan, 2014. "Discretization orders for protein side chains," Journal of Global Optimization, Springer, vol. 60(2), pages 333-349, October.
    6. Phil Duxbury & Carlile Lavor & Leo Liberti & Luiz Leduino Salles-Neto, 2022. "Unassigned distance geometry and molecular conformation problems," Journal of Global Optimization, Springer, vol. 83(1), pages 73-82, May.
    7. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.
    8. Simon J. L. Billinge & Phillip M. Duxbury & Douglas S. Gonçalves & Carlile Lavor & Antonio Mucherino, 2018. "Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures," Annals of Operations Research, Springer, vol. 271(1), pages 161-203, December.
    9. Douglas S. Gonçalves & Antonio Mucherino & Carlile Lavor & Leo Liberti, 2017. "Recent advances on the interval distance geometry problem," Journal of Global Optimization, Springer, vol. 69(3), pages 525-545, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00756943. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.