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The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances

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  • Carlile Lavor
  • Leo Liberti
  • Antonio Mucherino

Abstract

The Distance Geometry Problem in three dimensions consists in finding an embedding in $${\mathbb{R}^3}$$ of a given nonnegatively weighted simple undirected graph such that edge weights are equal to the corresponding Euclidean distances in the embedding. This is a continuous search problem that can be discretized under some assumptions on the minimum degree of the vertices. In this paper we discuss the case where we consider the full-atom representation of the protein backbone and some of the edge weights are subject to uncertainty within a given nonnegative interval. We show that a discretization is still possible and propose the iBP algorithm to solve the problem. The approach is validated by some computational experiments on a set of artificially generated instances. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Carlile Lavor & Leo Liberti & Antonio Mucherino, 2013. "The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances," Journal of Global Optimization, Springer, vol. 56(3), pages 855-871, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:855-871
    DOI: 10.1007/s10898-011-9799-6
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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).
    5. 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.
    6. Maurizio Bruglieri & Roberto Cordone & Leo Liberti, 2022. "Maximum feasible subsystems of distance geometry constraints," Journal of Global Optimization, Springer, vol. 83(1), pages 29-47, 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. Bradley Worley & Florent Delhommel & Florence Cordier & Thérèse E. Malliavin & Benjamin Bardiaux & Nicolas Wolff & Michael Nilges & Carlile Lavor & Leo Liberti, 2018. "Tuning interval Branch-and-Prune for protein structure determination," Journal of Global Optimization, Springer, vol. 72(1), pages 109-127, September.

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